1.
Musical acoustics
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Musical acoustics or music acoustics is a branch of acoustics concerned with researching and describing the physics of music – how sounds are employed to make music. Examples of areas of study are the function of musical instruments, the voice, computer analysis of melody. As a result, any sound wave that is not a wave can be modeled by many different sine waves of the appropriate frequencies and amplitudes. In humans the hearing apparatus can usually isolate these tones and hear them distinctly, when two or more tones are played at once, a variation of air pressure at the ear contains the pitches of each, and the ear and/or brain isolate and decode them into distinct tones. When the original sources are perfectly periodic, the note consists of several related sine waves called the fundamental. The sounds have harmonic frequency spectra, the lowest frequency present is the fundamental, and is the frequency at which the entire wave vibrates. The overtones vibrate faster than the fundamental, but must vibrate at integer multiples of the frequency for the total wave to be exactly the same each cycle. Real instruments are close to periodic, but the frequencies of the overtones are slightly imperfect, variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to the subjective experience called sound. Most sound that people recognize as musical is dominated by periodic or regular vibrations rather than non-periodic ones, the transmission of these variations through air is via a sound wave. Pure tones can be produced by tuning forks or whistling, the rate at which the air pressure oscillates is the frequency of the tone, which is measured in oscillations per second, called hertz. Frequency is the determinant of the perceived pitch. Frequency of musical instruments can change with altitude due to changes in air pressure, *This chart only displays down to C0, though some pipe organs, such as the Boardwalk Hall Auditorium Organ, extend down to C−1. Also, the frequency of the subcontrabass tuba is B♭−1. The fundamental is the frequency at which the entire wave vibrates, overtones are other sinusoidal components present at frequencies above the fundamental. All of the components that make up the total waveform, including the fundamental. Together they form the harmonic series, overtones that are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, but not exact, it is called a harmonic partial. Sometimes overtones are created that are not anywhere near a harmonic, the fundamental frequency is considered the first harmonic and the first partial
2.
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
3.
Fork
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A fork, in cutlery or kitchenware, is a tool consisting of a handle with several narrow tines on one end. The usually metal utensil is used to food to the mouth or to hold ingredients in place while they are being cut by a knife. Food can be lifted either by spearing it on the tines or by holding it on top of the tines, the early history of the fork is obscure. As a kitchen and dining utensil it is believed to have originated in the Roman Empire. The personal table fork most likely originated in the Eastern Roman Empire and its use spread to what is now the Middle East during the first millennium AD and then spread into southern Europe during the second millennium. It did not become common in northern Europe until the 18th century and was not common in North America until the 19th century, the fork is a primarily Western utensil, whereas in east Asia chopsticks have been more prevalent. Today, forks are available throughout east Asia. The word fork comes from the Latin furca, meaning pitchfork, some of the earliest known uses of forks with food occurred in Ancient Egypt, where large forks were used as cooking utensils. Bone forks had been found in the site of the Bronze Age Qijia culture as well as later Chinese dynasties tombs. The Ancient Greeks used the fork as a serving utensil, the Greek name for fork is still used in some European languages, for instance in the Venetian, Greek, and Albanian languages. In the Roman Empire, bronze and silver forks were used, the use varied according to local customs, social class and the nature of food, but forks of the earlier periods were mostly used as cooking and serving utensils. The personal table fork was most likely invented in the Eastern Roman Empire, records show that by the 9th century a similar utensil known as a barjyn was in limited use in Persia within some elite circles. By the 10th century, the fork was in common use throughout the Middle East. By the 11th century, the fork had become increasingly prevalent in the Italian peninsula. At first, pasta was consumed using a wooden spike. In Italy, it became commonplace by the 14th century and was almost universally used by the merchant and upper classes by 1600. It was proper for a guest to arrive with his own fork and spoon enclosed in a box called a cadena, in Portugal, forks were first used at the time of Infanta Beatrice, Duchess of Viseu, King Manuel I of Portugals mother around 1450. However, forks were not commonly used in Southern Europe until the 16th century when they part of Italian etiquette
4.
Tine (structural)
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Tines or prongs or teeth are parallel or branching spikes forming parts of a tool or natural object. They are used to spear, hook, move or otherwise act on other objects and they may be made of metal, wood, bone or other hard, strong materials. The number of tines on tools varies widely – a pitchfork may have just two, a fork may have four, and a rake or harrow many. Tines may be blunt, such as those on a used as an eating utensil, or sharp, as on a pitchfork, or even barbed. The terms tine and prong are mostly interchangeable, a tooth of a comb is a tine. Tines and prongs occur in nature—for example, forming the branched bony antlers of deer or the horns of pronghorn antelopes. The term tine is also used for mountains, such as the fictional Silvertine in The Lord of the Rings, in chaos theory, the branches of a bifurcation diagram are called tines and subtines
5.
Elastic deformation
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In materials science, deformation refers to any changes in the shape or size of an object due to- an applied force or a change in temperature. The first case can be a result of forces, compressive forces, shear. The movement or displacement of such mobile defects is thermally activated, deformation is often described as strain. As deformation occurs, internal inter-molecular forces arise that oppose the applied force, a larger applied force may lead to a permanent deformation of the object or even to its structural failure. In the figure it can be seen that the compressive loading has caused deformation in the cylinder so that the shape has changed into one with bulging sides. The sides bulge because the material, although enough to not crack or otherwise fail, is not strong enough to support the load without change. Internal forces resist the applied load, the concept of a rigid body can be applied if the deformation is negligible. Depending on the type of material, size and geometry of the object, the image to the right shows the engineering stress vs. strain diagram for a typical ductile material such as steel. Different deformation modes may occur under different conditions, as can be depicted using a deformation mechanism map and this type of deformation is reversible. Once the forces are no longer applied, the returns to its original shape. Elastomers and shape memory metals such as Nitinol exhibit large elastic deformation ranges, however elasticity is nonlinear in these materials. Normal metals, ceramics and most crystals show linear elasticity and an elastic range. This relationship only applies in the range and indicates that the slope of the stress vs. strain curve can be used to find Youngs modulus. Engineers often use this calculation in tensile tests, the elastic range ends when the material reaches its yield strength. At this point plastic deformation begins, note that not all elastic materials undergo linear elastic deformation, some, such as concrete, gray cast iron, and many polymers, respond in a nonlinear fashion. For these materials Hookes law is inapplicable and this type of deformation is irreversible. However, an object in the plastic deformation range will first have undergone elastic deformation, soft thermoplastics have a rather large plastic deformation range as do ductile metals such as copper, silver, and gold. Steel does, too, but not cast iron, hard thermosetting plastics, rubber, crystals, and ceramics have minimal plastic deformation ranges
6.
