1.
Frequency (statistics)
–
In statistics the frequency of an event i is the number n i of times the event occurred in an experiment or study. These frequencies are often represented in histograms. The cumulative frequency is the total of the frequencies of all events at or below a certain point in an ordered list of events. The relative frequency of an event is the absolute frequency normalized by the number of events. The values of f i for all events i can be plotted to produce a frequency distribution, in the case when n i =0 for certain i, pseudocounts can be added. The height of a rectangle is equal to the frequency density of the interval. The total area of the histogram is equal to the number of data, a histogram may also be normalized displaying relative frequencies. It then shows the proportion of cases fall into each of several categories. The categories are usually specified as consecutive, non-overlapping intervals of a variable, the categories must be adjacent, and often are chosen to be of the same size. The rectangles of a histogram are drawn so that they touch each other to indicate that the variable is continuous. A bar chart or bar graph is a chart with rectangular bars with lengths proportional to the values that they represent, the bars can be plotted vertically or horizontally. A vertical bar chart is called a column bar chart. A frequency distribution table is an arrangement of the values one or more variables take in a sample. This interpretation is often contrasted with Bayesian probability, in fact, the term frequentist was first used by M. G. Kendall in 1949, to contrast with Bayesians, whom he called non-frequentists. He observed 3. we may distinguish two main attitudes. It might be thought that the differences between the frequentists and the non-frequentists are largely due to the differences of the domains which they purport to cover, I assert that this is not so. Aperiodic frequency Cumulative frequency analysis Law of large numbers Probability density function Statistical regularity Word frequency
Frequency (statistics)
–
Histogram of travel time (to work), US 2000 census. Histograms depict the frequencies of observations occurring in certain ranges of values
2.
SI unit
–
The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
SI unit
–
Stone marking the
Austro-Hungarian /Italian border at
Pontebba displaying
myriametres, a unit of 10 km used in
Central Europe in the 19th century (but since
deprecated).
SI unit
–
The seven base units in the International System of Units
SI unit
–
Carl Friedrich Gauss
SI unit
–
Thomson
3.
Hertz
–
The hertz is the unit of frequency in the International System of Units and is defined as one cycle per second. It is named for Heinrich Rudolf Hertz, the first person to provide proof of the existence of electromagnetic waves. Hertz are commonly expressed in SI multiples kilohertz, megahertz, gigahertz, kilo means thousand, mega meaning million, giga meaning billion and tera for trillion. Some of the units most common uses are in the description of waves and musical tones, particularly those used in radio-. It is also used to describe the speeds at which computers, the hertz is equivalent to cycles per second, i. e. 1/second or s −1. In English, hertz is also used as the plural form, as an SI unit, Hz can be prefixed, commonly used multiples are kHz, MHz, GHz and THz. One hertz simply means one cycle per second,100 Hz means one hundred cycles per second, and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz, the rate of aperiodic or stochastic events occur is expressed in reciprocal second or inverse second in general or, the specific case of radioactive decay, becquerels. Whereas 1 Hz is 1 cycle per second,1 Bq is 1 aperiodic radionuclide event per second, the conversion between a frequency f measured in hertz and an angular velocity ω measured in radians per second is ω =2 π f and f = ω2 π. This SI unit is named after Heinrich Hertz, as with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that degree Celsius conforms to this rule because the d is lowercase. — Based on The International System of Units, the hertz is named after the German physicist Heinrich Hertz, who made important scientific contributions to the study of electromagnetism. The name was established by the International Electrotechnical Commission in 1930, the term cycles per second was largely replaced by hertz by the 1970s. One hobby magazine, Electronics Illustrated, declared their intention to stick with the traditional kc. Mc. etc. units, sound is a traveling longitudinal wave which is an oscillation of pressure. Humans perceive frequency of waves as pitch. Each musical note corresponds to a frequency which can be measured in hertz. An infants ear is able to perceive frequencies ranging from 20 Hz to 20,000 Hz, the range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtoHz into the terahertz range and beyond. Electromagnetic radiation is described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz. Radio frequency radiation is measured in kilohertz, megahertz, or gigahertz
Hertz
–
Details of a
heartbeat as an example of a non-
sinusoidal periodic phenomenon that can be described in terms of hertz. Two complete cycles are illustrated.
Hertz
–
A
sine wave with varying frequency
4.
SI base unit
–
The International System of Units defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science, thus, the kelvin, named after Lord Kelvin, has the symbol K and the ampere, named after André-Marie Ampère, has the symbol A. Many other units, such as the litre, are not part of the SI. The definitions of the units have been modified several times since the Metre Convention in 1875. Since the redefinition of the metre in 1960, the kilogram is the unit that is directly defined in terms of a physical artifact. However, the mole, the ampere, and the candela are linked through their definitions to the mass of the platinum–iridium cylinder stored in a vault near Paris. It has long been an objective in metrology to define the kilogram in terms of a fundamental constant, two possibilities have attracted particular attention, the Planck constant and the Avogadro constant. The 23rd CGPM decided to postpone any formal change until the next General Conference in 2011
SI base unit
–
The seven SI base units and the interdependency of their definitions: for example, to extract the definition of the metre from the
speed of light, the definition of the second must be known while the
ampere and
candela are both dependent on the definition of
energy which in turn is defined in terms of
length,
mass and
time.
5.
Second
–
The second is the base unit of time in the International System of Units. It is qualitatively defined as the division of the hour by sixty. SI definition of second is the duration of 9192631770 periods of the corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. Seconds may be measured using a mechanical, electrical or an atomic clock, SI prefixes are combined with the word second to denote subdivisions of the second, e. g. the millisecond, the microsecond, and the nanosecond. Though SI prefixes may also be used to form multiples of the such as kilosecond. The second is also the unit of time in other systems of measurement, the centimetre–gram–second, metre–kilogram–second, metre–tonne–second. Absolute zero implies no movement, and therefore zero external radiation effects, the second thus defined is consistent with the ephemeris second, which was based on astronomical measurements. The realization of the second is described briefly in a special publication from the National Institute of Standards and Technology. 1 international second is equal to, 1⁄60 minute 1⁄3,600 hour 1⁄86,400 day 1⁄31,557,600 Julian year 1⁄, more generally, = 1⁄, the Hellenistic astronomers Hipparchus and Ptolemy subdivided the day into sixty parts. They also used an hour, simple fractions of an hour. No sexagesimal unit of the day was used as an independent unit of time. The modern second is subdivided using decimals - although the third remains in some languages. The earliest clocks to display seconds appeared during the last half of the 16th century, the second became accurately measurable with the development of mechanical clocks keeping mean time, as opposed to the apparent time displayed by sundials. The earliest spring-driven timepiece with a hand which marked seconds is an unsigned clock depicting Orpheus in the Fremersdorf collection. During the 3rd quarter of the 16th century, Taqi al-Din built a clock with marks every 1/5 minute, in 1579, Jost Bürgi built a clock for William of Hesse that marked seconds. In 1581, Tycho Brahe redesigned clocks that displayed minutes at his observatory so they also displayed seconds, however, they were not yet accurate enough for seconds. In 1587, Tycho complained that his four clocks disagreed by plus or minus four seconds, in 1670, London clockmaker William Clement added this seconds pendulum to the original pendulum clock of Christiaan Huygens. From 1670 to 1680, Clement made many improvements to his clock and this clock used an anchor escapement mechanism with a seconds pendulum to display seconds in a small subdial
Second
–
FOCS 1, a continuous cold caesium fountain atomic clock in Switzerland, started operating in 2004 at an uncertainty of one second in 30 million years.
Second
–
Key concepts
6.
Dimensional analysis
–
Converting from one dimensional unit to another is often somewhat complex. Dimensional analysis, or more specifically the method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra. The concept of physical dimension was introduced by Joseph Fourier in 1822, Physical quantities that are measurable have the same dimension and can be directly compared to each other, even if they are originally expressed in differing units of measure. If physical quantities have different dimensions, they cannot be compared by similar units, hence, it is meaningless to ask whether a kilogram is greater than, equal to, or less than an hour. Any physically meaningful equation will have the dimensions on their left and right sides. Checking for dimensional homogeneity is an application of dimensional analysis. Dimensional analysis is routinely used as a check of the plausibility of derived equations and computations. It is generally used to categorize types of quantities and units based on their relationship to or dependence on other units. Many parameters and measurements in the sciences and engineering are expressed as a concrete number – a numerical quantity. Often a quantity is expressed in terms of other quantities, for example, speed is a combination of length and time. Compound relations with per are expressed with division, e. g.60 mi/1 h, other relations can involve multiplication, powers, or combinations thereof. A base unit is a unit that cannot be expressed as a combination of other units, for example, units for length and time are normally chosen as base units. Units for volume, however, can be factored into the units of length. Sometimes the names of units obscure that they are derived units, for example, an ampere is a unit of electric current, which is equivalent to electric charge per unit time and is measured in coulombs per second, so 1 A =1 C/s. Similarly, one newton is 1 kg⋅m/s2, percentages are dimensionless quantities, since they are ratios of two quantities with the same dimensions. In other words, the % sign can be read as 1/100, derivatives with respect to a quantity add the dimensions of the variable one is differentiating with respect to on the denominator. Thus, position has the dimension L, derivative of position with respect to time has dimension LT−1 – length from position, time from the derivative, the second derivative has dimension LT−2. In economics, one distinguishes between stocks and flows, a stock has units of units, while a flow is a derivative of a stock, in some contexts, dimensional quantities are expressed as dimensionless quantities or percentages by omitting some dimensions
Dimensional analysis
–
Base quantity
7.
Multiplicative inverse
–
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity,1. The multiplicative inverse of a fraction a/b is b/a, for the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth, the reciprocal function, the function f that maps x to 1/x, is one of the simplest examples of a function which is its own inverse. In the phrase multiplicative inverse, the qualifier multiplicative is often omitted, multiplicative inverses can be defined over many mathematical domains as well as numbers. In these cases it can happen that ab ≠ ba, then inverse typically implies that an element is both a left and right inverse. The notation f −1 is sometimes used for the inverse function of the function f. For example, the multiplicative inverse 1/ = −1 is the cosecant of x, only for linear maps are they strongly related. The terminology difference reciprocal versus inverse is not sufficient to make this distinction, since many authors prefer the opposite naming convention, in the real numbers, zero does not have a reciprocal because no real number multiplied by 0 produces 1. With the exception of zero, reciprocals of every real number are real, reciprocals of every rational number are rational, the property that every element other than zero has a multiplicative inverse is part of the definition of a field, of which these are all examples. On the other hand, no other than 1 and −1 has an integer reciprocal. In modular arithmetic, the multiplicative inverse of a is also defined. This multiplicative inverse exists if and only if a and n are coprime, for example, the inverse of 3 modulo 11 is 4 because 4 ·3 ≡1. The extended Euclidean algorithm may be used to compute it, the sedenions are an algebra in which every nonzero element has a multiplicative inverse, but which nonetheless has divisors of zero, i. e. nonzero elements x, y such that xy =0. A square matrix has an inverse if and only if its determinant has an inverse in the coefficient ring, the linear map that has the matrix A−1 with respect to some base is then the reciprocal function of the map having A as matrix in the same base. Thus, the two notions of the inverse of a function are strongly related in this case, while they must be carefully distinguished in the general case. A ring in which every element has a multiplicative inverse is a division ring. As mentioned above, the reciprocal of every complex number z = a + bi is complex. In particular, if ||z||=1, then 1 / z = z ¯, consequently, the imaginary units, ±i, have additive inverse equal to multiplicative inverse, and are the only complex numbers with this property
Multiplicative inverse
–
The reciprocal function: y = 1/ x. For every x except 0, y represents its multiplicative inverse. The graph forms a
rectangular hyperbola.
8.
Time
–
Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is often referred to as the dimension, along with the three spatial dimensions. Time has long been an important subject of study in religion, philosophy, and science, nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems. Two contrasting viewpoints on time divide prominent philosophers, one view is that time is part of the fundamental structure of the universe—a dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is referred to as Newtonian time. This second view, in the tradition of Gottfried Leibniz and Immanuel Kant, holds that time is neither an event nor a thing, Time in physics is unambiguously operationally defined as what a clock reads. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities, Time is used to define other quantities—such as velocity—so defining time in terms of such quantities would result in circularity of definition. The operational definition leaves aside the question there is something called time, apart from the counting activity just mentioned, that flows. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Furthermore, it may be there is a subjective component to time. Temporal measurement has occupied scientists and technologists, and was a motivation in navigation. Periodic events and periodic motion have long served as standards for units of time, examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is also of significant social importance, having economic value as well as value, due to an awareness of the limited time in each day. In day-to-day life, the clock is consulted for periods less than a day whereas the calendar is consulted for periods longer than a day, increasingly, personal electronic devices display both calendars and clocks simultaneously. The number that marks the occurrence of an event as to hour or date is obtained by counting from a fiducial epoch—a central reference point. Artifacts from the Paleolithic suggest that the moon was used to time as early as 6,000 years ago. Lunar calendars were among the first to appear, either 12 or 13 lunar months, without intercalation to add days or months to some years, seasons quickly drift in a calendar based solely on twelve lunar months
Time
–
The flow of
sand in an
hourglass can be used to keep track of elapsed time. It also concretely represents the
present as being between the
past and the
future.
