1.
Physics
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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
2.
Wave
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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
3.
Amplitude
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The amplitude of a periodic variable is a measure of its change over a single period. There are various definitions of amplitude, which are all functions of the magnitude of the difference between the extreme values. In older texts the phase is called the amplitude. Peak-to-peak amplitude is the change between peak and trough, with appropriate circuitry, peak-to-peak amplitudes of electric oscillations can be measured by meters or by viewing the waveform on an oscilloscope. Peak-to-peak is a measurement on an oscilloscope, the peaks of the waveform being easily identified and measured against the graticule. This remains a common way of specifying amplitude, but sometimes other measures of amplitude are more appropriate. In audio system measurements, telecommunications and other areas where the measurand is a signal that swings above and below a value but is not sinusoidal. If the reference is zero, this is the absolute value of the signal, if the reference is a mean value. Semi-amplitude means half the peak-to-peak amplitude, some scientists use amplitude or peak amplitude to mean semi-amplitude, that is, half the peak-to-peak amplitude. It is the most widely used measure of orbital wobble in astronomy, the RMS of the AC waveform. For complicated waveforms, especially non-repeating signals like noise, the RMS amplitude is used because it is both unambiguous and has physical significance. For example, the power transmitted by an acoustic or electromagnetic wave or by an electrical signal is proportional to the square of the RMS amplitude. For alternating current electric power, the practice is to specify RMS values of a sinusoidal waveform. One property of root mean square voltages and currents is that they produce the same heating effect as direct current in a given resistance, the peak-to-peak value is used, for example, when choosing rectifiers for power supplies, or when estimating the maximum voltage that insulation must withstand. Some common voltmeters are calibrated for RMS amplitude, but respond to the value of a rectified waveform. Many digital voltmeters and all moving coil meters are in this category, the RMS calibration is only correct for a sine wave input since the ratio between peak, average and RMS values is dependent on waveform. If the wave shape being measured is greatly different from a sine wave, true RMS-responding meters were used in radio frequency measurements, where instruments measured the heating effect in a resistor to measure current. The advent of microprocessor controlled meters capable of calculating RMS by sampling the waveform has made true RMS measurement commonplace
4.
Phase (waves)
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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
5.
Node (physics)
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A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the length of the vibrating string. The opposite of a node is an anti-node, a point where the amplitude of the wave is a maximum. These occur midway between the nodes, standing waves result when two sinusoidal wave trains of the same frequency are moving in opposite directions in the same space and interfere with each other. In a standing wave the nodes are a series of locations at equally spaced intervals where the amplitude is zero. At these points the two waves add with opposite phase and cancel each other out and they occur at intervals of half a wavelength. Midway between each pair of nodes are locations where the amplitude is maximum, at these points the two waves add with the same phase and reinforce each other. In cases where the two opposite wave trains are not the amplitude, they do not cancel perfectly, so the amplitude of the standing wave at the nodes is not zero. This occurs when the reflection at the boundary is imperfect and this is indicated by a finite standing wave ratio, the ratio of the amplitude of the wave at the antinode to the amplitude at the node. These can be visible by sprinkling sand on the surface. In transmission lines a voltage node is a current antinode, in this type the derivative of the waves amplitude is forced to zero at the boundary. So there is a maximum at the boundary, the first node occurs a quarter wavelength from the end. A sound wave consists of alternating cycles of compression and expansion of the wave medium, during compression, the molecules of the medium are forced together, resulting in the increased pressure and density. During expansion the molecules are forced apart, resulting in the decreased pressure, the number of nodes in a specified length is directly proportional to the frequency of the wave. Occasionally on a guitar, violin, or other stringed instrument, when the finger is placed on top of the string at a certain point, but does not push the string all the way down to the fretboard, a third node is created and a harmonic is sounded. During normal play when the frets are used, the harmonics are always present, with the artificial node method, the overtone is louder and the fundamental tone is quieter. If the finger is placed at the midpoint of the string, the first overtone is heard, when two additional nodes divide the string into thirds, this creates an octave and a perfect fifth
6.
Antinode
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A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the length of the vibrating string. The opposite of a node is an anti-node, a point where the amplitude of the wave is a maximum. These occur midway between the nodes, standing waves result when two sinusoidal wave trains of the same frequency are moving in opposite directions in the same space and interfere with each other. In a standing wave the nodes are a series of locations at equally spaced intervals where the amplitude is zero. At these points the two waves add with opposite phase and cancel each other out and they occur at intervals of half a wavelength. Midway between each pair of nodes are locations where the amplitude is maximum, at these points the two waves add with the same phase and reinforce each other. In cases where the two opposite wave trains are not the amplitude, they do not cancel perfectly, so the amplitude of the standing wave at the nodes is not zero. This occurs when the reflection at the boundary is imperfect and this is indicated by a finite standing wave ratio, the ratio of the amplitude of the wave at the antinode to the amplitude at the node. These can be visible by sprinkling sand on the surface. In transmission lines a voltage node is a current antinode, in this type the derivative of the waves amplitude is forced to zero at the boundary. So there is a maximum at the boundary, the first node occurs a quarter wavelength from the end. A sound wave consists of alternating cycles of compression and expansion of the wave medium, during compression, the molecules of the medium are forced together, resulting in the increased pressure and density. During expansion the molecules are forced apart, resulting in the decreased pressure, the number of nodes in a specified length is directly proportional to the frequency of the wave. Occasionally on a guitar, violin, or other stringed instrument, when the finger is placed on top of the string at a certain point, but does not push the string all the way down to the fretboard, a third node is created and a harmonic is sounded. During normal play when the frets are used, the harmonics are always present, with the artificial node method, the overtone is louder and the fundamental tone is quieter. If the finger is placed at the midpoint of the string, the first overtone is heard, when two additional nodes divide the string into thirds, this creates an octave and a perfect fifth
7.
Michael Faraday
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Michael Faraday FRS was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, diamagnetism, although Faraday received little formal education, he was one of the most influential scientists in history. It was by his research on the field around a conductor carrying a direct current that Faraday established the basis for the concept of the electromagnetic field in physics. Faraday also established that magnetism could affect rays of light and that there was a relationship between the two phenomena. He similarly discovered the principles of induction and diamagnetism. His inventions of electromagnetic rotary devices formed the foundation of electric motor technology, Faraday ultimately became the first and foremost Fullerian Professor of Chemistry at the Royal Institution of Great Britain, a lifetime position. James Clerk Maxwell took the work of Faraday and others and summarized it in a set of equations which is accepted as the basis of all theories of electromagnetic phenomena. The SI unit of capacitance is named in his honour, the farad, albert Einstein kept a picture of Faraday on his study wall, alongside pictures of Isaac Newton and James Clerk Maxwell. Faraday was born in Newington Butts, which is now part of the London Borough of Southwark but was then a part of Surrey. His family was not well off and his father, James, was a member of the Glassite sect of Christianity. James Faraday moved his wife and two children to London during the winter of 1790 from Outhgill in Westmorland, where he had been an apprentice to the village blacksmith, Michael was born in the autumn of that year. The young Michael Faraday, who was the third of four children, at the age of 14 he became an apprentice to George Riebau, a local bookbinder and bookseller in Blandford Street. During his seven-year apprenticeship Faraday read many books, including Isaac Wattss The Improvement of the Mind, at this time he also developed an interest in science, especially in electricity. Faraday was particularly inspired by the book Conversations on Chemistry by Jane Marcet, many of the tickets for these lectures were given to Faraday by William Dance, who was one of the founders of the Royal Philharmonic Society. Faraday subsequently sent Davy a 300-page book based on notes that he had taken during these lectures, davys reply was immediate, kind, and favourable. In 1813, when Davy damaged his eyesight in an accident with nitrogen trichloride, very soon Davy entrusted Faraday with the preparation of nitrogen trichloride samples, and they both were injured in an explosion of this very sensitive substance. In the class-based English society of the time, Faraday was not considered a gentleman, Faraday was forced to fill the role of valet as well as assistant throughout the trip. Davys wife, Jane Apreece, refused to treat Faraday as an equal, the trip did, however, give him access to the scientific elite of Europe and exposed him to a host of stimulating ideas
8.