Steel
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Steel is an alloy of iron and other elements, primarily carbon, that is widely used in construction and other applications because of its high tensile strength and low cost. Steels base metal is iron, which is able to take on two forms, body centered cubic and face centered cubic, depending on its temperature. It is the interaction of those allotropes with the elements, primarily carbon. In the body-centred cubic arrangement, there is an atom in the centre of each cube. Carbon, other elements, and inclusions within iron act as hardening agents that prevent the movement of dislocations that otherwise occur in the lattices of iron atoms. The carbon in steel alloys may contribute up to 2. 1% of its weight. Steels strength compared to pure iron is possible at the expense of irons ductility. With the invention of the Bessemer process in the mid-19th century and this was followed by Siemens-Martin process and then Gilchrist-Thomas process that refined the quality of steel. With their introductions, mild steel replaced wrought iron, further refinements in the process, such as basic oxygen steelmaking, largely replaced earlier methods by further lowering the cost of production and increasing the quality of the product. Today, steel is one of the most common materials in the world and it is a major component in buildings, infrastructure, tools, ships, automobiles, machines, appliances, and weapons. Modern steel is generally identified by various grades defined by assorted standards organizations, the noun steel originates from the Proto-Germanic adjective stakhlijan, which is related to stakhla. The carbon content of steel is between 0. 002% and 2. 1% by weight for plain iron–carbon alloys and these values vary depending on alloying elements such as manganese, chromium, nickel, iron, tungsten, carbon and so on. Basically, steel is an alloy that does not undergo eutectic reaction. In contrast, cast iron does undergo eutectic reaction, too little carbon content leaves iron quite soft, ductile, and weak. Carbon contents higher than those of steel make an alloy, commonly called pig iron, while iron alloyed with carbon is called carbon steel, alloy steel is steel to which other alloying elements have been intentionally added to modify the characteristics of steel. Common alloying elements include, manganese, nickel, chromium, molybdenum, boron, titanium, vanadium, tungsten, cobalt, and niobium. Additional elements are important in steel, phosphorus, sulfur, silicon, and traces of oxygen, nitrogen, and copper. Alloys with a higher than 2. 1% carbon content, depending on other element content, cast iron is not malleable even when hot, but it can be formed by casting as it has a lower melting point than steel and good castability properties
7.
Acoustic resonance
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Acoustic resonance is a phenomenon where acoustic systems amplify sound waves whose frequency matches one of its own natural frequencies of vibration. An acoustically resonant object usually has more than one resonance frequency and it will easily vibrate at those frequencies, and vibrate less strongly at other frequencies. It will pick out its resonance frequency from a complex excitation, in effect, it is filtering out all frequencies other than its resonance. Acoustic resonance is also important for hearing, for example, resonance of a stiff structural element, called the basilar membrane within the cochlea of the inner ear allows hair cells on the membrane to detect sound. Like mechanical resonance, acoustic resonance can result in failure of the vibrator. The classic example of this is breaking a glass with sound at the precise resonant frequency of the glass. In musical instruments, strings under tension, as in lutes, harps, guitars, pianos, violins and so forth, have resonant frequencies directly related to the mass, length, and tension of the string. The wavelength that will create the first resonance on the string is equal to twice the length of the string, higher resonances correspond to wavelengths that are integer divisions of the fundamental wavelength. The corresponding frequencies are related to the v of a wave traveling down the string by the equation f = n v 2 L where L is the length of the string. Higher tension and shorter lengths increase the resonant frequencies, when the string is excited with an impulsive function, the string vibrates at all the frequencies present in the impulse. Those frequencies that are not one of the resonances are quickly filtered out—they are attenuated—and all that is left is the vibrations that we hear as a musical note. String resonance occurs on string instruments, strings or parts of strings may resonate at their fundamental or overtone frequencies when other strings are sounded. For example, an A string at 440 Hz will cause an E string at 330 Hz to resonate, the resonance of a tube of air is related to the length of the tube, its shape, and whether it has closed or open ends. Musically useful tube shapes are conical and cylindrical, a pipe that is closed at one end is said to be stopped while an open pipe is open at both ends. Modern orchestral flutes behave as open pipes, clarinets and lip-reed instruments behave as closed cylindrical pipes, and saxophones, oboes. Vibrating air columns also have resonances at harmonics, like strings, an open tube is a tube in which both ends are open. The tube resonates at many frequencies or notes and its lowest resonance occurs at the same frequency as a closed tube of half its length. An open tube will resonate if there is a displacement antinode at each open end and these displacement antinodes are places where there is a maximum movement of air in and out of the ends of the tube
8.