Time
Time
–
Horizontal
sundial in
Taganrog
Time
–
A contemporary
quartz watch
9.
Turn (geometry)
–
A turn is a unit of plane angle measurement equal to 2π radians, 360° or 400 gon. A turn is also referred to as a revolution or complete rotation or full circle or cycle or rev or rot, a turn can be subdivided in many different ways, into half turns, quarter turns, centiturns, milliturns, binary angles, points etc. A turn can be divided in 100 centiturns or 1000 milliturns, with each corresponding to an angle of 0. 36°. A protractor divided in centiturns is normally called a percentage protractor, binary fractions of a turn are also used. Sailors have traditionally divided a turn into 32 compass points, the binary degree, also known as the binary radian, is 1⁄256 turn. The binary degree is used in computing so that an angle can be represented to the maximum possible precision in a single byte, other measures of angle used in computing may be based on dividing one whole turn into 2n equal parts for other values of n. The notion of turn is used for planar rotations. Two special rotations have acquired appellations of their own, a rotation through 180° is commonly referred to as a half-turn, the word turn originates via Latin and French from the Greek word τόρνος. In 1697, David Gregory used π/ρ to denote the perimeter of a divided by its radius. However, earlier in 1647, William Oughtred had used δ/π for the ratio of the diameter to perimeter, the first use of the symbol π on its own with its present meaning was in 1706 by the Welsh mathematician William Jones. Euler adopted the symbol with that meaning in 1737, leading to its widespread use, percentage protractors have existed since 1922, but the terms centiturns and milliturns were introduced much later by Sir Fred Hoyle. The German standard DIN1315 proposed the unit symbol pla for turns, since 2011, the HP 39gII and HP Prime support the unit symbol tr for turns. In 2016, support for turns was also added to newRPL for the HP 50g, one turn is equal to 2π radians. In 1958, Albert Eagle proposed the Greek letter tau τ as a symbol for 1/2π and his proposal used a pi with three legs symbol to denote the constant. In 2010, Michael Hartl proposed to use tau to represent Palais circle constant, τ=2π. First, τ is the number of radians in one turn, which allows fractions of a turn to be expressed directly, for instance. Second, τ visually resembles π, whose association with the constant is unavoidable. Hartls Tau Manifesto gives many examples of formulas that are simpler if tau is used instead of pi, however, a rebuttal was given in The Pi Manifesto, stating a variety of reasons tau should not supplant pi
Turn (geometry)
–
Counterclockwise
rotations about the center point where a complete rotation is equal to 1 turn
10.
Heart sound
–
Heart sounds are the noises generated by the beating heart and the resultant flow of blood through it. Specifically, the sounds reflect the turbulence created when the heart valves snap shut, in cardiac auscultation, an examiner may use a stethoscope to listen for these unique and distinct sounds that provide important auditory data regarding the condition of the heart. In healthy adults, there are two normal heart sounds often described as a lubb and a dub, that occur in sequence with each heartbeat and these are the first heart sound and second heart sound, produced by the closing of the atrioventricular valves and semilunar valves, respectively. In addition to these sounds, a variety of other sounds may be present including heart murmurs, adventitious sounds. Heart murmurs are generated by turbulent flow of blood, which may occur inside or outside the heart, Murmurs may be physiological or pathological. Abnormal murmurs can be caused by restricting the opening of a heart valve. Abnormal murmurs may occur with valvular insufficiency, which allows backflow of blood when the incompetent valve closes with only partial effectiveness. Different murmurs are audible in different parts of the cardiac cycle, normal heart sounds are associated with heart valves closing, The first heart sound, or S1, forms the lub of lub-dub and is composed of components M1 and T1. It is caused by the closure of the valves, i. e. tricuspid and mitral, at the beginning of ventricular contraction. When the ventricles begin to contract, so do the muscles in each ventricle. The papillary muscles are attached to the cusps or leaflets of the tricuspid, when the papillary muscles contract, the chordae tendineae become tense and thereby prevent the backflow of blood into the lower pressure environment of the atria. It is the pressure created from ventricular contraction that closes the valve, the contraction of the ventricle begins just prior to AV valves closing and prior to the semilunar valves opening. The S1 sound results from reverberation within the associated with the sudden block of flow reversal by the valves. If M1 occurs slightly after T1, then the patient likely has a dysfunction of conduction of the side of the heart such as a left bundle branch blockage. The second heart sound, or S2, forms the dub of lub-dub and is composed of components A2, normally A2 precedes P2 especially during inhalation where a split of S2 can be heard. It is caused by the closure of the valves at the end of ventricular systole. As the left ventricle empties, its pressure falls below the pressure in the aorta, aortic blood flow quickly reverses back toward the left ventricle, catching the pocket-like cusps of the aortic valve, and is stopped by aortic valve closure. Similarly, as the pressure in the right ventricle falls below the pressure in the pulmonary artery, the S2 sound results from reverberation within the blood associated with the sudden block of flow reversal
Heart sound
–
Front of
thorax, showing surface relations of
bones,
lungs (purple),
pleura (blue), and
heart (red outline). The location of best auscultation for each
heart valve are labeled with "M", "T", "A", and "P". First heart sound: caused by atrioventricular valves -
Mitral (M) and
Tricuspid (T). Second heart sound caused by semilunar valves --
Aortic (A) and
Pulmonary/Pulmonic (P).
11.
Oscillation
–
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The term vibration is used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current power, the simplest mechanical oscillating system is a weight attached to a linear spring subject to only weight and tension. Such a system may be approximated on an air table or ice surface, the system is in an equilibrium state when the spring is static. If the system is displaced from the equilibrium, there is a net restoring force on the mass, tending to bring it back to equilibrium. However, in moving the back to the equilibrium position, it has acquired momentum which keeps it moving beyond that position. If a constant force such as gravity is added to the system, the time taken for an oscillation to occur is often referred to as the oscillatory period. All real-world oscillator systems are thermodynamically irreversible and this means there are dissipative processes such as friction or electrical resistance which continually convert some of the energy stored in the oscillator into heat in the environment. Thus, oscillations tend to decay with time there is some net source of energy into the system. The simplest description of this process can be illustrated by oscillation decay of the harmonic oscillator. In addition, a system may be subject to some external force. In this case the oscillation is said to be driven, some systems can be excited by energy transfer from the environment. This transfer typically occurs where systems are embedded in some fluid flow, at sufficiently large displacements, the stiffness of the wing dominates to provide the restoring force that enables an oscillation. The harmonic oscillator and the systems it models have a degree of freedom. More complicated systems have more degrees of freedom, for two masses and three springs. In such cases, the behavior of each variable influences that of the others and this leads to a coupling of the oscillations of the individual degrees of freedom. For example, two pendulum clocks mounted on a wall will tend to synchronise. This phenomenon was first observed by Christiaan Huygens in 1665, more special cases are the coupled oscillators where energy alternates between two forms of oscillation
Oscillation
–
Experimental Setup of Huygens synchronization of two clocks
Oscillation
–
Two pendulums with the same period fixed on a string act as pair of coupled oscillators. The oscillation alternates between the two.
12.
Vibration
–
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin vibrationem, the oscillations may be periodic, such as the motion of a pendulum—or random, such as the movement of a tire on a gravel road. Vibration can be desirable, for example, the motion of a fork, the reed in a woodwind instrument or harmonica. In many cases, however, vibration is undesirable, wasting energy, for example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations could be caused by imbalances in the parts, uneven friction. Careful designs usually minimize unwanted vibrations, the studies of sound and vibration are closely related. Sound, or pressure waves, are generated by vibrating structures, hence, attempts to reduce noise are often related to issues of vibration. Free vibration occurs when a system is set in motion with an initial input. Examples of this type of vibration are pulling a child back on a swing and letting go, or hitting a tuning fork, the mechanical system vibrates at one or more of its natural frequencies and damps down to motionlessness. Forced vibration is when a disturbance is applied to a mechanical system. The disturbance can be a periodic and steady-state input, a transient input, the periodic input can be a harmonic or a non-harmonic disturbance. Damped vibration, When the energy of a system is gradually dissipated by friction and other resistances. The vibrations gradually reduce or change in frequency or intensity or cease, Vibration testing is accomplished by introducing a forcing function into a structure, usually with some type of shaker. Alternately, a DUT is attached to the table of a shaker, Vibration testing is performed to examine the response of a device under test to a defined vibration environment. The measured response may be life, resonant frequencies or squeak. Squeak and rattle testing is performed with a type of quiet shaker that produces very low sound levels while under operation. For relatively low frequency forcing, servohydraulic shakers are used, for higher frequencies, electrodynamic shakers are used. Generally, one or more input or control points located on the DUT-side of a fixture is kept at a specified acceleration, other response points experience maximum vibration level or minimum vibration level
Vibration
–
Car Suspension: designing vibration control is undertaken as part of
acoustic,
automotive or
mechanical engineering.
Vibration
–
One of the possible modes of
vibration of a circular drum (see other modes).
13.
Sound
–
In physics, sound is a vibration that propagates as a typically audible mechanical wave of pressure and displacement, through a transmission medium such as air or water. In physiology and psychology, sound is the reception of such waves, humans can hear sound waves with frequencies between about 20 Hz and 20 kHz. Sound above 20 kHz is ultrasound and below 20 Hz is infrasound, other animals have different hearing ranges. Acoustics is the science that deals with the study of mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound. A scientist who works in the field of acoustics is an acoustician, an audio engineer, on the other hand, is concerned with the recording, manipulation, mixing, and reproduction of sound. Auditory sensation evoked by the oscillation described in, sound can propagate through a medium such as air, water and solids as longitudinal waves and also as a transverse wave in solids. The sound waves are generated by a source, such as the vibrating diaphragm of a stereo speaker. The sound source creates vibrations in the surrounding medium, as the source continues to vibrate the medium, the vibrations propagate away from the source at the speed of sound, thus forming the sound wave. At a fixed distance from the source, the pressure, velocity, at an instant in time, the pressure, velocity, and displacement vary in space. Note that the particles of the medium do not travel with the sound wave and this is intuitively obvious for a solid, and the same is true for liquids and gases. During propagation, waves can be reflected, refracted, or attenuated by the medium, the behavior of sound propagation is generally affected by three things, A complex relationship between the density and pressure of the medium. This relationship, affected by temperature, determines the speed of sound within the medium, if the medium is moving, this movement may increase or decrease the absolute speed of the sound wave depending on the direction of the movement. For example, sound moving through wind will have its speed of propagation increased by the speed of the if the sound and wind are moving in the same direction. If the sound and wind are moving in opposite directions, the speed of the wave will be decreased by the speed of the wind. Medium viscosity determines the rate at which sound is attenuated, for many media, such as air or water, attenuation due to viscosity is negligible. When sound is moving through a medium that does not have constant physical properties, the mechanical vibrations that can be interpreted as sound can travel through all forms of matter, gases, liquids, solids, and plasmas. The matter that supports the sound is called the medium, sound cannot travel through a vacuum. Sound is transmitted through gases, plasma, and liquids as longitudinal waves and it requires a medium to propagate
Sound
–
A
drum produces sound via a vibrating membrane.
Sound
–
Audio engineers in R&D design audio equipment
Sound
–
U.S. Navy
F/A-18 approaching the sound barrier. The white halo is formed by condensed water droplets thought to result from a drop in air pressure around the aircraft (see
Prandtl-Glauert Singularity).
Sound
–
Human ear
14.