Interference (wave propagation)
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In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves or matter waves. If a crest of a wave meets a crest of wave of the same frequency at the same point. If a crest of one wave meets a trough of another wave, constructive interference occurs when the phase difference between the waves is an even multiple of π, whereas destructive interference occurs when the difference is an odd multiple of π. If the difference between the phases is intermediate between two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values. Consider, for example, what happens when two identical stones are dropped into a pool of water at different locations. Each stone generates a circular wave propagating outwards from the point where the stone was dropped, when the two waves overlap, the net displacement at a particular point is the sum of the displacements of the individual waves. At some points, these will be in phase, and will produce a maximum displacement, in other places, the waves will be in anti-phase, and there will be no net displacement at these points. Thus, parts of the surface will be stationary—these are seen in the figure above, prime examples of light interference are the famous Double-slit experiment, laser speckle, optical thin layers and films and interferometers. Dark areas in the slit are not available to the photons. Thin films also behave in a quantum manner, the above can be demonstrated in one dimension by deriving the formula for the sum of two waves. Suppose a second wave of the frequency and amplitude but with a different phase is also traveling to the right W2 = A cos where ϕ is the phase difference between the waves in radians. Constructive interference, If the phase difference is a multiple of pi. Interference is essentially a redistribution process. The energy which is lost at the interference is regained at the constructive interference. One wave is travelling horizontally, and the other is travelling downwards at an angle θ to the first wave, assuming that the two waves are in phase at the point B, then the relative phase changes along the x-axis. Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. Thus, a fringe pattern is produced, where the separation of the maxima is d f = λ sin θ
9.
Resonance
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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
10.
Resonator
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The oscillations in a resonator can be either electromagnetic or mechanical. Resonators are used to generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones, another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of very precise frequency. A cavity resonator is one in which waves exist in a space inside the device. Acoustic cavity resonators, in sound is produced by air vibrating in a cavity with one opening, are known as Helmholtz resonators. A physical system can have as many resonant frequencies as it has degrees of freedom, systems with one degree of freedom, such as a mass on a spring, pendulums, balance wheels, and LC tuned circuits have one resonant frequency. Systems with two degrees of freedom, such as coupled pendulums and resonant transformers can have two resonant frequencies, a crystal lattice composed of N atoms bound together can have N resonant frequencies. As the number of coupled harmonic oscillators grows, the time it takes to transfer energy from one to the next becomes significant, the vibrations in them begin to travel through the coupled harmonic oscillators in waves, from one oscillator to the next. The term resonator is most often used for an object in which vibrations travel as waves, at an approximately constant velocity, bouncing back. The material of the resonator, through which the waves flow, therefore, they can have millions of resonant frequencies, although only a few may be used in practical resonators. The oppositely moving waves interfere with other, and at its resonant frequencies reinforce each other to create a pattern of standing waves in the resonator. If the distance between the sides is d, the length of a trip is 2 d. To cause resonance, the phase of a sinusoidal wave after a round trip must be equal to the initial phase so the waves self-reinforce. The above analysis assumes the medium inside the resonator is homogeneous, so the waves travel at a constant speed, and they are then called overtones instead of harmonics. There may be several such series of resonant frequencies in a single resonator, an electrical circuit composed of discrete components can act as a resonator when both an inductor and capacitor are included. Oscillations are limited by the inclusion of resistance, either via a specific resistor component, such resonant circuits are also called RLC circuits after the circuit symbols for the components. A distributed-parameter resonator has capacitance, inductance, and resistance that cannot be isolated into separate lumped capacitors, inductors, an example of this, much used in filtering, is the helical resonator. A single layer coil that is used as a secondary or tertiary winding in a Tesla coil or magnifying transmitter is also a distributed resonator
11.
Resonant frequency
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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
12.
Average
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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
13.
Flux
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Flux is either of two separate simple and ubiquitous concepts throughout physics and applied mathematics. Within a discipline, the term is used consistently. Both concepts have mathematical rigor, enabling comparison of the underlying math when the terminology is unclear, for transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In electromagnetism, flux is a quantity, defined as the surface integral of the component of a vector field perpendicular to the surface at each point. As will be clear, the easiest way to relate the two concepts is that the surface integral of a flux according to the first definition is a flux according to the second definition. The word flux comes from Latin, fluxus means flow, as fluxion, this term was introduced into differential calculus by Isaac Newton. One could argue, based on the work of James Clerk Maxwell, the specific quote from Maxwell is, In the case of fluxes, we have to take the integral, over a surface, of the flux through every element of the surface. The result of operation is called the surface integral of the flux. It represents the quantity which passes through the surface, according to the first definition, flux may be a single vector, or flux may be a vector field / function of position. In the latter case flux can readily be integrated over a surface, by contrast, according to the second definition, flux is the integral over a surface, it makes no sense to integrate a second-definition flux for one would be integrating over a surface twice. Thus, Maxwells quote only makes sense if flux is being used according to the first definition and this is ironic because Maxwell was one of the major developers of what we now call electric flux and magnetic flux according to the second definition. This implies that Maxwell conceived as these fields as flows/fluxes of some sort, given a flux according to the second definition, the corresponding flux density, if that term is used, refers to its derivative along the surface that was integrated. By the Fundamental theorem of calculus, the flux density is a flux according to the first definition. Given a current such as electric current—charge per time, current density would also be a flux according to the first definition—charge per time per area. Concrete fluxes in the rest of this article will be used in accordance to their acceptance in the literature. In transport phenomena, flux is defined as the rate of flow of a property per unit area, the area is of the surface the property is flowing through or across. Here are 3 definitions in increasing order of complexity, each is a special case of the following. In all cases the frequent symbol j, is used for flux, q for the quantity that flows, t for time
14.