Pitch (music)
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Pitch can be determined only in sounds that have a frequency that is clear and stable enough to distinguish from noise. Pitch is a major attribute of musical tones, along with duration, loudness. Pitch may be quantified as a frequency, but pitch is not a purely objective physical property, Pitch is an auditory sensation in which a listener assigns musical tones to relative positions on a musical scale based primarily on their perception of the frequency of vibration. Pitch is closely related to frequency, but the two are not equivalent, frequency is an objective, scientific attribute that can be measured. Pitch is each persons subjective perception of a wave, which cannot be directly measured. However, this not necessarily mean that most people wont agree on which notes are higher and lower. Sound waves themselves do not have pitch, but their oscillations can be measured to obtain a frequency and it takes a sentient mind to map the internal quality of pitch. However, pitches are usually associated with, and thus quantified as frequencies in cycles per second, or hertz, by comparing sounds with pure tones, Complex and aperiodic sound waves can often be assigned a pitch by this method. According to the American National Standards Institute, pitch is the attribute of sound according to which sounds can be ordered on a scale from low to high. That is, high pitch means very rapid oscillation, and low pitch corresponds to slower oscillation, despite that, the idiom relating vertical height to sound pitch is shared by most languages. At least in English, it is just one of many deep conceptual metaphors that involve up/down, the exact etymological history of the musical sense of high and low pitch is still unclear. There is evidence that humans do actually perceive that the source of a sound is slightly higher or lower in vertical space when the frequency is increased or reduced. The pitch of tones can be ambiguous, meaning that two or more different pitches can be perceived, depending upon the observer. In a situation like this, the percept at 200 Hz is commonly referred to as the missing fundamental, Pitch depends to a lesser degree on the sound pressure level of the tone, especially at frequencies below 1,000 Hz and above 2,000 Hz. The pitch of lower tones gets lower as sound pressure increases, for instance, a tone of 200 Hz that is very loud seems one semitone lower in pitch than if it is just barely audible. Above 2,000 Hz, the pitch gets higher as the sound gets louder, theories of pitch perception try to explain how the physical sound and specific physiology of the auditory system work together to yield the experience of pitch. In general, pitch perception theories can be divided into place coding, place theory holds that the perception of pitch is determined by the place of maximum excitation on the basilar membrane. However, a purely place-based theory cannot account for the accuracy of pitch perception in the low, temporal theories offer an alternative that appeals to the temporal structure of action potentials, mostly the phase-locking and mode-locking of action potentials to frequencies in a stimulus
9.
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
10.
Musical tuning
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In music, there are two common meanings for tuning, Tuning practice, the act of tuning an instrument or voice. Tuning systems, the systems of pitches used to tune an instrument. Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones, Tuning is usually based on a fixed reference, such as A =440 Hz. Out of tune refers to a pitch/tone that is too high or too low in relation to a given reference pitch. While an instrument might be in relative to its own range of notes. Some instruments become out of tune with damage or time and must be readjusted or repaired, different methods of sound production require different methods of adjustment, Tuning to a pitch with ones voice is called matching pitch and is the most basic skill learned in ear training. Turning pegs to increase or decrease the tension on strings so as to control the pitch, instruments such as the harp, piano, and harpsichord require a wrench to turn the tuning pegs, while others such as the violin can be tuned manually. Modifying the length or width of the tube of an instrument, brass instrument, pipe, bell. The sounds of instruments such as cymbals are inharmonic—they have irregular overtones not conforming to the harmonic series. Tuning may be done aurally by sounding two pitches and adjusting one of them to match or relate to the other, a tuning fork or electronic tuning device may be used as a reference pitch, though in ensemble rehearsals often a piano is used. Symphony orchestras and concert bands tend to tune to an A or a B♭, respectively, interference beats are used to objectively measure the accuracy of tuning. As the two approach a harmonic relationship, the frequency of beating decreases. When tuning a unison or octave it is desired to reduce the beating frequency until it cannot be detected, for other intervals, this is dependent on the tuning system being used. Harmonics may be used to facilitate tuning of strings that are not themselves tuned to the unison, for example, lightly touching the highest string of a cello at the middle while bowing produces the same pitch as doing the same a third of the way down its second-highest string. The resulting unison is more easily and quickly judged than the quality of the fifth between the fundamentals of the two strings. In music, the open string refers to the fundamental note of the unstopped. The strings of a guitar are tuned to fourths, as are the strings of the bass guitar. Violin, viola, and cello strings are tuned to fifths, however, non-standard tunings exist to change the sound of the instrument or create other playing options
11.
Trumpet
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A trumpet is a musical instrument commonly used in classical and jazz ensembles. The trumpet group contains the instruments with the highest register in the brass family, trumpets are used in art music styles, for instance in orchestras, concert bands, and jazz ensembles, as well as in popular music. They are played by blowing air through almost-closed lips, producing a sound that starts a standing wave vibration in the air column inside the instrument. Since the late 15th century they have primarily been constructed of brass tubing, there are many distinct types of trumpet, with the most common being pitched in B♭, having a tubing length of about 1.48 m. Early trumpets did not provide means to change the length of tubing, most trumpets have valves of the piston type, while some have the rotary type. The use of rotary-valved trumpets is more common in orchestral settings, each valve, when engaged, increases the length of tubing, lowering the pitch of the instrument. A musician who plays the trumpet is called a trumpet player or trumpeter, the earliest trumpets date back to 1500 BC and earlier. The bronze and silver trumpets from Tutankhamuns grave in Egypt, bronze lurs from Scandinavia, trumpets from the Oxus civilization of Central Asia have decorated swellings in the middle, yet are made out of one sheet of metal, which is considered a technical wonder. The Shofar, made from a ram horn and the Hatzotzeroth and they were played in Solomons Temple around 3000 years ago. They were said to be used to blow down the walls of Jericho and they are still used on certain religious days. The Salpinx was a straight trumpet 62 inches long, made of bone or bronze, Salpinx contests were a part of the original Olympic Games. The Moche people of ancient Peru depicted trumpets in their art going back to AD300, the earliest trumpets were signaling instruments used for military or religious purposes, rather than music in the modern sense, and the modern bugle continues this signaling tradition. Improvements to instrument design and metal making in the late Middle Ages, the natural trumpets of this era consisted of a single coiled tube without valves and therefore could only produce the notes of a single overtone series. Changing keys required the player to change crooks of the instrument, the development of the upper, clarino register by specialist trumpeters—notably Cesare Bendinelli—would lend itself well to the Baroque era, also known as the Golden Age of the natural trumpet. During this period, a vast body of music was written for virtuoso trumpeters, the art was revived in the mid-20th century and natural trumpet playing is again a thriving art around the world. The melody-dominated homophony of the classical and romantic periods relegated the trumpet to a role by most major composers owing to the limitations of the natural trumpet. Berlioz wrote in 1844, Notwithstanding the real loftiness and distinguished nature of its quality of tone, there are few instruments that have been more degraded. The attempt to give the trumpet more chromatic freedom in its range saw the development of the keyed trumpet, the symphonies of Mozart, Beethoven, and as late as Brahms, were still played on natural trumpets
12.