Radio wave
–
Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies as high as 300 GHz to as low as 3 kHz, though some definitions describe waves above 1 or 3 GHz as microwaves, at 300 GHz, the corresponding wavelength is 1 mm, and at 3 kHz is 100 km. Like all other electromagnetic waves, they travel at the speed of light, naturally occurring radio waves are generated by lightning, or by astronomical objects. Radio waves are generated by radio transmitters and received by radio receivers, the radio spectrum is divided into a number of radio bands on the basis of frequency, allocated to different uses. Radio waves were first predicted by mathematical work done in 1867 by Scottish mathematical physicist James Clerk Maxwell, Maxwell noticed wavelike properties of light and similarities in electrical and magnetic observations. Radio waves were first used for communication in the mid 1890s by Guglielmo Marconi, different frequencies experience different combinations of these phenomena in the Earths atmosphere, making certain radio bands more useful for specific purposes than others. It does not necessarily require a cleared sight path, at lower frequencies radio waves can pass through buildings, foliage and this is the only method of propagation possible at microwave frequencies and above. On the surface of the Earth, line of propagation is limited by the visual horizon to about 40 miles. This is the used by cell phones, cordless phones, walkie-talkies, wireless networks, FM and television broadcasting. Indirect propagation, Radio waves can reach points beyond the line-of-sight by diffraction, diffraction allows a radio wave to bend around obstructions such as a building edge, a vehicle, or a turn in a hall. Radio waves also reflect from surfaces such as walls, floors, ceilings, vehicles and these effects are used in short range radio communication systems. Ground waves allow mediumwave and longwave broadcasting stations to have coverage areas beyond the horizon, the nonzero resistance of the earth absorbs energy from ground waves, so as they propagate the waves lose power and the wavefronts bend over at an angle to the surface. As frequency decreases, the decrease and the achievable range increases. Military very low frequency and extremely low frequency communication systems can communicate over most of the Earth, and with submarines hundreds of feet underwater. Tropospheric propagation, In the VHF and UHF bands, radio waves can travel somewhat beyond the horizon due to refraction in the troposphere. This is due to changes in the index of air with temperature and pressure. At times, radio waves can travel up to 500 -1000 km due to tropospheric ducting and these effects are variable and not as reliable as ionospheric propagation, below. So radio waves directed at an angle into the sky can return to Earth beyond the horizon, by using multiple skips communication at intercontinental distances can be achieved
Radio wave
–
Diagram of the
electric fields (E) and
magnetic fields (H) of radio waves emitted by a
monopole radio transmitting
antenna (small dark vertical line in the center). The E and H fields are perpendicular as implied by the phase diagram in the lower right.
15.
Light
–
Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to light, which is visible to the human eye and is responsible for the sense of sight. Visible light is defined as having wavelengths in the range of 400–700 nanometres, or 4.00 × 10−7 to 7.00 × 10−7 m. This wavelength means a range of roughly 430–750 terahertz. The main source of light on Earth is the Sun, sunlight provides the energy that green plants use to create sugars mostly in the form of starches, which release energy into the living things that digest them. This process of photosynthesis provides virtually all the used by living things. Historically, another important source of light for humans has been fire, with the development of electric lights and power systems, electric lighting has effectively replaced firelight. Some species of animals generate their own light, a process called bioluminescence, for example, fireflies use light to locate mates, and vampire squids use it to hide themselves from prey. Visible light, as all types of electromagnetic radiation, is experimentally found to always move at this speed in a vacuum. In physics, the term sometimes refers to electromagnetic radiation of any wavelength. In this sense, gamma rays, X-rays, microwaves and radio waves are also light, like all types of light, visible light is emitted and absorbed in tiny packets called photons and exhibits properties of both waves and particles. This property is referred to as the wave–particle duality, the study of light, known as optics, is an important research area in modern physics. Generally, EM radiation, or EMR, is classified by wavelength into radio, microwave, infrared, the behavior of EMR depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths, when EMR interacts with single atoms and molecules, its behavior depends on the amount of energy per quantum it carries. There exist animals that are sensitive to various types of infrared, infrared sensing in snakes depends on a kind of natural thermal imaging, in which tiny packets of cellular water are raised in temperature by the infrared radiation. EMR in this range causes molecular vibration and heating effects, which is how these animals detect it, above the range of visible light, ultraviolet light becomes invisible to humans, mostly because it is absorbed by the cornea below 360 nanometers and the internal lens below 400. Furthermore, the rods and cones located in the retina of the eye cannot detect the very short ultraviolet wavelengths and are in fact damaged by ultraviolet. Many animals with eyes that do not require lenses are able to detect ultraviolet, by quantum photon-absorption mechanisms, various sources define visible light as narrowly as 420 to 680 to as broadly as 380 to 800 nm
Light
–
An example of refraction of light. The straw appears bent, because of refraction of light as it enters liquid from air.
Light
–
A triangular prism dispersing a beam of white light. The longer wavelengths (red) and the shorter wavelengths (blue) get separated.
Light
–
A
cloud illuminated by
sunlight
Light
–
A
city illuminated by
artificial lighting
16.
Sine wave
–
A sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. It is named after the sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time is, y = A sin = A sin where, A = the amplitude, F = the ordinary frequency, the number of oscillations that occur each second of time. ω = 2πf, the frequency, the rate of change of the function argument in units of radians per second φ = the phase. When φ is non-zero, the entire waveform appears to be shifted in time by the amount φ /ω seconds, a negative value represents a delay, and a positive value represents an advance. The sine wave is important in physics because it retains its shape when added to another sine wave of the same frequency and arbitrary phase. It is the only periodic waveform that has this property and this property leads to its importance in Fourier analysis and makes it acoustically unique. The wavenumber is related to the frequency by. K = ω v =2 π f v =2 π λ where λ is the wavelength, f is the frequency, and v is the linear speed. This equation gives a wave for a single dimension, thus the generalized equation given above gives the displacement of the wave at a position x at time t along a single line. This could, for example, be considered the value of a wave along a wire, in two or three spatial dimensions, the same equation describes a travelling plane wave if position x and wavenumber k are interpreted as vectors, and their product as a dot product. For more complex such as the height of a water wave in a pond after a stone has been dropped in. This wave pattern occurs often in nature, including wind waves, sound waves, a cosine wave is said to be sinusoidal, because cos = sin , which is also a sine wave with a phase-shift of π/2 radians. Because of this start, it is often said that the cosine function leads the sine function or the sine lags the cosine. The human ear can recognize single sine waves as sounding clear because sine waves are representations of a frequency with no harmonics. Presence of higher harmonics in addition to the fundamental causes variation in the timbre, on the other hand, if the sound contains aperiodic waves along with sine waves, then the sound will be perceived noisy as noise is characterized as being aperiodic or having a non-repetitive pattern. In 1822, French mathematician Joseph Fourier discovered that sinusoidal waves can be used as building blocks to describe and approximate any periodic waveform
Sine wave
–
The graphs of the sine and
cosine functions are sinusoids of different phases.
17.
Wave
–
In physics, a wave is an oscillation accompanied by a transfer of energy that travels through a medium. Frequency refers to the addition of time, wave motion transfers energy from one point to another, which displace particles of the transmission medium–that is, with little or no associated mass transport. Waves consist, instead, of oscillations or vibrations, around almost fixed locations, there are two main types of waves. Mechanical waves propagate through a medium, and the substance of this medium is deformed, restoring forces then reverse the deformation. For example, sound waves propagate via air molecules colliding with their neighbors, when the molecules collide, they also bounce away from each other. This keeps the molecules from continuing to travel in the direction of the wave, the second main type, electromagnetic waves, do not require a medium. Instead, they consist of periodic oscillations of electrical and magnetic fields generated by charged particles. These types vary in wavelength, and include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, waves are described by a wave equation which sets out how the disturbance proceeds over time. The mathematical form of this varies depending on the type of wave. Further, the behavior of particles in quantum mechanics are described by waves, in addition, gravitational waves also travel through space, which are a result of a vibration or movement in gravitational fields. While mechanical waves can be transverse and longitudinal, all electromagnetic waves are transverse in free space. A single, all-encompassing definition for the wave is not straightforward. A vibration can be defined as a back-and-forth motion around a reference value, however, a vibration is not necessarily a wave. An attempt to define the necessary and sufficient characteristics that qualify a phenomenon as a results in a blurred line. The term wave is often understood as referring to a transport of spatial disturbances that are generally not accompanied by a motion of the medium occupying this space as a whole. In a wave, the energy of a vibration is moving away from the source in the form of a disturbance within the surrounding medium and it may appear that the description of waves is closely related to their physical origin for each specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a rather than an electromagnetic wave transfer caused by vibration. Concepts such as mass, momentum, inertia, or elasticity and this difference in origin introduces certain wave characteristics particular to the properties of the medium involved
Wave
–
Surface waves in
water
Wave
–
Wavelength λ, can be measured between any two corresponding points on a waveform
Wave
–
Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism
18.
Rotation
–
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object always rotates around a line called a rotation axis. If the axis passes through the center of mass, the body is said to rotate upon itself. A rotation about a point, e. g. the Earth about the Sun, is called a revolution or orbital revolution. The axis is called a pole, mathematically, a rotation is a rigid body movement which, unlike a translation, keeps a point fixed. This definition applies to rotations within both two and three dimensions All rigid body movements are rotations, translations, or combinations of the two, a rotation is simply a progressive radial orientation to a common point. That common point lies within the axis of that motion, the axis is 90 degrees perpendicular to the plane of the motion. If the axis of the rotation lies external of the body in question then the body is said to orbit, there is no fundamental difference between a “rotation” and an “orbit” and or spin. The key distinction is simply where the axis of the rotation lies and this distinction can be demonstrated for both “rigid” and “non rigid” bodies. If a rotation around a point or axis is followed by a rotation around the same point/axis. The reverse of a rotation is also a rotation, thus, the rotations around a point/axis form a group. However, a rotation around a point or axis and a rotation around a different point/axis may result in something other than a rotation, Rotations around the x, y and z axes are called principal rotations. Rotation around any axis can be performed by taking a rotation around the x axis, followed by a rotation around the y axis and that is to say, any spatial rotation can be decomposed into a combination of principal rotations. In flight dynamics, the rotations are known as yaw, pitch. This terminology is used in computer graphics. In astronomy, rotation is an observed phenomenon. Stars, planets and similar bodies all spin around on their axes, the rotation rate of planets in the solar system was first measured by tracking visual features. Stellar rotation is measured through Doppler shift or by tracking active surface features and this rotation induces a centrifugal acceleration in the reference frame of the Earth which slightly counteracts the effect of gravity the closer one is to the equator
Rotation
–
Star trails caused by the
Earth's rotation during the
camera's long exposure time.
Rotation
–
A
sphere rotating about an axis
19.
Physics
–
Physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental disciplines, the main goal of physics is to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy, Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the mechanisms of other sciences while opening new avenues of research in areas such as mathematics. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs, the United Nations named 2005 the World Year of Physics. Astronomy is the oldest of the natural sciences, the stars and planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, according to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy. The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn Al-Haitham, in which he was not only the first to disprove the ancient Greek idea about vision, but also came up with a new theory. In the book, he was also the first to study the phenomenon of the pinhole camera, many later European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haythams Optics ranks alongside that of Newtons work of the same title, the translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the devices as what Ibn al-Haytham did. From this, such important things as eyeglasses, magnifying glasses, telescopes, Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics. Newton also developed calculus, the study of change, which provided new mathematical methods for solving physical problems. The discovery of new laws in thermodynamics, chemistry, and electromagnetics resulted from greater research efforts during the Industrial Revolution as energy needs increased, however, inaccuracies in classical mechanics for very small objects and very high velocities led to the development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory, both of these theories came about due to inaccuracies in classical mechanics in certain situations. Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger, from this early work, and work in related fields, the Standard Model of particle physics was derived. Areas of mathematics in general are important to this field, such as the study of probabilities, in many ways, physics stems from ancient Greek philosophy
Physics
–
Further information:
Outline of physics
Physics
–
Ancient
Egyptian astronomy is evident in monuments like the
ceiling of Senemut's tomb from the
Eighteenth Dynasty of Egypt.
Physics
–
Sir Isaac Newton (1643–1727), whose
laws of motion and
universal gravitation were major milestones in classical physics
Physics
–
Albert Einstein (1879–1955), whose work on the
photoelectric effect and the
theory of relativity led to a revolution in 20th century physics
20.