Lee waves
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In meteorology, lee waves are atmospheric stationary waves. The most common form is mountain waves, which are atmospheric internal gravity waves and these were discovered in 1933 by two German glider pilots, Hans Deutschmann and Wolf Hirth, above the Krkonoše. They can also be caused by the wind blowing over an escarpment or plateau. The vertical motion forces periodic changes in speed and direction of the air within this air current and they always occur in groups on the lee side of the terrain that triggers them. Usually a turbulent vortex, with its axis of rotation parallel to the range, is generated around the first trough. The strongest lee waves are produced when the lapse rate shows a layer above the obstruction, with an unstable layer above. Lee waves are a form of gravity waves produced when stably stratified flow is forced over an obstacle. This disturbance elevates air parcels above their level of neutral buoyancy, oscillations tilted off the vertical axis at an angle of ϕ will occur at a lower frequency of N cos ϕ. These air parcel oscillations occur in concert, parallel to the wave fronts and these wave fronts represent extrema in the perturbed pressure field, while the areas between wave fronts represent extrema in the perturbed buoyancy field. Energy is transmitted along the fronts, which is the direction of the wave group velocity. In contrast, the propagation of the waves points perpendicular to energy transmission. Waves may also form in dry air without cloud markers, Wave clouds do not move downwind as clouds usually do, but remain fixed in position relative to the obstruction that forms them. Around the crest of the wave, adiabatic expansion cooling can form a cloud in shape of a lens, multiple lenticular clouds can be stacked on top of each other if there are alternating layers of relatively dry and moist air aloft. The rotor may generate cumulus or cumulus fractus in its upwelling portion, the rotor cloud looks like a line of cumulus. It forms on the lee side and parallel to the ridge line and its base is near the height of the mountain peak, though the top can extend well above the peak and can merge with the lenticular clouds above. Rotor clouds have ragged edges and are dangerously turbulent. A foehn wall cloud may exist at the lee side of the mountains, a pileus or cap cloud, similar to a lenticular cloud, may form above the mountain or cumulus cloud generating the wave. Adiabatic compression heating in the trough of each wave oscillation may also evaporate cumulus or stratus clouds in the airmass, lee waves provide a possibility for gliders to gain altitude or fly long distances when soaring
15.
Gliding
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The word soaring is also used for the sport. Gliding as a sport began in the 1920s, initially the objective was to increase the duration of flights but soon pilots attempted cross-country flights away from the place of launch. Improvements in aerodynamics and in the understanding of phenomena have allowed greater distances at higher average speeds. Long distances are now flown using any of the sources of rising air, ridge lift, thermals. When conditions are favourable, experienced pilots can now fly hundreds of kilometres before returning to their home airfields, some competitive pilots fly in races around pre-defined courses. These gliding competitions test pilots abilities to make best use of weather conditions as well as their flying skills. Local and national competitions are organized in countries, and there are biennial World Gliding Championships. Techniques to maximize a gliders speed around the task in a competition have been developed, including the optimum speed to fly, navigation using GPS. If the weather deteriorates pilots are unable to complete a cross-country flight. Consequently, they may need to land elsewhere, perhaps in a field, powered-aircraft and winches are the two most common means of launching gliders. These and other methods require assistance and facilities such as airfields, tugs. These are usually provided by gliding clubs who also train new pilots, the development of heavier-than-air flight in the half century between Sir George Cayleys coachman in 1853 and the Wright brothers in 1903 mainly involved gliders. With the active support of the German government, there were 50,000 glider pilots by 1937, the first German gliding competition was held at the Wasserkuppe in 1920, organized by Oskar Ursinus. The best flight lasted two minutes and set a distance record of 2 kilometres. Within ten years, it had become an event in which the achieved durations. In 1931, Gunther Grönhoff flew 272 kilometres on the front of a storm from Munich to Kadaň in Western Czechoslovakia, in the 1930s, gliding spread to many other countries. In the 1936 Summer Olympics in Berlin gliding was a demonstration sport, a glider, the Olympia, was developed in Germany for the event, but World War II intervened. By 1939 the major gliding records were held by Russians, including a record of 748 kilometres
16.
Hydraulic jump
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A hydraulic jump is a phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, in an open channel flow, this manifests as the fast flow rapidly slowing and piling up on top of itself similar to how a shockwave forms. The phenomenon is dependent upon the fluid speed. If the initial speed of the fluid is below the critical speed, for initial flow speeds which are not significantly above the critical speed, the transition appears as an undulating wave. As the initial flow speed increases further, the transition becomes more abrupt, until at high enough speeds, when this happens, the jump can be accompanied by violent turbulence, eddying, air entrainment, and surface undulations, or waves. There are two main manifestations of hydraulic jumps and historically different terminology has been used for each, the different manifestations are, The stationary hydraulic jump – rapidly flowing water transitions in a stationary jump to slowly moving water as shown in Figures 1 and 2. The tidal bore – a wall or undulating wave of water moves upstream against water flowing downstream as shown in Figures 3 and 4. If considered from a frame of reference which moves with the wave front, a related case is a cascade – a wall or undulating wave of water moves downstream overtaking a shallower downstream flow of water as shown in Figure 5. If considered from a frame of reference which moves with the wave front and these phenomena are addressed in an extensive literature from a number of technical viewpoints. Hydraulic jumps can be seen in both a form, which is known as a hydraulic jump, and a dynamic or moving form. They can be described using the same approaches and are simply variants of a single phenomenon. A tidal bore is a jump which occurs when the incoming tide forms a wave of water that travel up a river or narrow bay against the direction of the current. Figure 3 shows a tidal bore with the common to shallow upstream water – a large elevation difference is observed. Figure 4 shows a tidal bore with the common to deep upstream water – a small elevation difference is observed. In both cases the tidal wave moves at the characteristic of waves in water of the depth found immediately behind the wave front. A key feature of tidal bores and positive surges is the turbulent mixing induced by the passage of the bore front. Another variation of the hydraulic jump is the cascade. In the cascade, a series of waves or undulating waves of water moves downstream overtaking a shallower downstream flow of water
17.
Rapid
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Rapids are sections of a river where the river bed has a relatively steep gradient, causing an increase in water velocity and turbulence. Rapids are hydrological features between a run and a cascade, rapids are characterised by the river becoming shallower with some rocks exposed above the flow surface. As flowing water splashes over and around the rocks, air bubbles become mixed in with it and portions of the surface acquire a white colour, forming what is called whitewater. Rapids occur where the bed material is resistant to the erosive power of the stream in comparison with the bed downstream of the rapids. Very young streams flowing across solid rock may be rapids for much of their length, rapids cause water aeration of the stream or river resulting in better water quality. Rapids are categorized in classes, generally running from I to VI, a Class 5 rapid may be categorized as Class 5. 1-5.9. While class I rapids are easy to negotiate and require no maneuvering, river rafting sports is carried out where many rapids are there in the course
18.