Lute
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The European lute and the modern Near-Eastern oud descend from a common ancestor via diverging evolutionary paths. The lute is used in a variety of instrumental music from the Medieval to the late Baroque eras and was the most important instrument for secular music in the Renaissance. It is also an instrument, especially in vocal works. The player of a lute is called a lutenist, lutanist or lutist, the words lute and oud possibly derive from Arabic al-ʿud. Recent research by Eckhard Neubauer suggests ʿud may in turn be an Arabized version of the Persian name rud and it has equally been suggested the wood in the name may have distinguished the instrument by its wooden soundboard from skin-faced predecessors. Gianfranco Lotti suggests the wood appellation originally carried derogatory connotations because of proscriptions of all music in early Islam. Lutes are made almost entirely of wood, the soundboard is a teardrop-shaped thin flat plate of resonant wood. In all lutes the soundboard has a single decorated sound hole under the strings called the rose. The sound hole is not open, but rather covered with a grille in the form of a vine or a decorative knot. Robert Lundberg, in his book Historical Lute Construction, suggests ancient builders placed bars according to ratios of the scale length. He further suggests the inward bend of the soundboard is an adaptation by ancient builders to afford the lutenists right hand more space between the strings and soundboard. Soundboard thickness varies, but generally hovers between 1.5 and 2 mm, some luthiers tune the belly as they build, removing mass and adapting bracing to produce desirable sonic results. The lute belly is almost never finished, but in cases the luthier may size the top with a very thin coat of shellac or glair to help keep it clean. After joining the top to the sides, a half-binding is usually installed around the edge of the soundboard, the half-binding is approximately half the thickness of the soundboard and is usually made of a contrasting color wood. The rebate for the half-binding must be precise to avoid compromising structural integrity. The back or the shell is assembled from strips of hardwood called ribs. There are braces inside on the soundboard to give it strength, the neck is made of light wood, with a veneer of hardwood to provide durability for the fretboard beneath the strings. Unlike most modern stringed instruments, the fretboard is mounted flush with the top
13.
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
14.
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
15.
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
16.
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
17.
A440 (pitch standard)
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A440 or A4, which has a frequency of 440 Hz, is the musical note A above middle C and serves as a general tuning standard for musical pitch. Prior to the standardization on 440 Hz, many countries and organizations followed the French standard since the 1860s of 435 Hz, which had also been the Austrian governments 1885 recommendation. Johann Heinrich Scheibler recommended A440 as a standard in 1834 after inventing the tonometer to measure pitch, the American music industry reached an informal standard of 440 Hz in 1926, and some began using it in instrument manufacturing. In 1936 the American Standards Association recommended that the A above middle C be tuned to 440 Hz and this standard was taken up by the International Organization for Standardization in 1955 as ISO16. It is designated A4 in scientific pitch notation because it occurs in the octave that starts with the fourth C key on a standard 88-key piano keyboard, A440 is widely used as concert pitch in the United Kingdom and the United States. In continental Europe the frequency of A4 commonly varies between 440 Hz and 444 Hz, in the period instrument movement, a consensus has arisen around a modern baroque pitch of 415 Hz, baroque for some special church music at 466 Hz, and classical pitch at 430 Hz. A440 is often used as a reference in just intonation regardless of the fundamental note or key. The US time and frequency station WWV broadcasts a 440 Hz signal at two minutes past every hour, with WWVH broadcasting the same tone at the first minute past every hour and this was added in 1936 to aid orchestras in tuning their instruments. History of pitch standards in Western music Concert pitch Pitch Electronic tuner A
18.
Concert pitch
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Concert pitch refers to the pitch reference to which a group of musical instruments are tuned for a performance. Concert pitch may vary from ensemble to ensemble, and has varied widely over musical history, in the literature this is also called international standard pitch. The most common modern tuning standard uses 440 Hz for A above middle C as a reference note, the term concert pitch is also used to distinguish between the written, and sounding notes of a transposing instrument - concert pitch here refers to the pitch on a non-transposing instrument. This pitch is referred to as concert B♭, the A above middle C is often set at 440 Hz. Historically, this A has been tuned to a variety of higher and lower pitches, historically, various standards have been used to fix the pitch of notes at certain frequencies. Various systems of musical tuning have also used to determine the relative frequency of notes in a scale. Until the 19th century, there was no coordinated effort to standardize pitch. Pitches did not just vary from place to place, or over time—pitch levels could vary even within the same city. The pitch used for an English cathedral organ in the 17th century, for example, even within one church, the pitch used could vary over time because of the way organs were tuned. Generally, the end of an organ pipe would be hammered inwards to a cone, or flared outwards, when the pipe ends became frayed by this constant process they were all trimmed down, thus raising the overall pitch of the organ. From the early 18th century, pitch could be controlled with the use of tuning forks. For example, a tuning fork associated with Handel, dating from 1740, is pitched at A =422.5 Hz, while a later one from 1780 is pitched at A =409 Hz, about a quarter-tone lower. Overall, there was a tendency towards the end of the 18th century for the frequency of the A above middle C to be in the range of 400 to 450 Hz. The frequencies quoted here are based on measurements and would not have been precisely known to musicians of the day. The term formerly used for the unit of pitch, cycle per second was renamed the hertz in the 20th century in honor of Heinrich Rudolf Hertz, during historical periods when instrumental music rose in prominence, there was a continuous tendency for pitch levels to rise. This pitch inflation seemed largely a product of competing with each other, each attempting to produce a brighter, more brilliant. This tendency was also prevalent with wind instrument manufacturers, who crafted their instruments to play generally at a higher pitch than those made by the same craftsmen years earlier, on at least two occasions, pitch inflation had become so severe that reform became needed. The standard voice ranges he cites show that the level of his time
19.