Engineering
–
The term Engineering is derived from the Latin ingenium, meaning cleverness and ingeniare, meaning to contrive, devise. Engineering has existed since ancient times as humans devised fundamental inventions such as the wedge, lever, wheel, each of these inventions is essentially consistent with the modern definition of engineering. The term engineering is derived from the engineer, which itself dates back to 1390 when an engineer originally referred to a constructor of military engines. In this context, now obsolete, a referred to a military machine. Notable examples of the obsolete usage which have survived to the present day are military engineering corps, the word engine itself is of even older origin, ultimately deriving from the Latin ingenium, meaning innate quality, especially mental power, hence a clever invention. The earliest civil engineer known by name is Imhotep, as one of the officials of the Pharaoh, Djosèr, he probably designed and supervised the construction of the Pyramid of Djoser at Saqqara in Egypt around 2630–2611 BC. Ancient Greece developed machines in both civilian and military domains, the Antikythera mechanism, the first known mechanical computer, and the mechanical inventions of Archimedes are examples of early mechanical engineering. In the Middle Ages, the trebuchet was developed, the first steam engine was built in 1698 by Thomas Savery. The development of this gave rise to the Industrial Revolution in the coming decades. With the rise of engineering as a profession in the 18th century, similarly, in addition to military and civil engineering, the fields then known as the mechanic arts became incorporated into engineering. The inventions of Thomas Newcomen and the Scottish engineer James Watt gave rise to mechanical engineering. The development of specialized machines and machine tools during the revolution led to the rapid growth of mechanical engineering both in its birthplace Britain and abroad. John Smeaton was the first self-proclaimed civil engineer and is regarded as the father of civil engineering. He was an English civil engineer responsible for the design of bridges, canals, harbours and he was also a capable mechanical engineer and an eminent physicist. Smeaton designed the third Eddystone Lighthouse where he pioneered the use of hydraulic lime and his lighthouse remained in use until 1877 and was dismantled and partially rebuilt at Plymouth Hoe where it is known as Smeatons Tower. The United States census of 1850 listed the occupation of engineer for the first time with a count of 2,000, there were fewer than 50 engineering graduates in the U. S. before 1865. In 1870 there were a dozen U. S. mechanical engineering graduates, in 1890 there were 6,000 engineers in civil, mining, mechanical and electrical. There was no chair of applied mechanism and applied mechanics established at Cambridge until 1875, the theoretical work of James Maxwell and Heinrich Hertz in the late 19th century gave rise to the field of electronics
Engineering
–
The
steam engine, a major driver in the
Industrial Revolution, underscores the importance of engineering in modern history. This
beam engine is on display in the
Technical University of Madrid.
Engineering
–
Relief map of the
Citadel of Lille, designed in 1668 by
Vauban, the foremost military engineer of his age.
Engineering
–
The Ancient Romans built
aqueducts to bring a steady supply of clean fresh water to cities and towns in the empire.
Engineering
–
The
International Space Station represents a modern engineering challenge from many disciplines.
21.
Optics
–
Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light, because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice, practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines, physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both wave-like and particle-like properties, explanation of these effects requires quantum mechanics. When considering lights particle-like properties, the light is modelled as a collection of particles called photons, quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, photography, practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics. Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, the earliest known lenses, made from polished crystal, often quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/Nimrud lens. The ancient Romans and Greeks filled glass spheres with water to make lenses, the word optics comes from the ancient Greek word ὀπτική, meaning appearance, look. Greek philosophy on optics broke down into two opposing theories on how vision worked, the theory and the emission theory. The intro-mission approach saw vision as coming from objects casting off copies of themselves that were captured by the eye, plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes. He also commented on the parity reversal of mirrors in Timaeus, some hundred years later, Euclid wrote a treatise entitled Optics where he linked vision to geometry, creating geometrical optics. Ptolemy, in his treatise Optics, held a theory of vision, the rays from the eye formed a cone, the vertex being within the eye. The rays were sensitive, and conveyed back to the observer’s intellect about the distance. He summarised much of Euclid and went on to describe a way to measure the angle of refraction, during the Middle Ages, Greek ideas about optics were resurrected and extended by writers in the Muslim world
Optics
–
Optics includes study of
dispersion of light.
Optics
–
The Nimrud lens
Optics
–
Reproduction of a page of
Ibn Sahl 's manuscript showing his knowledge of the law of refraction, now known as
Snell's law
Optics
–
Cover of the first edition of Newton's Opticks
22.
Acoustics
–
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of society with the most obvious being the audio. Hearing is one of the most crucial means of survival in the animal world, accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound, art, craft, science and technology have provoked one another to advance the whole, as in many other fields of knowledge. Robert Bruce Lindsays Wheel of Acoustics is a well accepted overview of the fields in acoustics. The word acoustic is derived from the Greek word ἀκουστικός, meaning of or for hearing, ready to hear and that from ἀκουστός, heard, audible, which in turn derives from the verb ἀκούω, I hear. The Latin synonym is sonic, after which the term used to be a synonym for acoustics. Frequencies above and below the range are called ultrasonic and infrasonic. If, for example, a string of a length would sound particularly harmonious with a string of twice the length. In modern parlance, if a string sounds the note C when plucked, a string twice as long will sound a C an octave lower. In one system of tuning, the tones in between are then given by 16,9 for D,8,5 for E,3,2 for F,4,3 for G,6,5 for A. Aristotle understood that sound consisted of compressions and rarefactions of air which falls upon, a very good expression of the nature of wave motion. The physical understanding of acoustical processes advanced rapidly during and after the Scientific Revolution, mainly Galileo Galilei but also Marin Mersenne, independently, discovered the complete laws of vibrating strings. Experimental measurements of the speed of sound in air were carried out successfully between 1630 and 1680 by a number of investigators, prominently Mersenne, meanwhile, Newton derived the relationship for wave velocity in solids, a cornerstone of physical acoustics. The eighteenth century saw advances in acoustics as mathematicians applied the new techniques of calculus to elaborate theories of sound wave propagation. Also in the 19th century, Wheatstone, Ohm, and Henry developed the analogy between electricity and acoustics, the twentieth century saw a burgeoning of technological applications of the large body of scientific knowledge that was by then in place. The first such application was Sabine’s groundbreaking work in architectural acoustics, Underwater acoustics was used for detecting submarines in the first World War
Acoustics
–
Principles of acoustics were applied since ancient times:
Roman theatre in the city of
Amman.
Acoustics
–
Artificial omni-directional sound source in an
anechoic chamber
Acoustics
–
Jay Pritzker Pavilion
Acoustics
23.
Radio
–
When radio waves strike an electrical conductor, the oscillating fields induce an alternating current in the conductor. The information in the waves can be extracted and transformed back into its original form, Radio systems need a transmitter to modulate some property of the energy produced to impress a signal on it, for example using amplitude modulation or angle modulation. Radio systems also need an antenna to convert electric currents into radio waves, an antenna can be used for both transmitting and receiving. The electrical resonance of tuned circuits in radios allow individual stations to be selected, the electromagnetic wave is intercepted by a tuned receiving antenna. Radio frequencies occupy the range from a 3 kHz to 300 GHz, a radio communication system sends signals by radio. The term radio is derived from the Latin word radius, meaning spoke of a wheel, beam of light, however, this invention would not be widely adopted. The switch to radio in place of wireless took place slowly and unevenly in the English-speaking world, the United States Navy would also play a role. Although its translation of the 1906 Berlin Convention used the terms wireless telegraph and wireless telegram, the term started to become preferred by the general public in the 1920s with the introduction of broadcasting. Radio systems used for communication have the following elements, with more than 100 years of development, each process is implemented by a wide range of methods, specialised for different communications purposes. Each system contains a transmitter, This consists of a source of electrical energy, the transmitter contains a system to modulate some property of the energy produced to impress a signal on it. This modulation might be as simple as turning the energy on and off, or altering more subtle such as amplitude, frequency, phase. Amplitude modulation of a carrier wave works by varying the strength of the signal in proportion to the information being sent. For example, changes in the strength can be used to reflect the sounds to be reproduced by a speaker. It was the used for the first audio radio transmissions. Frequency modulation varies the frequency of the carrier, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal. FM has the capture effect whereby a receiver only receives the strongest signal, Digital data can be sent by shifting the carriers frequency among a set of discrete values, a technique known as frequency-shift keying. FM is commonly used at Very high frequency radio frequencies for high-fidelity broadcasts of music, analog TV sound is also broadcast using FM. Angle modulation alters the phase of the carrier wave to transmit a signal
Radio
–
The
Alexandra Palace radio transmitter mast
Radio
–
Classic radio
receiver dial
Radio
–
Rooftop
television antennas.
Yagi-Uda antennas like these six are widely used at
VHF and
UHF frequencies.
Radio
–
Bakelite radio at the Bakelite Museum, Orchard Mill, Williton, Somerset, UK.
24.
Nu (letter)
–
Nu /njuː/, is the 13th letter of the Greek alphabet. In the system of Greek numerals it has a value of 50 and it is derived from the ancient Phoenician alphabet nun. Its Latin equivalent is N, though the lowercase resembles the Roman lowercase v, the name of the letter is written νῦ in Ancient Greek and traditional Modern Greek polytonic orthography, while in Modern Greek it is written νι. The uppercase nu is not used, because it is identical to Latin N. The lower-case letter ν is used as a symbol for, Degree of freedom in statistics, the frequency of a wave in physics and other fields, sometimes also spatial frequency. Poissons ratio, the ratio of strains perpendicular with and parallel with an applied force, any of three kinds of neutrino in particle physics. One of the Greeks in mathematical finance, known as vega, the number of neutrons released per fission of an atom in nuclear physics. A DNA polymerase found in eukaryotes and implicated in translesion synthesis. Molecular vibrational mode, νx where x is the number of the vibration, the greatest fixed point of a function, as commonly used in the μ-calculus. Free names of a process, as used in the π-calculus, the maximum conditioning possible for an unconditioned stimulus in the Rescorla-Wagner model. The true anomaly, a parameter that defines the position of a body moving along an orbit. Greek Nu/Coptic Ni Mathematical Nu These characters are used only as mathematical symbols, stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style
Nu (letter)
–
Greek alphabet
25.
Planck constant
–
The Planck constant is a physical constant that is the quantum of action, central in quantum mechanics. The light quantum behaved in some respects as a neutral particle. It was eventually called the photon, the Planck–Einstein relation connects the particulate photon energy E with its associated wave frequency f, E = h f This energy is extremely small in terms of ordinarily perceived everyday objects. Since the frequency f, wavelength λ, and speed of c are related by f = c λ. This leads to another relationship involving the Planck constant, with p denoting the linear momentum of a particle, the de Broglie wavelength λ of the particle is given by λ = h p. In applications where it is natural to use the frequency it is often useful to absorb a factor of 2π into the Planck constant. The resulting constant is called the reduced Planck constant or Dirac constant and it is equal to the Planck constant divided by 2π, and is denoted ħ, ℏ = h 2 π. The energy of a photon with angular frequency ω, where ω = 2πf, is given by E = ℏ ω, while its linear momentum relates to p = ℏ k and this was confirmed by experiments soon afterwards. This holds throughout quantum theory, including electrodynamics and these two relations are the temporal and spatial component parts of the special relativistic expression using 4-Vectors. P μ = = ℏ K μ = ℏ Classical statistical mechanics requires the existence of h, eventually, following upon Plancks discovery, it was recognized that physical action cannot take on an arbitrary value. Instead, it must be multiple of a very small quantity. This is the old quantum theory developed by Bohr and Sommerfeld, in which particle trajectories exist but are hidden. Thus there is no value of the action as classically defined, related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics. Classical physics cannot explain either quantization of energy or the lack of a particle motion. In many cases, such as for light or for atoms, quantization of energy also implies that only certain energy levels are allowed. The Planck constant has dimensions of physical action, i. e. energy multiplied by time, or momentum multiplied by distance, in SI units, the Planck constant is expressed in joule-seconds or or. The value of the Planck constant is, h =6.626070040 ×10 −34 J⋅s =4.135667662 ×10 −15 eV⋅s. The value of the reduced Planck constant is, ℏ = h 2 π =1.054571800 ×10 −34 J⋅s =6.582119514 ×10 −16 eV⋅s
Planck constant
–
Plaque at the
Humboldt University of Berlin: "Max Planck, discoverer of the elementary quantum of action h, taught in this building from 1889 to 1928."
26.
SI derived unit
–
The International System of Units specifies a set of seven base units from which all other SI units of measurement are derived. Each of these units is either dimensionless or can be expressed as a product of powers of one or more of the base units. For example, the SI derived unit of area is the metre. The degree Celsius has an unclear status, and is arguably an exception to this rule. The names of SI units are written in lowercase, the symbols for units named after persons, however, are always written with an uppercase initial letter. In addition to the two dimensionless derived units radian and steradian,20 other derived units have special names, some other units such as the hour, litre, tonne, bar and electronvolt are not SI units, but are widely used in conjunction with SI units. Until 1995, the SI classified the radian and the steradian as supplementary units, but this designation was abandoned, International System of Quantities International System of Units International Vocabulary of Metrology Metric prefix Metric system Non-SI units mentioned in the SI Planck units SI base unit I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC, Quantities, Units and Symbols in Physical Chemistry. CS1 maint, Multiple names, authors list
SI derived unit
–
Base units
27.