Saltstraumen
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Saltstraumen is a small strait with one of the strongest tidal currents in the world. It is located in the municipality of Bodø in Nordland county and it is located about 10 kilometres southeast of the town of Bodø. The narrow channel connects the outer Saltfjorden to the large Skjerstad Fjord between the islands of Straumøya and Knaplundsøya, the Saltstraumen Bridge on Norwegian County Road 17 crosses Saltstraumen. Saltstraumen has one of the strongest tidal currents in the world, up to 400,000,000 cubic metres of seawater forces its way through a 3-kilometre long and 150-metre wide strait every six hours. Vortices known as whirlpools or maelstroms up to 10 metres in diameter and 5 metres in depth are formed when the current is at its strongest, Saltstraumen has existed for about two to three thousand years. Before that, the area was different due to post-glacial rebound, the current is created when the tide tries to fill Skjerstad Fjord. The height difference between the sea level and the fjord inside can be up to 1 metre, when the current turns, there is a period when the strait is navigable. The above account of the Saltstraumen is rather different than what The Norwegian Pilot reports, the Pilot’s description of the normal current is based on the time of the high tide at Bodø. The greatest southbound current occurs about one and a quarter hours before Bodø high tide, the speed of the current has a broad maximum being greater than six knots from three hours before Bodø high tide until half an hour after Bodø high tide. The greatest northbound current occurs about four and a half hours after Bodø high tide, when the outflowing current reaches over eight knots. The speed of this current also has a broad maximum being above six knots from two hours and forty minutes after Bodø high tide until five and a half hours before the next Bodø high tide. The behavior of the current may differ from normal due to winds or when more fresh water than usual is entering into the fjord from the surrounding mountains. Saltstraumen is popular with anglers, due to its abundance of such as saithe, cod, wolffish, rose fish. Coalfish is a specialty of the area, the largest documented coalfish of 22.7 kilograms was caught in Saltstraumen on a fishing rod. The first element is the name of the district Salten and the last element is the form of straum. The remains of a 10, 000-year-old hunter settlement in the area are the oldest known traces of settlement in Bodø. These hunters lived on the edge of the ice, attracted by the abundance of fish caused by the strong currents
19.
River surfing
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River surfing is the sport of surfing either standing waves or tidal bores in rivers. Claims for its origins include a 1955 ride of 1.5 miles along the bore of the River Severn. River surfing on standing waves has been documented as far back as the early-1970s in Munich, Germany, today offering the worlds largest urban surfing spot. In this type of surfing, the wave is stationary on the river, caused by a high volume of water constricted by flowing over a rock. It is a form of hydraulic jump, a river surfer can face up-stream and catch this wave and have the feeling of traveling fast over water while not actually moving. Despite being many hundreds of kilometres from the nearest ocean, Munich has a reputation as a surfing hotspot, the Bavarian capital is the birthplace of river surfing. The city has been the center of surfboard riding on a stationary wave since the early-1970s, up to 100 surfers daily hit the waves in the citys Englischer Garten, the largest urban park in the world. An annual surfing competition is held on the standing wave, Munich has produced the best river surfers and was the first location that created a true surfing community around an inland river wave. The scene has around 1,000 active surfers, while 10,000 in Munich will have tried it at some point, on Austrias river Mur in Graz, river surfing is a regular on two waves built for surfing in 2001 and rebuilt in 2004 by KanuClub Graz. Near Salzburg in the Alm Canal there is a custom built surf wave, norway has several river waves, amongst the most famous are Bulken in Voss and an unnamed river wave in Sarpsborg. Oslo are in the phase of building a potential, artificial river wave in their main city river Akerselva. The Limmat in Zürich does not have any standing waves but is fast-flowing, local surfers have developed a pulley system known as upstream surfing which allows surfers to surf the river. The Habitat 67 standing wave in the Lachine Rapids in Montreal, corran Addison, an Olympic kayaker and three-time world freestyle kayak champion, was the first to surf the Habitat wave in 2002. His river-surfing school, Imagine Surfboards, has taught 3,500 students since 2005, a second Montreal river-surfing school, KSF, has hosted 1,500 students a year since 2003. From fewer than 10 original surfers, it is estimated that the current of participants numbers around 500, jackson Hole, Wyoming is known as the most famous river surfing community in the US. The first documented cases of surfing on the Snake River occurred in the late 1970s, the wave known as Lunch Counter is a standing wave that churns during times of snow runoff in the months between May and August each year. This wave is highly active during these months and the continues to grow as a surf destination. Pueblo, Colorado has also become a river surfing city, a kayak park was in built 2005 near downtown Pueblo and locals have been surfing features 3,4, and 7 ever since
20.
Fundamental frequency
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The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the frequency is the lowest frequency sinusoidal in the sum. In some contexts, the fundamental is usually abbreviated as f0, in other contexts, it is more common to abbreviate it as f1, the first harmonic. All sinusoidal and many non-sinusoidal waveforms are periodic, which is to say they repeat exactly over time. The period of a waveform is the T for which the equation is true. This means that this equation and a definition of the values over any interval of length T is all that is required to describe the waveform completely. Every waveform may be described using any multiple of this period, there exists a smallest period over which the function may be described completely and this period is the fundamental period. The fundamental frequency is defined as its reciprocal, f 0 =1 T Since the period is measured in units of time, when the time units are seconds, the frequency is in s −1, also known as Hertz. For a tube of length L with one end closed and the end open the wavelength of the fundamental harmonic is 4 L. If the ends of the tube are now both closed or both opened as in the last two animations, the wavelength of the fundamental harmonic becomes 2 L. By the same method as above, the frequency is found to be f 0 = v 2 L. At 20 °C the speed of sound in air is 343 m/s and this speed is temperature dependent and does increase at a rate of 0.6 m/s for each degree Celsius increase in temperature. The fundamental may be created by vibration over the length of a string or air column. The fundamental is one of the harmonics, a harmonic is any member of the harmonic series, an ideal set of frequencies that are positive integer multiples of a common fundamental frequency. The reason a fundamental is also considered a harmonic is because it is 1 times itself, the fundamental is the frequency at which the entire wave vibrates. Overtones are other components present at frequencies above the fundamental. All of the components that make up the total waveform, including the fundamental
21.
Overtone
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An overtone is any frequency greater than the fundamental frequency of a sound. Using the model of Fourier analysis, the fundamental and the overtones together are called partials, harmonics, or more precisely, harmonic partials, are partials whose frequencies are integer multiples of the fundamental. These overlapping terms are used when discussing the acoustic behavior of musical instruments. The model of Fourier analysis provides for the inclusion of inharmonic partials, when a resonant system such as a blown pipe or plucked string is excited, a number of overtones may be produced along with the fundamental tone. In simple cases, such as for most musical instruments, the frequencies of these tones are the same as the harmonics. Examples of exceptions include the drum, – a timpani whose first overtone is about 1.6 times its fundamental resonance frequency, gongs and cymbals. The human vocal tract is able to produce highly variable amplitudes of the overtones, called formants, most oscillators, from a guitar string to a flute, will naturally vibrate at a series of distinct frequencies known as normal modes. The lowest normal mode frequency is known as the fundamental frequency, often, when an oscillator is excited by, for example, plucking a guitar string, it will oscillate at several of its modal frequencies at the same time. So when a note is played, this gives the sensation of hearing other frequencies above the lowest frequency, timbre is the quality that gives the listener the ability to distinguish between the sound of different instruments. The timbre of an instrument is determined by which overtones it emphasizes and that is to say, the relative volumes of these overtones to each other determines the specific flavor or color of sound of that family of instruments. The intensity of each of these overtones is rarely constant for the duration of a note, over time, different overtones may decay at different rates, causing the relative intensity of each overtone to rise or fall independent of the overall volume of the sound. A carefully trained ear can hear these changes even in a single note and this is why the timbre of a note may be perceived differently when played staccato or legato. A driven non-linear oscillator, such as the folds, a blown wind instrument, or a bowed violin string will oscillate in a periodic. This generates the impression of sound at integer multiple frequencies of the known as harmonics, or more precisely. Thus, in music, overtones are often called harmonics, depending upon how the string is plucked or bowed, different overtones can be emphasized. However, some overtones in some instruments may not be of an integer multiplication of the fundamental frequency. High quality instruments are built in such a manner that their individual notes do not create disharmonious overtones. This is illustrated by the following, Consider a guitar string and this dead length actually varies from string to string, being more pronounced with thicker and/or stiffer strings
22.