Sheffield
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Sheffield is a city and metropolitan borough in South Yorkshire, England. Historically part of the West Riding of Yorkshire, its derives from the River Sheaf. With some of its southern suburbs annexed from Derbyshire, the city has grown from its industrial roots to encompass a wider economic base. The population of the City of Sheffield is 569,700, Sheffield is the third largest English district by population. The metropolitan population of Sheffield is 1,569,000, in the 19th century, Sheffield gained an international reputation for steel production. Known as the Steel City, many innovations were developed locally, including crucible and stainless steel, Sheffield received its municipal charter in 1843, becoming the City of Sheffield in 1893. International competition in iron and steel caused a decline in these industries in the 1970s and 1980s, the 21st century has seen extensive redevelopment in Sheffield along with other British cities. Sheffields gross value added has increased by 60% since 1997, standing at £9.2 billion in 2007, the economy has experienced steady growth averaging around 5% annually, greater than that of the broader region of Yorkshire and the Humber. The city is in the foothills of the Pennines, and the valleys of the River Don and its four tributaries, the Loxley, the Porter Brook, the Rivelin. 61% of Sheffields entire area is space, and a third of the city lies within the Peak District national park. The area now occupied by the City of Sheffield is believed to have inhabited since at least the late Upper Palaeolithic period. The earliest evidence of occupation in the Sheffield area was found at Creswell Crags to the east of the city. In the Iron Age the area became the southernmost territory of the Pennine tribe called the Brigantes and it is this tribe who are thought to have constructed several hill forts in and around Sheffield. Gradually, Anglian settlers pushed west from the kingdom of Deira, a Celtic presence within the Sheffield area is evidenced by two settlements called Wales and Waleswood close to Sheffield. The settlements that grew and merged to form Sheffield, however, date from the half of the first millennium. In Anglo-Saxon times, the Sheffield area straddled the border between the kingdoms of Mercia and Northumbria, after the Norman conquest, Sheffield Castle was built to protect the local settlements, and a small town developed that is the nucleus of the modern city. By 1296, a market had been established at what is now known as Castle Square, from 1570 to 1584, Mary, Queen of Scots, was imprisoned in Sheffield Castle and Sheffield Manor. During the 1740s, a form of the steel process was discovered that allowed the manufacture of a better quality of steel than had previously been possible
20.
England
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England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west, the Irish Sea lies northwest of England and the Celtic Sea lies to the southwest. England is separated from continental Europe by the North Sea to the east, the country covers five-eighths of the island of Great Britain in its centre and south, and includes over 100 smaller islands such as the Isles of Scilly, and the Isle of Wight. England became a state in the 10th century, and since the Age of Discovery. The Industrial Revolution began in 18th-century England, transforming its society into the worlds first industrialised nation, Englands terrain mostly comprises low hills and plains, especially in central and southern England. However, there are uplands in the north and in the southwest, the capital is London, which is the largest metropolitan area in both the United Kingdom and the European Union. In 1801, Great Britain was united with the Kingdom of Ireland through another Act of Union to become the United Kingdom of Great Britain and Ireland. In 1922 the Irish Free State seceded from the United Kingdom, leading to the latter being renamed the United Kingdom of Great Britain, the name England is derived from the Old English name Englaland, which means land of the Angles. The Angles were one of the Germanic tribes that settled in Great Britain during the Early Middle Ages, the Angles came from the Angeln peninsula in the Bay of Kiel area of the Baltic Sea. The earliest recorded use of the term, as Engla londe, is in the ninth century translation into Old English of Bedes Ecclesiastical History of the English People. According to the Oxford English Dictionary, its spelling was first used in 1538. The earliest attested reference to the Angles occurs in the 1st-century work by Tacitus, Germania, the etymology of the tribal name itself is disputed by scholars, it has been suggested that it derives from the shape of the Angeln peninsula, an angular shape. An alternative name for England is Albion, the name Albion originally referred to the entire island of Great Britain. The nominally earliest record of the name appears in the Aristotelian Corpus, specifically the 4th century BC De Mundo, in it are two very large islands called Britannia, these are Albion and Ierne. But modern scholarly consensus ascribes De Mundo not to Aristotle but to Pseudo-Aristotle, the word Albion or insula Albionum has two possible origins. Albion is now applied to England in a poetic capacity. Another romantic name for England is Loegria, related to the Welsh word for England, Lloegr, the earliest known evidence of human presence in the area now known as England was that of Homo antecessor, dating to approximately 780,000 years ago. The oldest proto-human bones discovered in England date from 500,000 years ago, Modern humans are known to have inhabited the area during the Upper Paleolithic period, though permanent settlements were only established within the last 6,000 years
21.
Flat (music)
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In music, flat, or bemolle means lower in pitch. In music notation, the symbol, ♭, derived from a stylised lowercase b. Intonation or tuning is said to be flat when it is below the true pitch, the order of flats in the key signatures of music notation, following the circle of fifths, is B♭, E♭, A♭, D♭, G♭, C♭, and F♭. A mnemonic for this is, Before Eating A Doughnut Get Coffee First, the Unicode character ♭ can be found in the block Miscellaneous Symbols, its HTML entity is ♭. Under twelve tone equal temperament, C♭ for instance is the same as, or enharmonically equivalent to, B♮, in any other tuning system, such enharmonic equivalences in general do not exist. To allow extended just intonation, composer Ben Johnston uses a sharp as an accidental to indicate a note is raised 70.6 cents, double flats also exist, which look like and lower a note by two semitones, or a whole step. Less often one will encounter half, or three-quarter, or otherwise altered flats, the Unicode character
22.
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
23.
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
24.
Trigonometric functions
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In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane, Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation and this measure is the ratio of the length of a circular arc to its radius. In the case of an angle, the arc is centered at the vertex. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. The word angle comes from the Latin word angulus, meaning corner, cognate words are the Greek ἀγκύλος, meaning crooked, curved, both are connected with the Proto-Indo-European root *ank-, meaning to bend or bow. Euclid defines a plane angle as the inclination to each other, in a plane, according to Proclus an angle must be either a quality or a quantity, or a relationship. In mathematical expressions, it is common to use Greek letters to serve as variables standing for the size of some angle, lower case Roman letters are also used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples, in geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB, sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex. However, in geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant. Otherwise, a convention may be adopted so that ∠BAC always refers to the angle from B to C. Angles smaller than an angle are called acute angles. An angle equal to 1/4 turn is called a right angle, two lines that form a right angle are said to be normal, orthogonal, or perpendicular. Angles larger than an angle and smaller than a straight angle are called obtuse angles. An angle equal to 1/2 turn is called a straight angle, Angles larger than a straight angle but less than 1 turn are called reflex angles
25.