Heinrich Hertz
–
Heinrich Rudolf Hertz was a German physicist who first conclusively proved the existence of the electromagnetic waves theorized by James Clerk Maxwells electromagnetic theory of light. The unit of frequency – cycle per second – was named the hertz in his honor, Heinrich Rudolf Hertz was born in 1857 in Hamburg, then a sovereign state of the German Confederation, into a prosperous and cultured Hanseatic family. His father Gustav Ferdinand Hertz was a barrister and later a senator and his mother was Anna Elisabeth Pfefferkorn. Hertzs paternal grandfather, Heinrich David Hertz, was a businessman and their first son, Wolff Hertz, was chairman of the Jewish community. Heinrich Rudolf Hertzs father and paternal grandparents had converted from Judaism to Christianity in 1834 and his mothers family was a Lutheran pastors family. While studying at the Gelehrtenschule des Johanneums in Hamburg, Heinrich Rudolf Hertz showed an aptitude for sciences as well as languages, learning Arabic and Sanskrit. He studied sciences and engineering in the German cities of Dresden, Munich and Berlin, in 1880, Hertz obtained his PhD from the University of Berlin, and for the next three years remained for post-doctoral study under Helmholtz, serving as his assistant. In 1883, Hertz took a post as a lecturer in physics at the University of Kiel. In 1885, Hertz became a professor at the University of Karlsruhe. In 1886, Hertz married Elisabeth Doll, the daughter of Dr. Max Doll and they had two daughters, Johanna, born on 20 October 1887 and Mathilde, born on 14 January 1891, who went on to become a notable biologist. During this time Hertz conducted his research into electromagnetic waves. Hertz took a position of Professor of Physics and Director of the Physics Institute in Bonn on 3 April 1889, during this time he worked on theoretical mechanics with his work published in the book Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt, published posthumously in 1894. In 1892, Hertz was diagnosed with an infection and underwent operations to treat the illness and he died of granulomatosis with polyangiitis at the age of 36 in Bonn, Germany in 1894, and was buried in the Ohlsdorf Cemetery in Hamburg. Hertzs wife, Elisabeth Hertz née Doll, did not remarry, Hertz left two daughters, Johanna and Mathilde. Hertzs daughters never married and he has no descendants, Hertz always had a deep interest in meteorology, probably derived from his contacts with Wilhelm von Bezold. In 1886–1889, Hertz published two articles on what was to become known as the field of contact mechanics, joseph Valentin Boussinesq published some critically important observations on Hertzs work, nevertheless establishing this work on contact mechanics to be of immense importance. His work basically summarises how two objects placed in contact will behave under loading, he obtained results based upon the classical theory of elasticity. It was natural to neglect adhesion in that age as there were no methods of testing for it
Heinrich Hertz
–
Heinrich Hertz
Heinrich Hertz
–
Memorial of Heinrich Hertz on the campus of the
Karlsruhe Institute of Technology, which translates as At this site, Heinrich Hertz discovered electromagnetic waves in the years 1885–1889.
Heinrich Hertz
–
Official English translation of Untersuchungen über die Ausbreitung der elektrischen Kraft published in 1893, a year before Hertz's death.
Heinrich Hertz
28.
Cycle per second
–
The cycle per second was a once-common English name for the unit of frequency now known as the hertz. The plural form was used, often written cycles per second, cycles/second, c. p. s, c/s. The term comes from the fact that waves have a frequency measurable in their number of vibrations, or cycles. With the organization of the International System of Units in 1960, symbolically, cycle per second units are cycle/second, while hertz is 1/second or s −1. This particular mandate has been so widely adopted as to render the old cycle per second all, for higher frequencies, kilocycles, as an abbreviation of kilocycles per second were often used on components or devices. Other higher units like megacycle and less commonly kilomegacycle were used before 1960 and these have modern equivalents such as kilohertz, megahertz, and gigahertz. Thus,1 Bq is 1 event per second on average whereas 1 hertz is 1 event per second on a regular cycle. Cycle can also be a unit for measuring usage of reciprocating machines, especially presses, cycles per instruction Heinrich Hertz Instructions per cycle Instructions per second MKS system of units a predecessor of the SI set of units Normalized frequency Radian per second
Cycle per second
–
Crystal resonators, the 1940s-era center unit is marked in kc.
29.
Ocean surface wave
–
In fluid dynamics, wind waves, or wind-generated waves, are surface waves that occur on the free surface of bodies of water. They result from the wind blowing over an area of fluid surface, Waves in the oceans can travel thousands of miles before reaching land. Wind waves on Earth range in size from small ripples, to waves over 100 ft high, when directly generated and affected by local winds, a wind wave system is called a wind sea. After the wind ceases to blow, wind waves are called swells, more generally, a swell consists of wind-generated waves that are not significantly affected by the local wind at that time. They have been generated elsewhere or some time ago, wind waves in the ocean are called ocean surface waves. Wind waves have an amount of randomness, subsequent waves differ in height, duration. The key statistics of wind waves in evolving sea states can be predicted with wind wave models, although waves are usually considered in the water seas of Earth, the hydrocarbon seas of Titan may also have wind-driven waves. The great majority of large breakers seen at a result from distant winds. Water depth All of these work together to determine the size of wind waves. Further exposure to that wind could only cause a dissipation of energy due to the breaking of wave tops. Waves in an area typically have a range of heights. For weather reporting and for analysis of wind wave statistics. This figure represents an average height of the highest one-third of the waves in a time period. The significant wave height is also the value a trained observer would estimate from visual observation of a sea state, given the variability of wave height, the largest individual waves are likely to be somewhat less than twice the reported significant wave height for a particular day or storm. Wave formation on a flat water surface by wind is started by a random distribution of normal pressure of turbulent wind flow over the water. This pressure fluctuation produces normal and tangential stresses in the surface water and it is assumed that, The water is originally at rest. There is a distribution of normal pressure to the water surface from the turbulent wind. Correlations between air and water motions are neglected, the second mechanism involves wind shear forces on the water surface
Ocean surface wave
–
Hurricane Marie storm waves
Ocean surface wave
–
Ocean waves
Ocean surface wave
Ocean surface wave
–
NOAA ship Delaware II in bad weather on
Georges Bank.
30.
Omega (letter)
–
Omega is the 24th and last letter of the Greek alphabet. In the Greek numeric system, it has a value of 800, the word literally means great O, as opposed to omicron, which means little O. In phonetic terms, the Ancient Greek Ω is a long open-mid o, in Modern Greek, Ω represents the mid back rounded vowel /o/, the same sound as omicron. The letter omega is transcribed ō or simply o, as the last letter of the Greek alphabet, Omega is often used to denote the last, the end, or the ultimate limit of a set, in contrast to alpha, the first letter of the Greek alphabet. Ω was not part of the early Greek alphabets and it was introduced in the late 7th century BC in the Ionian cities of Asia Minor to denote the long half-open. It is a variant of omicron, broken up at the side, the name Ωμέγα is Byzantine, in Classical Greek, the letter was called ō, whereas the omicron was called ou. In addition to the Greek alphabet, Omega was also adopted into the early Cyrillic alphabet, a Raetic variant is conjectured to be at the origin or parallel evolution of the Elder Futhark ᛟ. Omega was also adopted into the Latin alphabet, as a letter of the 1982 revision to the African reference alphabet, the uppercase letter Ω is used as a symbol, In chemistry, For oxygen-18, a natural, stable isotope of oxygen. In physics, For ohm – SI unit of resistance, formerly also used upside down to represent mho. Unicode has a code point for the ohm sign, but it is included only for backward compatibility. In statistical mechanics, Ω refers to the multiplicity in a system, the solid angle or the rate of precession in a gyroscope. In particle physics to represent the Omega baryons, in astronomy, Ω refers to the density of the universe, also called the density parameter. In astronomy, Ω refers to the longitude of the node of an orbit. In mathematics and computer science, In complex analysis, the Omega constant, a solution of Lamberts W function In differential geometry, a variable for a 2-dimensional region in calculus, usually corresponding to the domain of a double integral. In topos theory, the subobject classifier of an elementary topos, in combinatory logic, the looping combinator, In group theory, the omega and agemo subgroups of a p-group, Ω and ℧ In group theory, Cayleys Ω process as a partial differential operator. In statistics, it is used as the symbol for the sample space, in number theory, Ω is the number of prime divisors of n. In notation related to Big O notation to describe the behavior of functions. As part of logo or trademark, The logo of Omega Watches SA, part of the Badge of the Supreme Court of the United Kingdom
Omega (letter)
–
Greek alphabet
31.
Angular displacement
–
Angular displacement of a body is the angle in radians through which a point or line has been rotated in a specified sense about a specified axis. When an object rotates about its axis, the motion cannot simply be analyzed as a particle, since in circular motion it undergoes a changing velocity, when dealing with the rotation of an object, it becomes simpler to consider the body itself rigid. A body is generally considered rigid when the separations between all the particles remains constant throughout the motion, so for example parts of its mass are not flying off. In a realistic sense, all things can be deformable, however this impact is minimal, Thus the rotation of a rigid body over a fixed axis is referred to as rotational motion. In the example illustrated to the right, a particle on object P is at a distance r from the origin, O. It becomes important to represent the position of particle P in terms of its polar coordinates. In this particular example, the value of θ is changing, if using radians, it provides a very simple relationship between distance traveled around the circle and the distance r from the centre. Therefore,1 revolution is 2 π radians, when object travels from point P to point Q, as it does in the illustration to the left, over δ t the radius of the circle goes around a change in angle. Δ θ = θ2 − θ1 which equals the Angular Displacement, in three dimensions, angular displacement is an entity with a direction and a magnitude. The direction specifies the axis of rotation, which exists by virtue of the Eulers rotation theorem. This entity is called an axis-angle, despite having direction and magnitude, angular displacement is not a vector because it does not obey the commutative law for addition. Nevertheless, when dealing with infinitesimal rotations, second order infinitesimals can be discarded, several ways to describe angular displacement exist, like rotation matrices or Euler angles. See charts on SO for others, given that any frame in the space can be described by a rotation matrix, the displacement among them can also be described by a rotation matrix. Being A0 and A f two matrices, the angular displacement matrix between them can be obtained as Δ A = A f, when this product is performed having a very small difference between both frames we will obtain a matrix close to the identity. In the limit, we will have a rotation matrix. An infinitesimal angular displacement is a rotation matrix, As any rotation matrix has a single real eigenvalue, which is +1. Its module can be deduced from the value of the infinitesimal rotation, when it is divided by the time, this will yield the angular velocity vector. Suppose we specify an axis of rotation by a unit vector, expanding the rotation matrix as an infinite addition, and taking the first order approach, the rotation matrix ΔR is represented as, Δ R = + Δ θ = I + A Δ θ
Angular displacement
–
Rotation of a rigid object P about a fixed object about a fixed axis O.
32.
Phase (waves)
–
Phase is the position of a point in time on a waveform cycle. A complete cycle is defined as the interval required for the waveform to return to its initial value. The graphic to the right shows how one cycle constitutes 360° of phase, the graphic also shows how phase is sometimes expressed in radians, where one radian of phase equals approximately 57. 3°. Phase can also be an expression of relative displacement between two corresponding features of two waveforms having the same frequency, in sinusoidal functions or in waves phase has two different, but closely related, meanings. One is the angle of a sinusoidal function at its origin and is sometimes called phase offset or phase difference. Another usage is the fraction of the cycle that has elapsed relative to the origin. Phase shift is any change that occurs in the phase of one quantity and this symbol, φ is sometimes referred to as a phase shift or phase offset because it represents a shift from zero phase. For infinitely long sinusoids, a change in φ is the same as a shift in time, if x is delayed by 14 of its cycle, it becomes, x = A ⋅ cos = A ⋅ cos whose phase is now φ − π2. It has been shifted by π2 radians, Phase difference is the difference, expressed in degrees or time, between two waves having the same frequency and referenced to the same point in time. Two oscillators that have the frequency and no phase difference are said to be in phase. Two oscillators that have the frequency and different phases have a phase difference. The amount by which such oscillators are out of phase with each other can be expressed in degrees from 0° to 360°, if the phase difference is 180 degrees, then the two oscillators are said to be in antiphase. If two interacting waves meet at a point where they are in antiphase, then interference will occur. It is common for waves of electromagnetic, acoustic or other energy to become superposed in their transmission medium, when that happens, the phase difference determines whether they reinforce or weaken each other. Complete cancellation is possible for waves with equal amplitudes, time is sometimes used to express position within the cycle of an oscillation. A phase difference is analogous to two athletes running around a track at the same speed and direction but starting at different positions on the track. They pass a point at different instants in time, but the time difference between them is a constant - same for every pass since they are at the same speed and in the same direction. If they were at different speeds, the difference is undefined
Phase (waves)
–
Illustration of phase shift. The horizontal axis represents an angle (phase) that is increasing with time.