Traveling wave
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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
23.
Transmission line
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This article covers two-conductor transmission line such as parallel line, coaxial cable, stripline, and microstrip. Ordinary electrical cables suffice to carry low frequency alternating current, such as power, which reverses direction 100 to 120 times per second. However, they cannot be used to carry currents in the frequency range, above about 30 kHz, because the energy tends to radiate off the cable as radio waves. Radio frequency currents tend to reflect from discontinuities in the cable such as connectors and joints. These reflections act as bottlenecks, preventing the signal power from reaching the destination, Transmission lines use specialized construction, and impedance matching, to carry electromagnetic signals with minimal reflections and power losses. Types of transmission line include parallel line, coaxial cable, and planar transmission lines such as stripline, the higher the frequency of electromagnetic waves moving through a given cable or medium, the shorter the wavelength of the waves. Transmission lines become necessary when the length of the cable is longer than a significant fraction of the transmitted frequencys wavelength. At microwave frequencies and above, power losses in transmission lines become excessive, and waveguides are used instead, some sources define waveguides as a type of transmission line, however, this article will not include them. At even higher frequencies, in the terahertz, infrared and light range, waveguides in turn become lossy, mathematical analysis of the behaviour of electrical transmission lines grew out of the work of James Clerk Maxwell, Lord Kelvin and Oliver Heaviside. In 1855 Lord Kelvin formulated a model of the current in a submarine cable. The model correctly predicted the performance of the 1858 trans-Atlantic submarine telegraph cable. In 1885 Heaviside published the first papers that described his analysis of propagation in cables, in many electric circuits, the length of the wires connecting the components can for the most part be ignored. That is, the voltage on the wire at a time can be assumed to be the same at all points. Stated another way, the length of the wire is important when the signal frequency components with corresponding wavelengths comparable to or less than the length of the wire. A common rule of thumb is that the cable or wire should be treated as a line if the length is greater than 1/10 of the wavelength. If the transmission line is uniform along its length, then its behaviour is described by a single parameter called the characteristic impedance. This is the ratio of the voltage of a given wave to the complex current of the same wave at any point on the line. Typical values of Z0 are 50 or 75 ohms for a cable, about 100 ohms for a twisted pair of wires
24.
Current (electricity)
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An electric current is a flow of electric charge. In electric circuits this charge is carried by moving electrons in a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionised gas. The SI unit for measuring a current is the ampere. Electric current is measured using a device called an ammeter, electric currents cause Joule heating, which creates light in incandescent light bulbs. They also create magnetic fields, which are used in motors, inductors and generators, the particles that carry the charge in an electric current are called charge carriers. In metals, one or more electrons from each atom are loosely bound to the atom and these conduction electrons are the charge carriers in metal conductors. The conventional symbol for current is I, which originates from the French phrase intensité de courant, current intensity is often referred to simply as current. The I symbol was used by André-Marie Ampère, after whom the unit of current is named, in formulating the eponymous Ampères force law. The notation travelled from France to Great Britain, where it became standard, in a conductive material, the moving charged particles which constitute the electric current are called charge carriers. In other materials, notably the semiconductors, the carriers can be positive or negative. Positive and negative charge carriers may even be present at the same time, a flow of positive charges gives the same electric current, and has the same effect in a circuit, as an equal flow of negative charges in the opposite direction. Since current can be the flow of positive or negative charges. The direction of current is arbitrarily defined as the same direction as positive charges flow. This is called the direction of current I. If the current flows in the direction, the variable I has a negative value. When analyzing electrical circuits, the direction of current through a specific circuit element is usually unknown. Consequently, the directions of currents are often assigned arbitrarily
25.
Voltage
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Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential energy between two points per unit electric charge. The voltage between two points is equal to the work done per unit of charge against an electric field to move the test charge between two points. This is measured in units of volts, voltage can be caused by static electric fields, by electric current through a magnetic field, by time-varying magnetic fields, or some combination of these three. A voltmeter can be used to measure the voltage between two points in a system, often a reference potential such as the ground of the system is used as one of the points. A voltage may represent either a source of energy or lost, used, given two points in space, x A and x B, voltage is the difference in electric potential between those two points. Electric potential must be distinguished from electric energy by noting that the potential is a per-unit-charge quantity. Like mechanical potential energy, the zero of electric potential can be chosen at any point, so the difference in potential, i. e. the voltage, is the quantity which is physically meaningful. The voltage between point A to point B is equal to the work which would have to be done, per unit charge, against or by the electric field to move the charge from A to B. The voltage between the two ends of a path is the energy required to move a small electric charge along that path. Mathematically this is expressed as the integral of the electric field. In the general case, both an electric field and a dynamic electromagnetic field must be included in determining the voltage between two points. Historically this quantity has also called tension and pressure. Pressure is now obsolete but tension is used, for example within the phrase high tension which is commonly used in thermionic valve based electronics. Voltage is defined so that negatively charged objects are pulled towards higher voltages, therefore, the conventional current in a wire or resistor always flows from higher voltage to lower voltage. Current can flow from lower voltage to higher voltage, but only when a source of energy is present to push it against the electric field. This is the case within any electric power source, for example, inside a battery, chemical reactions provide the energy needed for ion current to flow from the negative to the positive terminal. The electric field is not the only factor determining charge flow in a material, the electric potential of a material is not even a well defined quantity, since it varies on the subatomic scale. A more convenient definition of voltage can be found instead in the concept of Fermi level, in this case the voltage between two bodies is the thermodynamic work required to move a unit of charge between them
26.
Superposition principle
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So that if input A produces response X and input B produces response Y then input produces response. The homogeneity and additivity properties together are called the superposition principle, a linear function is one that satisfies the properties of superposition. It is defined as F = F + F Additivity F = a F Homogeneity for scalar a and this principle has many applications in physics and engineering because many physical systems can be modeled as linear systems. For example, a beam can be modeled as a system where the input stimulus is the load on the beam. Because physical systems are only approximately linear, the superposition principle is only an approximation of the true physical behaviour. The superposition principle applies to any system, including algebraic equations, linear differential equations. The stimuli and responses could be numbers, functions, vectors, vector fields, time-varying signals, note that when vectors or vector fields are involved, a superposition is interpreted as a vector sum. By writing a very general stimulus as the superposition of stimuli of a specific, simple form, for example, in Fourier analysis, the stimulus is written as the superposition of infinitely many sinusoids. Due to the principle, each of these sinusoids can be analyzed separately. According to the principle, the response to the original stimulus is the sum of all the individual sinusoidal responses. Fourier analysis is common for waves. For example, in theory, ordinary light is described as a superposition of plane waves. As long as the principle holds, the behavior of any light wave can be understood as a superposition of the behavior of these simpler plane waves. Waves are usually described by variations in some parameter space and time—for example, height in a water wave, pressure in a sound wave. The value of this parameter is called the amplitude of the wave, in any system with waves, the waveform at a given time is a function of the sources and initial conditions of the system. In many cases, the equation describing the wave is linear, when this is true, the superposition principle can be applied. That means that the net amplitude caused by two or more waves traversing the same space is the sum of the amplitudes that would have produced by the individual waves separately. For example, two waves traveling towards each other will pass right through each other without any distortion on the other side, with regard to wave superposition, Richard Feynman wrote, No-one has ever been able to define the difference between interference and diffraction satisfactorily
27.