Hyperbolic function
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In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular functions. The inverse hyperbolic functions are the hyperbolic sine arsinh and so on. Just as the form a circle with a unit radius. The hyperbolic functions take a real argument called a hyperbolic angle, the size of a hyperbolic angle is twice the area of its hyperbolic sector. The hyperbolic functions may be defined in terms of the legs of a triangle covering this sector. Laplaces equations are important in areas of physics, including electromagnetic theory, heat transfer, fluid dynamics. In complex analysis, the hyperbolic functions arise as the parts of sine and cosine. When considered defined by a variable, the hyperbolic functions are rational functions of exponentials. Hyperbolic functions were introduced in the 1760s independently by Vincenzo Riccati, Riccati used Sc. and Cc. to refer to circular functions and Sh. and Ch. to refer to hyperbolic functions. Lambert adopted the names but altered the abbreviations to what they are today, the abbreviations sh and ch are still used in some other languages, like French and Russian. The hyperbolic functions are, Hyperbolic sine, sinh x = e x − e − x 2 = e 2 x −12 e x =1 − e −2 x 2 e − x. Hyperbolic cosine, cosh x = e x + e − x 2 = e 2 x +12 e x =1 + e −2 x 2 e − x, the complex forms in the definitions above derive from Eulers formula. One also has sech 2 x =1 − tanh 2 x csch 2 x = coth 2 x −1 for the other functions, sinh = sinh 2 = sgn cosh −12 where sgn is the sign function. All functions with this property are linear combinations of sinh and cosh, in particular the exponential functions e x and e − x, and it is possible to express the above functions as Taylor series, sinh x = x + x 33. + ⋯ = ∑ n =0 ∞ x 2 n +1, the function sinh x has a Taylor series expression with only odd exponents for x. Thus it is an odd function, that is, −sinh x = sinh, the function cosh x has a Taylor series expression with only even exponents for x. Thus it is a function, that is, symmetric with respect to the y-axis. The sum of the sinh and cosh series is the series expression of the exponential function
26.
Metre
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The metre or meter, is the base unit of length in the International System of Units. The metre is defined as the length of the path travelled by light in a vacuum in 1/299792458 seconds, the metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a metre bar. In 1960, the metre was redefined in terms of a number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted, the imperial inch is defined as 0.0254 metres. One metre is about 3 3⁄8 inches longer than a yard, Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use meter. Measuring devices are spelled -meter in all variants of English, the suffix -meter has the same Greek origin as the unit of length. This range of uses is found in Latin, French, English. Thus calls for measurement and moderation. In 1668 the English cleric and philosopher John Wilkins proposed in an essay a decimal-based unit of length, as a result of the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. In 1668, Wilkins proposed using Christopher Wrens suggestion of defining the metre using a pendulum with a length which produced a half-period of one second, christiaan Huygens had observed that length to be 38 Rijnland inches or 39.26 English inches. This is the equivalent of what is now known to be 997 mm, no official action was taken regarding this suggestion. In the 18th century, there were two approaches to the definition of the unit of length. One favoured Wilkins approach, to define the metre in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the metre as one ten-millionth of the length of a quadrant along the Earths meridian, that is, the distance from the Equator to the North Pole. This means that the quadrant would have defined as exactly 10000000 metres at that time. To establish a universally accepted foundation for the definition of the metre, more measurements of this meridian were needed. This portion of the meridian, assumed to be the length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator
27.
Young's modulus
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Youngs modulus, also known as the elastic modulus, is a measure of the stiffness of a solid material. It is a property of linear elastic solid materials. It defines the relationship between stress and strain in a material, Youngs modulus is named after the 19th-century British scientist Thomas Young. The term modulus is the diminutive of the Latin term modus which means measure, a solid material will deform when a load is applied to it. If it returns to its shape after the load is removed. In the range where the ratio between load and deformation remains constant, the curve is linear. Not many materials are linear and elastic beyond a small amount of deformation, although such a material cannot exist, a material with a very high Youngs modulus can be approximated as rigid. g. The technical definition is, the ratio of the stress along an axis to the strain along that axis in the range of stress in which Hookes law holds, Youngs modulus is the ratio of stress to strain, and so Youngs modulus has units of pressure. Its SI unit is therefore the pascal, the practical units used are megapascals or gigapascals. In United States customary units, it is expressed as pounds per square inch, the abbreviation ksi refers to kips per square inch. A kip is an Imperial unit of force and is equal to 1000 pounds-force, the Youngs modulus enables the calculation of the change in the dimension of a bar made of an isotropic elastic material under tensile or compressive loads. For instance, it predicts how much a material sample extends under tension or shortens under compression, the Youngs modulus directly applies to cases of uniaxial stress, that is tensile or compressive stress in one direction and no stress in the other directions. Youngs modulus is used in order to predict the deflection that will occur in a statically determinate beam when a load is applied at a point in between the beams supports. Other elastic calculations usually require the use of one additional property, such as the shear modulus. Any two of these parameters are sufficient to fully describe elasticity in an isotropic material, Youngs modulus represents the factor of proportionality in Hookes law, which relates the stress and the strain. However, Hookes law is valid under the assumption of an elastic. If the range over which Hookes law is valid is large compared to the typical stress that one expects to apply to the material. Otherwise the material is said to be non-linear, steel, carbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear
28.