33.
Sine function
–
In mathematics, the sine is a trigonometric function of an angle. More generally, the definition of sine can be extended to any value in terms of the length of a certain line segment in a unit circle. The function sine can be traced to the jyā and koṭi-jyā functions used in Gupta period Indian astronomy, via translation from Sanskrit to Arabic and then from Arabic to Latin. The word sine comes from a Latin mistranslation of the Arabic jiba, to define the trigonometric functions for an acute angle α, start with any right triangle that contains an angle of measure α, in the accompanying figure, angle A in triangle ABC has measure α. The three sides of the triangle are named as follows, The opposite side is the side opposite to the angle of interest, the hypotenuse is the side opposite the right angle, in this case side h. The hypotenuse is always the longest side of a right-angled triangle, the adjacent side is the remaining side, in this case side b. It forms a side of both the angle of interest and the right angle, once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side divided by the length of the hypotenuse. As stated, the value sin appears to depend on the choice of right triangle containing an angle of measure α, however, this is not the case, all such triangles are similar, and so the ratio is the same for each of them. The trigonometric functions can be defined in terms of the rise, run, when the length of the line segment is 1, sine takes an angle and tells the rise. Sine takes an angle and tells the rise per unit length of the line segment, rise is equal to sin θ multiplied by the length of the line segment. In contrast, cosine is used for telling the run from the angle, arctan is used for telling the angle from the slope. The line segment is the equivalent of the hypotenuse in the right-triangle, in trigonometry, a unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. Let a line through the origin, making an angle of θ with the half of the x-axis. The x- and y-coordinates of this point of intersection are equal to cos θ and sin, the points distance from the origin is always 1. Unlike the definitions with the triangle or slope, the angle can be extended to the full set of real arguments by using the unit circle. This can also be achieved by requiring certain symmetries and that sine be a periodic function. Exact identities, These apply for all values of θ. sin = cos =1 csc The reciprocal of sine is cosecant, i. e. the reciprocal of sin is csc, or cosec. Cosecant gives the ratio of the length of the hypotenuse to the length of the opposite side, the inverse function of sine is arcsine or inverse sine
Sine function
–
Domain coloring of sin(z) over (-π,π) on x and y axes. Brightness indicates absolute magnitude, saturation represents imaginary and real magnitude.
Sine function
–
Sine
34.
Radian
–
The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement in radians of the angle that it subtends. The unit was formerly an SI supplementary unit, but this category was abolished in 1995, separately, the SI unit of solid angle measurement is the steradian. The radian is represented by the symbol rad, so for example, a value of 1.2 radians could be written as 1.2 rad,1.2 r,1. 2rad, or 1. 2c. Radian describes the angle subtended by a circular arc as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Conversely, the length of the arc is equal to the radius multiplied by the magnitude of the angle in radians. As the ratio of two lengths, the radian is a number that needs no unit symbol, and in mathematical writing the symbol rad is almost always omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and it follows that the magnitude in radians of one complete revolution is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees, the concept of radian measure, as opposed to the degree of an angle, is normally credited to Roger Cotes in 1714. He described the radian in everything but name, and he recognized its naturalness as a unit of angular measure, the idea of measuring angles by the length of the arc was already in use by other mathematicians. For example, al-Kashi used so-called diameter parts as units where one part was 1/60 radian. The term radian first appeared in print on 5 June 1873, in examination questions set by James Thomson at Queens College, Belfast. He had used the term as early as 1871, while in 1869, Thomas Muir, then of the University of St Andrews, in 1874, after a consultation with James Thomson, Muir adopted radian. As stated, one radian is equal to 180/π degrees, thus, to convert from radians to degrees, multiply by 180/π. The length of circumference of a circle is given by 2 π r, so, to convert from radians to gradians multiply by 200 / π, and to convert from gradians to radians multiply by π /200. This is because radians have a mathematical naturalness that leads to a more elegant formulation of a number of important results, most notably, results in analysis involving trigonometric functions are simple and elegant when the functions arguments are expressed in radians. Because of these and other properties, the trigonometric functions appear in solutions to problems that are not obviously related to the functions geometrical meanings
Radian
–
A chart to convert between degrees and radians
Radian
–
An arc of a
circle with the same length as the
radius of that circle corresponds to an angle of 1 radian. A full circle corresponds to an angle of 2
π radians.
35.
Discrete-time signal
–
A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities. In other words, it is a series that is a function over a domain of integers. Discrete-time signals may have several origins, but can usually be classified into one of two groups, By acquiring values of a signal at constant or variable rate. By observing an inherently discrete-time process, such as the peak value of a particular economic indicator
Discrete-time signal
–
Discrete sampled signal
36.
Meter (unit)
–
The metre or meter, is the base unit of length in the International System of Units. The metre is defined as the length of the path travelled by light in a vacuum in 1/299792458 seconds, the metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a metre bar. In 1960, the metre was redefined in terms of a number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted, the imperial inch is defined as 0.0254 metres. One metre is about 3 3⁄8 inches longer than a yard, Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use meter. Measuring devices are spelled -meter in all variants of English, the suffix -meter has the same Greek origin as the unit of length. This range of uses is found in Latin, French, English. Thus calls for measurement and moderation. In 1668 the English cleric and philosopher John Wilkins proposed in an essay a decimal-based unit of length, as a result of the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. In 1668, Wilkins proposed using Christopher Wrens suggestion of defining the metre using a pendulum with a length which produced a half-period of one second, christiaan Huygens had observed that length to be 38 Rijnland inches or 39.26 English inches. This is the equivalent of what is now known to be 997 mm, no official action was taken regarding this suggestion. In the 18th century, there were two approaches to the definition of the unit of length. One favoured Wilkins approach, to define the metre in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the metre as one ten-millionth of the length of a quadrant along the Earths meridian, that is, the distance from the Equator to the North Pole. This means that the quadrant would have defined as exactly 10000000 metres at that time. To establish a universally accepted foundation for the definition of the metre, more measurements of this meridian were needed. This portion of the meridian, assumed to be the length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator
Meter (unit)
–
Belfry, Dunkirk —the northern end of the meridian arc
Meter (unit)
–
Fortress of Montjuïc —the southerly end of the meridian arc
Meter (unit)
–
Creating the metre-alloy in 1874 at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville and Debray
Meter (unit)
–
Closeup of National Prototype Metre Bar No. 27, made in 1889 by the
International Bureau of Weights and Measures (BIPM) and given to the United States, which served as the standard for defining all units of length in the US from 1893 to 1960
37.
Dispersion relation
–
In physical sciences and electrical engineering, dispersion relations describe the effect of dispersion in a medium on the properties of a wave traveling within that medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency, from this relation the phase velocity and group velocity of the wave have convenient expressions which then determine the refractive index of the medium. Dispersion may be caused either by geometric boundary conditions or by interaction of the waves with the transmitting medium, elementary particles, considered as matter waves, have a nontrivial dispersion relation even in the absence of geometric constraints and other media. In the presence of dispersion, wave velocity is no uniquely defined, giving rise to the distinction of phase velocity. Dispersion occurs when pure plane waves of different wavelengths have different propagation velocities, the speed of a plane wave, v, is a function of the waves wavelength λ, v = v. The waves speed, wavelength, and frequency, f, are related by the identity v = λ f, the function f expresses the dispersion relation of the given medium. Dispersion relations are more commonly expressed in terms of the angular frequency ω =2 π f, rewriting the relation above in these variables gives ω = v k. where we now view f as a function of k. The use of ω to describe the relation has become standard because both the phase velocity ω/k and the group velocity dω/dk have convenient representations via this function. Plane waves in vacuum are the simplest case of propagation, no geometric constraint. For electromagnetic waves in vacuum, the frequency is proportional to the wavenumber. This is a dispersion relation. In this case, the velocity and the group velocity are the same, v = ω k = d ω d k = c, they are given by c, the speed of light in vacuum. In the nonrelativistic limit, m c 2 is a constant and p 2 /2 m is the familiar kinetic energy expressed in terms of the momentum p = m v. According to the de Broglie relations, their kinetic energy E can be expressed as a frequency ω, accordingly, angular frequency and wavenumber are connected through a dispersion relation, which in the nonrelativistic limit reads ω = ℏ k 22 m. For particles, this translates to a knowledge of energy as a function of momentum, the name dispersion relation originally comes from optics. In this case, the waveform will spread over time, such that a pulse will become an extended pulse. In these materials, ∂ ω ∂ k is known as the velocity and corresponds to the speed at which the peak of the pulse propagates. The dispersion relation for water waves is often written as ω = g k
Dispersion relation
–
The
refraction of a light in a
prism is due to
dispersion.
38.
Wavelength
–
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the waves shape repeats, and thus the inverse of the spatial frequency. Wavelength is commonly designated by the Greek letter lambda, the concept can also be applied to periodic waves of non-sinusoidal shape. The term wavelength is also applied to modulated waves. Wavelength depends on the medium that a wave travels through, examples of wave-like phenomena are sound waves, light, water waves and periodic electrical signals in a conductor. A sound wave is a variation in air pressure, while in light and other electromagnetic radiation the strength of the electric, water waves are variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary, wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. For example, in waves over deep water a particle near the waters surface moves in a circle of the same diameter as the wave height. The range of wavelengths or frequencies for wave phenomena is called a spectrum, the name originated with the visible light spectrum but now can be applied to the entire electromagnetic spectrum as well as to a sound spectrum or vibration spectrum. In linear media, any pattern can be described in terms of the independent propagation of sinusoidal components. The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by λ = v f, in a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear. In the case of electromagnetic radiation—such as light—in free space, the speed is the speed of light. Thus the wavelength of a 100 MHz electromagnetic wave is about, the wavelength of visible light ranges from deep red, roughly 700 nm, to violet, roughly 400 nm. For sound waves in air, the speed of sound is 343 m/s, the wavelengths of sound frequencies audible to the human ear are thus between approximately 17 m and 17 mm, respectively. Note that the wavelengths in audible sound are much longer than those in visible light, a standing wave is an undulatory motion that stays in one place. A sinusoidal standing wave includes stationary points of no motion, called nodes, the upper figure shows three standing waves in a box. The walls of the box are considered to require the wave to have nodes at the walls of the box determining which wavelengths are allowed, the stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities. Consequently, wavelength, period, and wave velocity are related just as for a traveling wave, for example, the speed of light can be determined from observation of standing waves in a metal box containing an ideal vacuum. In that case, the k, the magnitude of k, is still in the same relationship with wavelength as shown above
Wavelength
–
Wavelength is decreased in a medium with slower propagation.
Wavelength
–
Wavelength of a
sine wave, λ, can be measured between any two points with the same
phase, such as between crests, or troughs, or corresponding
zero crossings as shown.
Wavelength
–
Various local wavelengths on a crest-to-crest basis in an ocean wave approaching shore
Wavelength
–
A wave on a line of atoms can be interpreted according to a variety of wavelengths.
39.