Frequency
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Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as frequency, which emphasizes the contrast to spatial frequency. The period is the duration of time of one cycle in a repeating event, for example, if a newborn babys heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as vibrations, audio signals, radio waves. For cyclical processes, such as rotation, oscillations, or waves, in physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by the Greek letter ν or ν. For a simple motion, the relation between the frequency and the period T is given by f =1 T. The SI unit of frequency is the hertz, named after the German physicist Heinrich Hertz, a previous name for this unit was cycles per second. The SI unit for period is the second, a traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. As a matter of convenience, longer and slower waves, such as ocean surface waves, short and fast waves, like audio and radio, are usually described by their frequency instead of period. Spatial frequency is analogous to temporal frequency, but the axis is replaced by one or more spatial displacement axes. Y = sin = sin d θ d x = k Wavenumber, in the case of more than one spatial dimension, wavenumber is a vector quantity. For periodic waves in nondispersive media, frequency has a relationship to the wavelength. Even in dispersive media, the frequency f of a wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave. In the special case of electromagnetic waves moving through a vacuum, then v = c, where c is the speed of light in a vacuum, and this expression becomes, f = c λ. When waves from a monochrome source travel from one medium to another, their remains the same—only their wavelength. For example, if 71 events occur within 15 seconds the frequency is, the latter method introduces a random error into the count of between zero and one count, so on average half a count. This is called gating error and causes an error in the calculated frequency of Δf = 1/, or a fractional error of Δf / f = 1/ where Tm is the timing interval. This error decreases with frequency, so it is a problem at low frequencies where the number of counts N is small, an older method of measuring the frequency of rotating or vibrating objects is to use a stroboscope
28.
Anti-node
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A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the length of the vibrating string. The opposite of a node is an anti-node, a point where the amplitude of the wave is a maximum. These occur midway between the nodes, standing waves result when two sinusoidal wave trains of the same frequency are moving in opposite directions in the same space and interfere with each other. In a standing wave the nodes are a series of locations at equally spaced intervals where the amplitude is zero. At these points the two waves add with opposite phase and cancel each other out and they occur at intervals of half a wavelength. Midway between each pair of nodes are locations where the amplitude is maximum, at these points the two waves add with the same phase and reinforce each other. In cases where the two opposite wave trains are not the amplitude, they do not cancel perfectly, so the amplitude of the standing wave at the nodes is not zero. This occurs when the reflection at the boundary is imperfect and this is indicated by a finite standing wave ratio, the ratio of the amplitude of the wave at the antinode to the amplitude at the node. These can be visible by sprinkling sand on the surface. In transmission lines a voltage node is a current antinode, in this type the derivative of the waves amplitude is forced to zero at the boundary. So there is a maximum at the boundary, the first node occurs a quarter wavelength from the end. A sound wave consists of alternating cycles of compression and expansion of the wave medium, during compression, the molecules of the medium are forced together, resulting in the increased pressure and density. During expansion the molecules are forced apart, resulting in the decreased pressure, the number of nodes in a specified length is directly proportional to the frequency of the wave. Occasionally on a guitar, violin, or other stringed instrument, when the finger is placed on top of the string at a certain point, but does not push the string all the way down to the fretboard, a third node is created and a harmonic is sounded. During normal play when the frets are used, the harmonics are always present, with the artificial node method, the overtone is louder and the fundamental tone is quieter. If the finger is placed at the midpoint of the string, the first overtone is heard, when two additional nodes divide the string into thirds, this creates an octave and a perfect fifth
29.
Electrical impedance
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Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied. In quantitative terms, it is the ratio of the voltage to the current in an alternating current circuit. Impedance extends the concept of resistance to AC circuits, and possesses both magnitude and phase, unlike resistance, which has only magnitude. When a circuit is driven with direct current, there is no distinction between impedance and resistance, the latter can be thought of as impedance with zero phase angle. The impedance caused by two effects is collectively referred to as reactance and forms the imaginary part of complex impedance whereas resistance forms the real part. The symbol for impedance is usually Z and it may be represented by writing its magnitude, however, cartesian complex number representation is often more powerful for circuit analysis purposes. The term impedance was coined by Oliver Heaviside in July 1886, arthur Kennelly was the first to represent impedance with complex numbers in 1893. Impedance is defined as the frequency ratio of the voltage to the current. In other words, it is the voltage–current ratio for a complex exponential at a particular frequency ω. In general, impedance will be a number, with the same units as resistance. For a sinusoidal current or voltage input, the form of the complex impedance relates the amplitude and phase of the voltage. In particular, The magnitude of the impedance is the ratio of the voltage amplitude to the current amplitude. The phase of the impedance is the phase shift by which the current lags the voltage. The reciprocal of impedance is admittance, Impedance is represented as a complex quantity Z and the term complex impedance may be used interchangeably. J is the unit, and is used instead of i in this context to avoid confusion with the symbol for electric current. In Cartesian form, impedance is defined as Z = R + j X where the part of impedance is the resistance R. Where it is needed to add or subtract impedances, the form is more convenient, but when quantities are multiplied or divided. A circuit calculation, such as finding the total impedance of two impedances in parallel, may require conversion between forms several times during the calculation, conversion between the forms follows the normal conversion rules of complex numbers
30.
Impedance matching
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In the case of a complex source impedance ZS and load impedance ZL, maximum power transfer is obtained when Z S = Z L ∗ where the asterisk indicates the complex conjugate of the variable. Impedance is the opposition by a system to the flow of energy from a source, for constant signals, this impedance can also be constant. For varying signals, it changes with frequency. The energy involved can be electrical, mechanical, acoustic, magnetic, the concept of electrical impedance is perhaps the most commonly known. Electrical impedance, like electrical resistance, is measured in ohms, in general, impedance has a complex value, this means that loads generally have a resistance component which forms the real part of Z and a reactance component which forms the imaginary part of Z. In simple cases the reactance may be negligible or zero, the impedance can be considered a pure resistance, in the following summary we will consider the general case when resistance and reactance are both significant, and the special case in which the reactance is negligible. Impedance matching to minimize reflections is achieved by making the load impedance equal to the source impedance, if the source impedance, load impedance and transmission line characteristic impedance are purely resistive, then reflection-less matching is the same as maximum power transfer matching. Complex conjugate matching is used when maximum power transfer is required and this differs from reflection-less matching only when the source or load have a reactive component. If the source has a component, but the load is purely resistive, then matching can be achieved by adding a reactance of the same magnitude. This simple matching network, consisting of an element, will usually only achieve a perfect match at a single frequency. For wide bandwidth applications, a complex network must be designed. For two impedances to be complex conjugates their resistances must be equal, and their reactances must be equal in magnitude, in low-frequency or DC systems the reactances are zero, or small enough to be ignored. In this case, maximum power occurs when the resistance of the load is equal to the resistance of the source. Impedance matching is not always necessary, for example, if a source with a low impedance is connected to a load with a high impedance the power that can pass through the connection is limited by the higher impedance. This maximum-voltage connection is a configuration called impedance bridging or voltage bridging. In such applications, delivering a voltage is often more important than maximum power transfer. In older audio systems, the source and load resistances were matched at 600 ohms, one reason for this was to maximize power transfer, as there were no amplifiers available that could restore lost signal. Most modern audio circuits, on the hand, use active amplification and filtering
31.