Pascal (unit)
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The pascal is the SI derived unit of pressure used to quantify internal pressure, stress, Youngs modulus and ultimate tensile strength. It is defined as one newton per square meter and it is named after the French polymath Blaise Pascal. Common multiple units of the pascal are the hectopascal which is equal to one millibar, the unit of measurement called standard atmosphere is defined as 101,325 Pa and approximates to the average pressure at sea-level at the latitude 45° N. Meteorological reports typically state atmospheric pressure in hectopascals, the unit is named after Blaise Pascal, noted for his contributions to hydrodynamics and hydrostatics, and experiments with a barometer. The name pascal was adopted for the SI unit newton per square metre by the 14th General Conference on Weights, one pascal is the pressure exerted by a force of magnitude one newton perpendicularly upon an area of one square metre. The unit of measurement called atmosphere or standard atmosphere is 101325 Pa and this value is often used as a reference pressure and specified as such in some national and international standards, such as ISO2787, ISO2533 and ISO5024. In contrast, IUPAC recommends the use of 100 kPa as a standard pressure when reporting the properties of substances, geophysicists use the gigapascal in measuring or calculating tectonic stresses and pressures within the Earth. Medical elastography measures tissue stiffness non-invasively with ultrasound or magnetic resonance imaging, in materials science and engineering, the pascal measures the stiffness, tensile strength and compressive strength of materials. In engineering use, because the pascal represents a small quantity. The pascal is also equivalent to the SI unit of energy density and this applies not only to the thermodynamics of pressurised gases, but also to the energy density of electric, magnetic, and gravitational fields. In measurements of sound pressure, or loudness of sound, one pascal is equal to 94 decibels SPL, the quietest sound a human can hear, known as the threshold of hearing, is 0 dB SPL, or 20 µPa. The airtightness of buildings is measured at 50 Pa, the units of atmospheric pressure commonly used in meteorology were formerly the bar, which was close to the average air pressure on Earth, and the millibar. Since the introduction of SI units, meteorologists generally measure pressures in hectopascals unit, exceptions include Canada and Portugal, which use kilopascals. In many other fields of science, the SI is preferred, many countries also use the millibar or hectopascal to give aviation altimeter settings. In practically all fields, the kilopascal is used instead. Centimetre of water Metric prefix Orders of magnitude Pascals law
29.
Second moment of area
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The second moment of area is typically denoted with either an I for an axis that lies in the plane or with a J for an axis perpendicular to the plane. In both cases, it is calculated with an integral over the object in question. Its unit of dimension when working with the International System of Units is meters to the fourth power, in each case the integral is over all the infinitesimal elements of area, dA, in some two-dimensional cross-section. The MOI, in sense, is the analog of mass for rotational problems. In engineering, Moment of Inertia commonly refers to the moment of the area. The parallel axis theorem states I x ′ = I x + A d 2 where A is the area of the shape, a similar statement can be made about a y ′ axis and the parallel centroidal y axis. Or, in general, any centroidal B axis and a parallel B ′ axis, for the simplicity of calculation, it is often desired to define the polar moment of area in terms of two area moments of inertia. The simplest case relates J z to I x and I y, for more complex areas, it is often easier to divide the area into a series of simpler shapes. The second moment of area for the shape is the sum of the second moment of areas of all of its parts about a common axis. This can include shapes that are missing, in case the second moment of area of the missing areas are subtracted. In other words, the moment of area of missing parts are considered negative for the method of composite shapes. See list of moments of area for other shapes. Consider a rectangle with base b and height h whose centroid is located at the origin, because of the symmetry of the annulus, the centroid also lies at the origin. We can determine the moment of inertia, J z. This polar moment of inertia is equivalent to the moment of inertia of a circle with radius r 2 minus the polar moment of inertia of a circle with radius r 1. First, let us derive the polar moment of inertia of a circle with radius r with respect to the origin, in this case, it is easier to directly calculate J z as we already have r 2, which has both an x and y component. Instead of obtaining the second moment of area from Cartesian coordinates as done in the previous section and this would be done like this. A polygon is assumed to have n vertices, numbered in counter-clockwise fashion, if polygon vertices are numbered clockwise, returned values will be negative, but absolute values will be correct
30.
Density
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The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume, ρ = m V, where ρ is the density, m is the mass, and V is the volume. In some cases, density is defined as its weight per unit volume. For a pure substance the density has the numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity, osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. Thus a relative density less than one means that the floats in water. The density of a material varies with temperature and pressure and this variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object, increasing the temperature of a substance decreases its density by increasing its volume. In most materials, heating the bottom of a results in convection of the heat from the bottom to the top. This causes it to rise relative to more dense unheated material, the reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is a property in that increasing the amount of a substance does not increase its density. Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass, upon this discovery, he leapt from his bath and ran naked through the streets shouting, Eureka. As a result, the term eureka entered common parlance and is used today to indicate a moment of enlightenment, the story first appeared in written form in Vitruvius books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time, from the equation for density, mass density has units of mass divided by volume. As there are units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per metre and the cgs unit of gram per cubic centimetre are probably the most commonly used units for density.1,000 kg/m3 equals 1 g/cm3. In industry, other larger or smaller units of mass and or volume are often more practical, see below for a list of some of the most common units of density
31.