Lambda
–
Lambda is the 11th letter of the Greek alphabet. In the system of Greek numerals lambda has a value of 30, Lambda is related to the Phoenician letter Lamed. Letters in other alphabets that stemmed from lambda include the Latin L, the ancient grammarians and dramatists give evidence to the pronunciation as in Classical Greek times. In Modern Greek the name of the letter, Λάμδα, is pronounced, in early Greek alphabets, the shape and orientation of lambda varied. Most variants consisted of two strokes, one longer than the other, connected at their ends. The angle might be in the upper-left, lower-left, or top, other variants had a vertical line with a horizontal or sloped stroke running to the right. With the general adoption of the Ionic alphabet, Greek settled on an angle at the top, the HTML4 character entity references for the Greek capital and small letter lambda are Λ, and λ, respectively. The Unicode code points for lambda are U+039B and U+03BB, the lambda particle is a type of subatomic particle in subatomic particle physics. Lambda is the set of axioms in the axiomatic method of logical deduction in first-order logic. Lambda was used as a pattern by the Spartan army. This stood for Lacedaemon, the name of the polis of the Spartans, Lambda is the von Mangoldt function in mathematical number theory. Lambda is a associated with the Identitarian movement, intended to emulate a Spartan shield pattern. In statistics, Wilkss lambda is used in analysis of variance to compare group means on a combination of dependent variables. In the spectral decomposition of matrices, lambda indicates the diagonal matrix of the eigenvalues of the matrix, in computer science, lambda is the time window over which a process is observed for determining the working memory set for a digital computers virtual memory management. In astrophysics, lambda represents the likelihood that a body will encounter a planet or a dwarf planet leading to a deflection of a significant magnitude. An object with a value of lambda is expected to have cleared its neighborhood. In crystal optics, lambda is used to represent the period of a lattice, in NATO military operations, a chevron is painted on the vehicles of this military alliance for identification. In chemistry there are Δ and Λ isomers, see, coordination complex In electrochemistry, in cosmology, lambda is the symbol for the cosmological constant, a term added to some dynamical equations to account for the acceleration of the universe
Lambda
–
The Greek alphabet on a
black figure vessel, with a Phoenician-lamed-shaped lambda. (The gamma has the shape of modern lambda.)
40.
Division (mathematics)
–
Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication. The division of two numbers is the process of calculating the number of times one number is contained within one another. For example, in the picture on the right, the 20 apples are divided into groups of five apples, Division can also be thought of as the process of evaluating a fraction, and fractional notation is commonly used to represent division. Division is the inverse of multiplication, if a × b = c, then a = c ÷ b, as long as b is not zero. Division by zero is undefined for the numbers and most other contexts, because if b =0, then a cannot be deduced from b and c. In some contexts, division by zero can be defined although to a limited extent, in division, the dividend is divided by the divisor to get a quotient. In the above example,20 is the dividend, five is the divisor, in some cases, the divisor may not be contained fully by the dividend, for example,10 ÷3 leaves a remainder of one, as 10 is not a multiple of three. Sometimes this remainder is added to the quotient as a fractional part, but in the context of integer division, where numbers have no fractional part, the remainder is kept separately or discarded. Besides dividing apples, division can be applied to other physical, Division has been defined in several contexts, such as for the real and complex numbers and for more abstract contexts such as for vector spaces and fields. Division is the most mentally difficult of the four operations of arithmetic. Teaching the objective concept of dividing integers introduces students to the arithmetic of fractions, unlike addition, subtraction, and multiplication, the set of all integers is not closed under division. Dividing two integers may result in a remainder, to complete the division of the remainder, the number system is extended to include fractions or rational numbers as they are more generally called. When students advance to algebra, the theory of division intuited from arithmetic naturally extends to algebraic division of variables, polynomials. Division is often shown in algebra and science by placing the dividend over the divisor with a line, also called a fraction bar. For example, a divided by b is written a b This can be read out loud as a divided by b, a fraction is a division expression where both dividend and divisor are integers, and there is no implication that the division must be evaluated further. A second way to show division is to use the obelus, common in arithmetic, in this manner, ISO 80000-2-9.6 states it should not be used. The obelus is also used alone to represent the operation itself. In some non-English-speaking cultures, a divided by b is written a, b and this notation was introduced in 1631 by William Oughtred in his Clavis Mathematicae and later popularized by Gottfried Wilhelm Leibniz
Division (mathematics)
–
This article is about the arithmetical operation. For other uses, see
Division (disambiguation).
41.
Vacuum
–
Vacuum is space void of matter. The word stems from the Latin adjective vacuus for vacant or void, an approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. In engineering and applied physics on the hand, vacuum refers to any space in which the pressure is lower than atmospheric pressure. The Latin term in vacuo is used to describe an object that is surrounded by a vacuum, the quality of a partial vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressure means higher-quality vacuum, for example, a typical vacuum cleaner produces enough suction to reduce air pressure by around 20%. Ultra-high vacuum chambers, common in chemistry, physics, and engineering, operate below one trillionth of atmospheric pressure, outer space is an even higher-quality vacuum, with the equivalent of just a few hydrogen atoms per cubic meter on average. In the electromagnetism in the 19th century, vacuum was thought to be filled with a medium called aether, in modern particle physics, the vacuum state is considered the ground state of matter. Vacuum has been a frequent topic of debate since ancient Greek times. Evangelista Torricelli produced the first laboratory vacuum in 1643, and other techniques were developed as a result of his theories of atmospheric pressure. A torricellian vacuum is created by filling a glass container closed at one end with mercury. Vacuum became an industrial tool in the 20th century with the introduction of incandescent light bulbs and vacuum tubes. The recent development of human spaceflight has raised interest in the impact of vacuum on human health, the word vacuum comes from Latin an empty space, void, noun use of neuter of vacuus, meaning empty, related to vacare, meaning be empty. Vacuum is one of the few words in the English language that contains two consecutive letters u. Historically, there has been dispute over whether such a thing as a vacuum can exist. Ancient Greek philosophers debated the existence of a vacuum, or void, in the context of atomism, Aristotle believed that no void could occur naturally, because the denser surrounding material continuum would immediately fill any incipient rarity that might give rise to a void. Almost two thousand years after Plato, René Descartes also proposed a geometrically based alternative theory of atomism, without the problematic nothing–everything dichotomy of void, by the ancient definition however, directional information and magnitude were conceptually distinct. The explanation of a clepsydra or water clock was a topic in the Middle Ages. Although a simple wine skin sufficed to demonstrate a partial vacuum, in principle and he concluded that airs volume can expand to fill available space, and he suggested that the concept of perfect vacuum was incoherent. However, according to Nader El-Bizri, the physicist Ibn al-Haytham and the Mutazili theologians disagreed with Aristotle and Al-Farabi, using geometry, Ibn al-Haytham mathematically demonstrated that place is the imagined three-dimensional void between the inner surfaces of a containing body
Vacuum
–
Pump to demonstrate vacuum
Vacuum
–
A large
vacuum chamber
Vacuum
–
The
Crookes tube, used to discover and study
cathode rays, was an evolution of the
Geissler tube.
Vacuum
–
A glass McLeod gauge, drained of mercury
42.
Speed of light
–
The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299792458 metres per second, it is exact because the unit of length, the metre, is defined from this constant, according to special relativity, c is the maximum speed at which all matter and hence information in the universe can travel. It is the speed at which all particles and changes of the associated fields travel in vacuum. Such particles and waves travel at c regardless of the motion of the source or the reference frame of the observer. In the theory of relativity, c interrelates space and time, the speed at which light propagates through transparent materials, such as glass or air, is less than c, similarly, the speed of radio waves in wire cables is slower than c. The ratio between c and the speed v at which light travels in a material is called the index n of the material. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, the light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light limits the theoretical maximum speed of computers. The speed of light can be used time of flight measurements to measure large distances to high precision. Ole Rømer first demonstrated in 1676 that light travels at a speed by studying the apparent motion of Jupiters moon Io. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, in 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame is a constant and is independent of the motion of the light source. He explored the consequences of that postulate by deriving the theory of relativity and in doing so showed that the parameter c had relevance outside of the context of light and electromagnetism. After centuries of increasingly precise measurements, in 1975 the speed of light was known to be 299792458 m/s with a measurement uncertainty of 4 parts per billion. In 1983, the metre was redefined in the International System of Units as the distance travelled by light in vacuum in 1/299792458 of a second, as a result, the numerical value of c in metres per second is now fixed exactly by the definition of the metre. The speed of light in vacuum is usually denoted by a lowercase c, historically, the symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant later shown to equal √2 times the speed of light in vacuum, in 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, sometimes c is used for the speed of waves in any material medium, and c0 for the speed of light in vacuum. This article uses c exclusively for the speed of light in vacuum, since 1983, the metre has been defined in the International System of Units as the distance light travels in vacuum in 1⁄299792458 of a second
Speed of light
–
One of the last and most accurate time of flight measurements, Michelson, Pease and Pearson's 1930-35 experiment used a rotating mirror and a one-mile (1.6 km) long vacuum chamber which the light beam traversed 10 times. It achieved accuracy of ±11 km/s
Speed of light
–
Sunlight takes about 8 minutes 17 seconds to travel the average distance from the surface of the
Sun to the
Earth.
Speed of light
–
Diagram of the
Fizeau apparatus
Speed of light
–
Rømer's observations of the occultations of Io from Earth
43.
Monochrome
–
Monochrome describes paintings, drawings, design, or photographs in one color or values of one color. A monochromatic object or image reflects colors in shades of limited colors or hues, images using only shades of grey are called grayscale or black-and-white. However, scientifically speaking, monochromatic light refers to light of a narrow band of wavelengths. In computing, monochrome has two meanings, it may mean having only one color which is either on or off, a monochrome computer display is able to display only a single color, often green, amber, red or white, and often also shades of that color. In film photography, monochrome is typically the use of black-and-white film, originally, all photography was done in monochrome. Although color photography was possible even in the late 19th century, easily used color films, if the red channel is eliminated and the green and blue combined then the effect will be similar to that of orthochromatic film or the use of a cyan filter on panchromatic film. The selection of weighting thus allows a range of artistic expression in the final monochromatic image. For production of an image the original color stereogram source may first be reduced to monochrome in order to simplify the rendering of the image. This is sometimes required in cases where an image would render in a confusing manner given the colors and patterns present in the source image. In physics, monochromatic light is electromagnetic radiation of a single frequency, even very controlled sources such as lasers operate in a range of frequencies. In practice, filtered light, diffraction grating separated light and laser light are all referred to as monochromatic. Often light sources can be compared and one be labeled as “more monochromatic”
Monochrome
–
The
Eiffel Tower during the
Exposition Universelle (1889) for which the tower was built
Monochrome
–
A photograph of a
parrot rendered with a monochrome palette of a limited number of shades
Monochrome
–
Night vision devices typically produce a monochrome image, often in shades of green
Monochrome
–
Monochrome
anaglyph image stereogram rendered in red and cyan;
3D red cyan glasses are recommended to view this image correctly.
44.
Random error
–
Observational error is the difference between a measured value of quantity and its true value. In statistics, an error is not a mistake, variability is an inherent part of things being measured and of the measurement process. Measurement errors can be divided into two components, random error and systematic error, random errors are errors in measurement that lead to measurable values being inconsistent when repeated measures of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by an inaccuracy inherent in the system, systematic error may also refer to an error having a nonzero mean, so that its effect is not reduced when observations are averaged. There are two types of measurement error, systematic errors and random errors, a systematic error is associated with the fact that a measured value contains an offset. In general, an error, regarded as a quantity, is a component of error that remains constant or depends in a specific manner on some other quantity. A random error is associated with the fact that when a measurement is repeated it will provide a measured value that is different from the previous value. It is random in that the measured value cannot be predicted exactly from previous such values. In general, there can be a number of contributions to type of error. Every time we repeat a measurement with an instrument, we obtain slightly different results. Systematic error is sometimes called statistical bias and it may often be reduced by very carefully standardized procedures. Part of the education in science is how to use the standard instruments of the discipline. The random error is due to factors which we cannot control and it may be too expensive or we may be too ignorant of these factors to control them each time we measure. It may even be that whatever we are trying to measure is changing in time, random error often occurs when instruments are pushed to their limits. For example, it is common for digital balances to exhibit random error in their least significant digit, three measurements of a single object might read something like 0. 9111g,0. 9110g, and 0. 9112g. Measurement errors can be divided into two components, random error and systematic error, random error is always present in a measurement. It is caused by inherently unpredictable fluctuations in the readings of a measurement apparatus or in the interpretation of the instrumental reading. Random errors show up as different results for ostensibly the same repeated measurement and they can be estimated by comparing multiple measurements, and reduced by averaging multiple measurements
Random error
–
A scientist adjusts an atomic force microscopy (AFM) device, which is used to measure surface characteristics and imaging for semiconductor wafers, lithography masks, magnetic media, CDs/DVDs, biomaterials, optics, among a multitude of other samples.
45.