Short circuit
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A short circuit is an electrical circuit that allows a current to travel along an unintended path with no or a very low electrical impedance. The electrical opposite of a circuit is an open circuit. It is common to misuse short circuit to describe any electrical malfunction, a short circuit is an abnormal connection between two nodes of an electric circuit intended to be at different voltages. This results in an electric current limited only by the Thévenin equivalent resistance of the rest of the network and potentially causes circuit damage, overheating. Although usually the result of a fault, there are cases where short circuits are caused intentionally, for example, in circuit analysis, a short circuit is a connection between two nodes that forces them to be at the same voltage. In an ideal circuit, this means there is no resistance. In real circuits, the result is a connection with almost no resistance, in such a case, the current is limited by the rest of the circuit. A common type of short circuit occurs when the positive and negative terminals of a battery are connected with a low-resistance conductor, with low resistance in the connection, a high current exists, causing the cell to deliver a large amount of energy in a short time. Overloaded wires can also overheat, sometimes causing damage to the wires insulation, in mains circuits, short circuits may occur between two phases, between a phase and neutral or between a phase and earth. Such short circuits are likely to result in a high current. However, it is possible for circuits to arise between neutral and earth conductors, and between two conductors of the same phase. Such short circuits can be dangerous, particularly as they may not immediately result in a current and are therefore less likely to be detected. Possible effects include unexpected energisation of a circuit presumed to be isolated, to help reduce the negative effects of short circuits, power distribution transformers are deliberately designed to have a certain amount of leakage reactance. The leakage reactance helps limit both the magnitude and rate of rise of the fault current, a short circuit may lead to formation of an electric arc. The arc, a channel of hot ionized plasma, is highly conductive, surface erosion is a typical sign of electric arc damage. Even short arcs can remove significant amount of materials from the electrodes, a short circuit fault current can, within milliseconds, be thousands of times larger than the normal operating current of the system. Damage from short circuits can be reduced or prevented by employing fuses, circuit breakers, or other overload protection, overload protection must be chosen according to the current rating of the circuit. Circuits for large home appliances require protective devices set or rated for higher currents than lighting circuits, wire gauges specified in building and electrical codes are chosen to ensure safe operation in conjunction with the overload protection
32.
Standing wave ratio
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In radio engineering and telecommunications, standing wave ratio is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide. The SWR is usually thought of in terms of the maximum and minimum AC voltages along the transmission line, thus called the voltage standing wave ratio or VSWR. For example, the VSWR value 1.2,1 denotes an AC voltage due to standing waves along the line reaching a peak value 1.2 times that of the minimum AC voltage along that line. The SWR can as well be defined as the ratio of the amplitude to minimum amplitude of the transmission lines currents, electric field strength. Neglecting transmission line loss, these ratios are identical, the power standing wave ratio is defined as the square of the VSWR, however this terminology has no physical relation to actual powers involved in transmission. SWR is usually measured using an instrument called an SWR meter. In practice most transmission lines used in applications are coaxial cables with an impedance of either 50 or 75 ohms. Checking the SWR is a procedure in a radio station. Although the same information could be obtained by measuring the impedance with an impedance analyzer. By measuring the magnitude of the impedance mismatch at the output it reveals problems due to either the antenna or the transmission line. SWR is used as a measure of impedance matching of a load to the impedance of a transmission line carrying radio frequency signals. Impedance matching is achieved when the impedance is the complex conjugate of the load impedance. When there is a mismatch between the load impedance and the line, part of the forward wave sent toward the load is reflected back along the transmission line towards the source. The source then sees a different impedance than it expects which can lead to power being supplied by it. Such a mismatch is usually undesired and results in standing waves along the line which magnifies transmission line losses. The SWR is a measure of the depth of standing waves and is therefore a measure of the matching of the load to the transmission line. A matched load would result in an SWR of 1,1 implying no reflected wave, an infinite SWR represents complete reflection by a load unable to absorb electrical power, with all the incident power reflected back towards the source. However the SWR will generally not be 1,1, depending only on Zload, with a different length of transmission line, the source will see a different impedance than Zload which may or may not be a good match to the source
33.
Ocean
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An ocean is a body of saline water that composes much of a planets hydrosphere. On Earth, an ocean is one of the major divisions of the World Ocean. These are, in descending order by area, the Pacific, Atlantic, Indian, Southern, the word sea is often used interchangeably with ocean in American English but, strictly speaking, a sea is a body of saline water partly or fully enclosed by land. The ocean contains 97% of Earths water, and oceanographers have stated that less than 5% of the World Ocean has been explored, the total volume is approximately 1.35 billion cubic kilometers with an average depth of nearly 3,700 meters. As the world ocean is the component of Earths hydrosphere, it is integral to all known life, forms part of the carbon cycle. The world ocean is the habitat of 230,000 known species, but because much of it is unexplored, the origin of Earths oceans remains unknown, oceans are thought to have formed in the Hadean period and may have been the impetus for the emergence of life. Extraterrestrial oceans may be composed of water or other elements and compounds, the only confirmed large stable bodies of extraterrestrial surface liquids are the lakes of Titan, although there is evidence for the existence of oceans elsewhere in the Solar System. Early in their histories, Mars and Venus are theorized to have had large water oceans. The Mars ocean hypothesis suggests that nearly a third of the surface of Mars was once covered by water, compounds such as salts and ammonia dissolved in water lower its freezing point so that water might exist in large quantities in extraterrestrial environments as brine or convecting ice. Unconfirmed oceans are speculated beneath the surface of many planets and natural satellites, notably. The Solar Systems giant planets are thought to have liquid atmospheric layers of yet to be confirmed compositions. Oceans may also exist on exoplanets and exomoons, including surface oceans of water within a circumstellar habitable zone. Ocean planets are a type of planet with a surface completely covered with liquid. The concept of Ōkeanós has an Indo-European connection, Greek Ōkeanós has been compared to the Vedic epithet ā-śáyāna-, predicated of the dragon Vṛtra-, who captured the cows/rivers. Related to this notion, the Okeanos is represented with a dragon-tail on some early Greek vases, though generally described as several separate oceans, these waters comprise one global, interconnected body of salt water sometimes referred to as the World Ocean or global ocean. This concept of a body of water with relatively free interchange among its parts is of fundamental importance to oceanography. The major oceanic divisions – listed below in descending order of area and volume – are defined in part by the continents, various archipelagos, Oceans are fringed by smaller, adjoining bodies of water such as seas, gulfs, bays, bights, and straits. The Mid-Oceanic Ridge of the World are connected and form the Ocean Ridge, the continuous mountain range is 65,000 km long, and the total length of the oceanic ridge system is 80,000 km long
34.