Average
–
In colloquial language, an average is the sum of a list of numbers divided by the number of numbers in the list. In mathematics and statistics, this would be called the arithmetic mean, in statistics, mean, median, and mode are all known as measures of central tendency. The most common type of average is the arithmetic mean, one may find that A = /2 =5. Switching the order of 2 and 8 to read 8 and 2 does not change the value obtained for A. The mean 5 is not less than the minimum 2 nor greater than the maximum 8. If we increase the number of terms in the list to 2,8, and 11, one finds that A = /3 =7. Along with the arithmetic mean above, the mean and the harmonic mean are known collectively as the Pythagorean means. The geometric mean of n numbers is obtained by multiplying them all together. See Inequality of arithmetic and geometric means, thus for the above harmonic mean example, AM =50, GM ≈49, and HM =48 km/h. The mode, the median, and the mid-range are often used in addition to the mean as estimates of central tendency in descriptive statistics, the most frequently occurring number in a list is called the mode. For example, the mode of the list is 3 and it may happen that there are two or more numbers which occur equally often and more often than any other number. In this case there is no agreed definition of mode, some authors say they are all modes and some say there is no mode. The median is the number of the group when they are ranked in order. Thus to find the median, order the list according to its elements magnitude, if exactly one value is left, it is the median, if two values, the median is the arithmetic mean of these two. This method takes the list 1,7,3,13, then the 1 and 13 are removed to obtain the list 3,7. Since there are two elements in this remaining list, the median is their arithmetic mean, /2 =5, the table of mathematical symbols explains the symbols used below. Other more sophisticated averages are, trimean, trimedian, and normalized mean, one can create ones own average metric using the generalized f-mean, y = f −1 where f is any invertible function. The harmonic mean is an example of this using f = 1/x, however, this method for generating means is not general enough to capture all averages
Average
–
Comparison of
arithmetic mean,
median and
mode of two
log-normal distributions with different
skewness.
46.
Electromagnet
–
An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. The magnetic field disappears when the current is turned off, electromagnets usually consist of insulated wire wound into a coil. A current through the wire creates a field which is concentrated in the hole in the center of the coil. The main advantage of an electromagnet over a permanent magnet is that the field can be quickly changed by controlling the amount of electric current in the winding. However, unlike a permanent magnet that needs no power, an electromagnet requires a supply of current to maintain the magnetic field. Electromagnets are also employed in industry for picking up and moving heavy objects such as scrap iron. Danish scientist Hans Christian Ørsted discovered in 1820 that electric currents create magnetic fields, british scientist William Sturgeon invented the electromagnet in 1824. His first electromagnet was a piece of iron that was wrapped with about 18 turns of bare copper wire. The iron was varnished to insulate it from the windings, when a current was passed through the coil, the iron became magnetized and attracted other pieces of iron, when the current was stopped, it lost magnetization. Sturgeon displayed its power by showing that although it only weighed seven ounces, however, Sturgeons magnets were weak because the uninsulated wire he used could only be wrapped in a single spaced out layer around the core, limiting the number of turns. Beginning in 1830, US scientist Joseph Henry systematically improved and popularized the electromagnet, the first major use for electromagnets was in telegraph sounders. A portative electromagnet is one designed to just hold material in place, a tractive electromagnet applies a force and moves something. The solenoid is a coil of wire, and the plunger is made of a such as soft iron. Applying a current to the solenoid applies a force to the plunger, the plunger stops moving when the forces upon it are balanced. For example, the forces are balanced when the plunger is centered in the solenoid, the maximum uniform pull happens when one end of the plunger is at the middle of the solenoid. For units using inches, pounds force, and amperes with long, slender, solenoids, for example, a 12-inch long coil with a long plunger of 1-square inch cross section and 11,200 ampere-turns had a maximum pull of 8.75 pounds. The maximum pull is increased when a stop is inserted into the solenoid. The stop becomes a magnet that will attract the plunger, it adds little to the pull when the plunger is far away
Electromagnet
–
Industrial electromagnet lifting scrap iron, 1914
Electromagnet
–
A simple electromagnet consisting of a coil of insulated wire wrapped around an iron core. A core of ferromagnetic material like iron serves to increase the magnetic field created. The strength of magnetic field generated is proportional to the amount of current through the winding.
Electromagnet
–
Laboratory electromagnet. Produces 2 T field with 20 A current.
Electromagnet
–
Magnet in a
mass spectrometer
47.
Resonance
–
In physics, resonance is a phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at a specific preferential frequency. Frequencies at which the amplitude is a relative maximum are known as the systems resonant frequencies or resonance frequencies. At resonant frequencies, small periodic driving forces have the ability to produce large amplitude oscillations, Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes. However, there are some losses from cycle to cycle, called damping, when damping is small, the resonant frequency is approximately equal to the natural frequency of the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies, resonant systems can be used to generate vibrations of a specific frequency, or pick out specific frequencies from a complex vibration containing many frequencies. Resonance occurs widely in nature, and is exploited in many manmade devices and it is the mechanism by which virtually all sine waves and vibrations are generated. Many sounds we hear, such as when hard objects of metal, glass, light and other short wavelength electromagnetic radiation is produced by resonance on an atomic scale, such as electrons in atoms. A familiar example is a swing, which acts as a pendulum. Pushing a person in a swing in time with the interval of the swing makes the swing go higher and higher. This is because the energy the swing absorbs is maximized when the match the swings natural oscillations. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings, trains, avoiding resonance disasters is a major concern in every building, tower, and bridge construction project. As a countermeasure, shock mounts can be installed to absorb resonant frequencies, the Taipei 101 building relies on a 660-tonne pendulum —a tuned mass damper—to cancel resonance. Furthermore, the structure is designed to resonate at a frequency that does not typically occur, buildings in seismic zones are often constructed to take into account the oscillating frequencies of expected ground motion. Clocks keep time by mechanical resonance in a wheel, pendulum. The cadence of runners has been hypothesized to be energetically favorable due to resonance between the energy stored in the lower limb and the mass of the runner. Acoustic resonance is a branch of mechanical resonance that is concerned with the mechanical vibrations across the range of human hearing. Like mechanical resonance, acoustic resonance can result in failure of the object at resonance. The classic example of this is breaking a glass with sound at the precise resonant frequency of the glass
Resonance
–
Pushing a person in a
swing is a common example of resonance. The loaded swing, a
pendulum, has a
natural frequency of oscillation, its resonant frequency, and resists being pushed at a faster or slower rate.
Resonance
–
NMR Magnet at HWB-NMR, Birmingham, UK. In its strong 21.2-
tesla field, the proton resonance is at 900 MHz.
48.
Stroboscope
–
A stroboscope also known as a strobe, is an instrument used to make a cyclically moving object appear to be slow-moving, or stationary. It consists of either a disk with slots or holes or a lamp such as a flashtube which produces brief repetitive flashes of light. Usually the rate of the stroboscope is adjustable to different frequencies, when a rotating or vibrating object is observed with the stroboscope at its vibration frequency, it appears stationary. Thus stroboscopes are used to measure frequency. The principle is used for the study of rotating, reciprocating, oscillating or vibrating objects, machine parts and vibrating strings are common examples. A stroboscope used to set the timing of internal combustion engines is called a timing light. In its simplest mechanical form, a cylinder with evenly spaced holes or slots placed in the line of sight between the observer and the moving object. The observer looks through the holes/slots on the near and far side at the same time, when the holes/slots are aligned on opposite sides, the object is visible to the observer. Alternately, a single moving hole or slot can be used with a hole or slot. The stationary hole or slot limits the light to a single viewing path, viewing through a single line of holes/slots does not work, since the holes/slots appear to just sweep across the object without a strobe effect. The rotational speed is adjusted so that it becomes synchronised with the movement of the observed system, the illusion is caused by temporal aliasing, commonly known as the stroboscopic effect. In electronic versions, the disc is replaced by a lamp capable of emitting brief. Typically a gas-discharge or solid-state lamp is used, because they are capable of emitting light nearly instantly when power is applied, by comparison, incandescent lamps have a brief warm-up when energized, followed by a cool-down period when power is removed. These delays result in smearing and blurring of detail of objects partially illuminated during the warm-up, for most applications, incandescent lamps are too slow for clear stroboscopic effects. Yet when operated from an AC source they are mostly fast enough to cause audible hum on optical audio playback such as on film projection, xenon flash lamps are used for medium- and high-intensity strobe applications. Sufficiently rapid or bright flashing may require active cooling such as forced-air or water cooling to prevent the xenon flash lamp from melting. Joseph Plateau of Belgium is generally credited with the invention of the stroboscope in 1832, Plateau called his device the Phenakistoscope. There was a simultaneous and independent invention of the device by the Austrian Simon Ritter von Stampfer, which he named the Stroboscope, the etymology is from the Greek words στρόβος - strobos, meaning whirlpool and σκοπεῖν - skopein, meaning to look at
Stroboscope
–
A bouncing ball captured with a stroboscopic flash at 25 images per second.
Stroboscope
–
1540 Strobolume, a professional grade stroboscope produced by General Radio
Stroboscope
–
Close-up view of the 1540 Strobolume control box
49.
Strobe light
–
A strobe light or stroboscopic lamp, commonly called a strobe, is a device used to produce regular flashes of light. It is one of a number of devices that can be used as a stroboscope, the word originated from the Greek strobos, meaning act of whirling. A typical commercial strobe light has an energy in the region of 10 to 150 joules. Larger strobe lights can be used in “continuous” mode, producing extremely intense illumination, the light source is commonly a xenon flash lamp, or flashtube, which has a complex spectrum and a color temperature of approximately 5,600 kelvins. To obtain colored light, colored gels may be used, strobe lights usually use flashtubes with energy supplied from a capacitor, an energy storage device much like a battery, but capable of charging and releasing energy much faster. Recently, some lights have been found to use rectified mains electricity. In a capacitor-based strobe light, the capacitor is charged up to around 300 V, once the capacitor has been charged, a small amount of power is diverted into a trigger transformer, a small transformer with a high turns ratio. This generates the weak but high voltage required to ionize the xenon gas in a flash tube. An arc is created inside the tube, which acts as a bridge for the much bigger pulse to flow down later, arcs present almost a direct short circuit, allowing the capacitors to quickly release their energy into the arc. This rapidly heats the gas, creating an extremely bright plasma discharge. A strobe without a storage device simply discharges mains voltages across the tube once its fired. This type of strobe requires no charging time and allows for much quicker flash rates, such strobes require a form of current limiting, because as mentioned above, an arc acts as a kind of short circuit. Individual strobe flashes typically only last around 200 microseconds, but can be sustained for greater or lesser periods of time depending on the intended use. Since this stop is only apparent, a point on the rotating body will either appear to move backward or forward, or not move. If the flash occurs equal to the period of rotation the marked point will appear to not move. Any non integer flash setting will make the mark appear to move forward or backward, strobe lighting has also been used to see the movements of the vocal cords in slow motion during speech, a procedure known as video-stroboscopy. A common use of a flash is to optimize a car engines efficiency at a certain rotational period by directing the strobe-light towards a mark on the flywheel on the engines main axle. The strobe-light tool for such ignition timing is called a timing light, other applications are in alarm systems, emergency vehicle lighting, theatrical lighting, and as high-visibility running lights
Strobe light
–
Strobe light
50.
Frequency counter
–
A frequency counter is an electronic instrument, or component of one, that is used for measuring frequency. Frequency counters usually measure the number of oscillations or pulses per second in an electronic signal. Such an instrument is referred to as a cymometer, particularly one of Chinese manufacture. Most frequency counters work by using a counter which accumulates the number of events occurring within a period of time. After a preset period known as the time, the value in the counter is transferred to a display. The internal oscillator which provides the signals is called the timebase. If the event to be counted is already in electronic form, more complex signals may need some conditioning to make them suitable for counting. Most general purpose frequency counters will include some form of amplifier, DSP technology, sensitivity control and hysteresis are other techniques to improve performance. Other types of events that are not inherently electronic in nature will need to be converted using some form of transducer. For example, an event could be arranged to interrupt a light beam. Frequency counters designed for radio frequencies are also common and operate on the principles as lower frequency counters. Often, they have more range before they overflow, for very high frequencies, many designs use a high-speed prescaler to bring the signal frequency down to a point where normal digital circuitry can operate. The displays on such instruments take this into account so they still display the correct value, microwave frequency counters can currently measure frequencies up to almost 56 GHz. The accuracy of a counter is strongly dependent on the stability of its timebase. A timebase is very delicate like the hands of a watch and this can make a frequency reading, when referenced to the timebase, seem higher or lower than the actual value. For higher accuracy measurements, a frequency reference tied to a very high stability oscillator such as a GPS disciplined rubidium oscillator may be used. Where the frequency does not need to be known to such a degree of accuracy. It is also possible to measure using the same techniques in software in an embedded system
Frequency counter
–
Systron-Donner frequency counter from 1973 with
Nixie tube display
Frequency counter
–
Fluke PM6685R frequency counter