Microseism
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In seismology, a microseism is defined as a faint earth tremor caused by natural phenomena. Sometimes referred to as a hum, it should not be confused with the acoustic phenomenon of the same name. The term is most commonly used to refer to the dominant background seismic and electromagnetic noise signals on Earth, characteristics of microseism are discussed by Bhatt. Because the ocean wave oscillations are statistically homogenous over several hours, because the conversion from the ocean waves to the seismic waves is very weak, the amplitude of ground motions associated to microseisms does not generally exceed 10 micrometers. Microseisms are very well detected and measured by means of a broad-band seismograph, dominant microseism signals from the oceans are linked to characteristic ocean swell periods, and thus occur between approximately 4 to 30 seconds. Microseismic noise usually displays two predominant peaks, the weaker is for the larger periods, typically close to 16 s, and can be explained by the effect of surface gravity waves in shallow water. These microseisms have the period as the water waves that generate them. The stronger peak, for periods, is also due to surface gravity waves in water. These tremors have a period which is half of the wave period and are usually called secondary microseisms. A slight, but detectable, incessant excitation of the Earths free oscillations, or normal modes, with periods in the range 30 to 1000 s, and is often referred to as the Earth hum. The dominant sources of this vertical hum component are likely located along the shelf break, as a result, from the short period secondary microseisms to the long period hum, this seismic noise contains information on the sea states. It can be used to estimate ocean wave properties and their variation, on scales of individual events to their seasonal or multi-decadal evolution. Using these signals, however, requires an understanding of the microseisms generation processes. The details of the mechanism was first given by Hasselmann. It is a case of a wave-wave interaction process in which one wave is fixed. To visualize what happens, it is easier to study the propagation of waves over a sinusoidal bottom topography, for a real bottom, seismic waves are generated with all wavelengths and in all directions. The interaction of two trains of surface waves of different frequencies and directions generates wave groups, for wave propagating almost in the same direction, this gives the usual sets of waves that travel at the group speed, which is slower than phase speed of water waves. For typical ocean waves with a period around 10 seconds, this speed is close to 10 m/s
35.
Radian
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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
36.
Hertz
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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
37.
Wavelength
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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
38.
Trigonometric identity
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Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles and these identities are useful whenever expressions involving trigonometric functions need to be simplified. This article uses Greek letters such as alpha, beta, gamma, several different units of angle measure are widely used, including degrees, radians, and gradians,1 full circle =360 degrees = 2π radians =400 gons. The following table shows the conversions and values for some common angles, all angles in this article are re-assumed to be in radians, but angles ending in a degree symbol are in degrees. Per Nivens theorem multiples of 30° are the angles that are a rational multiple of one degree and also have a rational sine or cosine. The secondary trigonometric functions are the sine and cosine of an angle and these are sometimes abbreviated sin and cos, respectively, where θ is the angle, but the parentheses around the angle are often omitted, e. g. sin θ and cos θ. The sine of an angle is defined in the context of a right triangle, the tangent of an angle is the ratio of the sine to the cosine, tan θ = sin θ cos θ. These definitions are sometimes referred to as ratio identities, the inverse trigonometric functions are partial inverse functions for the trigonometric functions. For example, the function for the sine, known as the inverse sine or arcsine, satisfies sin = x for | x | ≤1. This can be viewed as a version of the Pythagorean theorem, and follows from the equation x2 + y2 =1 for the unit circle. Dividing this identity by either cos2 θ or sin2 θ yields the other two Pythagorean identities,1 + tan 2 θ = sec 2 θ and 1 + cot 2 θ = csc 2 θ. For example, the formula was used to calculate the distance between two points on a sphere. By examining the unit circle, the properties of the trigonometric functions can be established. When the trigonometric functions are reflected from certain angles, the result is one of the other trigonometric functions. This leads to the identities, Note that the sign in front of the trig function does not necessarily indicate the sign of the value. For example, +cos θ does not always mean that cos θ is positive, in particular, if θ = π, then +cos θ = −1. By shifting the function round by certain angles, it is possible to find different trigonometric functions that express particular results more simply. Some examples of this are shown by shifting functions round by π/2, π, because the periods of these functions are either π or 2π, there are cases where the new function is exactly the same as the old function without the shift
39.
Drumhead
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A drumhead or drum skin is a membrane stretched over one or both of the open ends of a drum. The drumhead is struck with sticks, mallets, or hands, so that it vibrates, originally, drumheads were made from animal hide and were first used in early human history, long before records began. In 1957, Remo Belli and Sam Muchnick together developed a polymer head leading to the development of the Remo drumhead company, despite the benefits of plastic heads, drummers in historical reenactment groups such as fife and drum use animal skin heads for historical accuracy. Another common material used for drumheads is aramid fiber, such as kevlar, kevlar heads are also used in marching percussion. The bolts, called tension rods, are screwed into threaded lugs attached to the shell, in order to tighten. A drum key is a four sided wrench used to screw the tension rods into the lugs, drummers muffle their drums using special drumheads. Some drumheads come pre-muffled such as Remo Powerstroke Pro, accessory Fetish A Complete List of Drum Head Manufacturers Resonant Drum Head Explained
40.
Chladni figure
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Ernst Florens Friedrich Chladni was a German physicist and musician. His most important work, for which he is labeled the father of acoustics, included research on vibrating plates. He also undertook pioneering work in the study of meteorites and so is regarded by some as the father of meteoritics. Although Chladni was born in Wittenberg in Saxony, his family originated from Kremnica, then part of the Kingdom of Hungary, Chladni has therefore been identified as German, Hungarian and Slovak. Chladni came from an family of academics and learned men. Chladnis great-grandfather, the Lutheran clergyman Georg Chladni, had left Kremnica in 1673 during the Counter Reformation, Chladnis grandfather, Martin Chladni, was also a Lutheran theologian and, in 1710, became professor of theology at the University of Wittenberg. He was dean of the faculty in 1720–1721 and later became the universitys rector. Chaldnis uncle, Justus Georg Chladni, was a law professor at the university, another uncle, Johann Martin Chladni, was a theologian, a historian and a professor at the University of Erlangen and the University of Leipzig. Chladnis father, Ernst Martin Chladni, was a law professor and rector of the University of Wittenberg and he had joined the law faculty there in 1746. Chladnis mother was Johanna Sophia and he was an only child and his father disapproved of his sons interest in science and insisted that Chladni become a lawyer. Chladni studied law and philosophy in Wittenberg and Leipzig, obtaining a law degree from the University of Leipzig in 1782 and that same year, his father died and he turned to physics in earnest. One of Chladnis best-known achievements was inventing a technique to show the modes of vibration of a rigid surface. When resonating, a plate or membrane is divided into regions that vibrate in opposite directions, Chladni repeated the pioneering experiments of Robert Hooke who, on July 8,1680, had observed the nodal patterns associated with the vibrations of glass plates. Hooke ran a bow along the edge of a plate covered with flour. Chladnis technique, first published in 1787 in his book Entdeckungen über die Theorie des Klanges, the plate was bowed until it reached resonance, when the vibration causes the sand to move and concentrate along the nodal lines where the surface is still, outlining the nodal lines. The patterns formed by these lines are what are now called Chladni figures, similar nodal patterns can also be found by assembling microscale materials on Faraday waves. When Chladni showed the technique in Paris, Napoleon set a prize for the best mathematical explanation, sophie Germains answer, although rejected due to flaws, was the only entry with the correct approach. Variations of this technique are still used in the design and construction of acoustic instruments such as violins, guitars