Kilogram
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The kilogram or kilogramme is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype of the Kilogram. The avoirdupois pound, used in both the imperial and US customary systems, is defined as exactly 0.45359237 kg, making one kilogram approximately equal to 2.2046 avoirdupois pounds. Other traditional units of weight and mass around the world are also defined in terms of the kilogram, the gram, 1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimeter of water at the melting point of ice. The final kilogram, manufactured as a prototype in 1799 and from which the IPK was derived in 1875, had an equal to the mass of 1 dm3 of water at its maximum density. The kilogram is the only SI base unit with an SI prefix as part of its name and it is also the only SI unit that is still directly defined by an artifact rather than a fundamental physical property that can be reproduced in different laboratories. Three other base units and 17 derived units in the SI system are defined relative to the kilogram, only 8 other units do not require the kilogram in their definition, temperature, time and frequency, length, and angle. At its 2011 meeting, the CGPM agreed in principle that the kilogram should be redefined in terms of the Planck constant, the decision was originally deferred until 2014, in 2014 it was deferred again until the next meeting. There are currently several different proposals for the redefinition, these are described in the Proposed Future Definitions section below, the International Prototype Kilogram is rarely used or handled. In the decree of 1795, the term gramme thus replaced gravet, the French spelling was adopted in the United Kingdom when the word was used for the first time in English in 1797, with the spelling kilogram being adopted in the United States. In the United Kingdom both spellings are used, with kilogram having become by far the more common, UK law regulating the units to be used when trading by weight or measure does not prevent the use of either spelling. In the 19th century the French word kilo, a shortening of kilogramme, was imported into the English language where it has used to mean both kilogram and kilometer. In 1935 this was adopted by the IEC as the Giorgi system, now known as MKS system. In 1948 the CGPM commissioned the CIPM to make recommendations for a practical system of units of measurement. This led to the launch of SI in 1960 and the subsequent publication of the SI Brochure, the kilogram is a unit of mass, a property which corresponds to the common perception of how heavy an object is. Mass is a property, that is, it is related to the tendency of an object at rest to remain at rest, or if in motion to remain in motion at a constant velocity. Accordingly, for astronauts in microgravity, no effort is required to hold objects off the cabin floor, they are weightless. However, since objects in microgravity still retain their mass and inertia, the ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses. On April 7,1795, the gram was decreed in France to be the weight of a volume of pure water equal to the cube of the hundredth part of the metre
32.
Area
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Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the surface of a three-dimensional object. It is the analog of the length of a curve or the volume of a solid. The area of a shape can be measured by comparing the shape to squares of a fixed size, in the International System of Units, the standard unit of area is the square metre, which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the area as three such squares. In mathematics, the square is defined to have area one. There are several formulas for the areas of simple shapes such as triangles, rectangles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles, for shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a motivation for the historical development of calculus. For a solid such as a sphere, cone, or cylinder. Formulas for the areas of simple shapes were computed by the ancient Greeks. Area plays an important role in modern mathematics, in addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, in general, area in higher mathematics is seen as a special case of volume for two-dimensional regions. Area can be defined through the use of axioms, defining it as a function of a collection of certain plane figures to the set of real numbers and it can be proved that such a function exists. An approach to defining what is meant by area is through axioms, area can be defined as a function from a collection M of special kind of plane figures to the set of real numbers which satisfies the following properties, For all S in M, a ≥0. If S and T are in M then so are S ∪ T and S ∩ T, if S and T are in M with S ⊆ T then T − S is in M and a = a − a. If a set S is in M and S is congruent to T then T is also in M, every rectangle R is in M. If the rectangle has length h and breadth k then a = hk, let Q be a set enclosed between two step regions S and T
33.
Musical instrument
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A musical instrument is an instrument created or adapted to make musical sounds. In principle, any object that produces sound can be a musical instrument—it is through purpose that the object becomes a musical instrument, the history of musical instruments dates to the beginnings of human culture. Early musical instruments may have used for ritual, such as a trumpet to signal success on the hunt. Cultures eventually developed composition and performance of melodies for entertainment, Musical instruments evolved in step with changing applications. The date and origin of the first device considered an instrument is disputed. The oldest object that some refer to as a musical instrument. Some consensus dates early flutes to about 37,000 years ago, many early musical instruments were made from animal skins, bone, wood, and other non-durable materials. Musical instruments developed independently in many populated regions of the world, however, contact among civilizations caused rapid spread and adaptation of most instruments in places far from their origin. By the Middle Ages, instruments from Mesopotamia were in maritime Southeast Asia, development in the Americas occurred at a slower pace, but cultures of North, Central, and South America shared musical instruments. By 1400, musical instrument development slowed in areas and was dominated by the Occident. Musical instrument classification is a discipline in its own right, Instruments can be classified by their effective range, their material composition, their size, etc. However, the most common method, Hornbostel-Sachs, uses the means by which they produce sound. The academic study of instruments is called organology. Once humans moved from making sounds with their bodies—for example, by using objects to create music from sounds. Primitive instruments were designed to emulate natural sounds, and their purpose was ritual rather than entertainment. The concept of melody and the pursuit of musical composition were unknown to early players of musical instruments. A player sounding a flute to signal the start of a hunt does so without thought of the notion of making music. Musical instruments are constructed in an array of styles and shapes
34.
Electronic tuner
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Guitar tuner redirects here, but can also refer to the string tension adjusters also called machine heads. For the radio receiver component, see Tuner In music, a tuner is a device that detects. Pitch is the highness or lowness of a note, which is typically measured in Hertz. Simple tuners indicate—typically with an analog needle-dial, LEDs, or an LCD screen—whether a pitch is lower, higher, in the 2010s, software applications can turn a smartphone, tablet, or personal computer into a tuner. More complex and expensive tuners indicate pitch more precisely, Tuners vary in size from units that fit in a pocket to 19 rack-mount units. Instrument technicians, piano tuners, and violin-family luthiers typically use more expensive, the simplest tuners detect and display tuning only for a single pitch—often A or E—or for a small number of pitches, such as the six used in the standard tuning of a guitar. More complex tuners offer chromatic tuning for all 12 pitches of the equally tempered octave, among the most accurate tuning devices, strobe tuners work differently than regular electronic tuners. They are stroboscopes that flicker a light at the frequency as the note. The light shines on a wheel that spins at a precise speed, the interaction of the light and regularly-spaced marks on the wheel creates a stroboscopic effect that makes the marks for a particular pitch appear to stand still when the pitch is in tune. These can tune instruments and audio devices more accurately than most non-strobe tuners, regular electronic tuners contain either an input jack for electric instruments, a microphone, or a clip-on sensor or some combination of these inputs. Pitch detection circuitry drives some type of display, some tuners have an output, or through-put, so the tuner can connect in-line from an electric instrument to an instrument amplifier or mixing console. Small tuners are usually battery powered, many battery powered tuners also have a jack for an optional AC power supply. Most musical instruments generate a complex waveform. It contains a number of partials, including the fundamental frequency. Each instrument produces different ratios of harmonics, which is what makes notes of the pitch played on different instruments sound different. As well, this waveform constantly changes and this means that for non-strobe tuners to be accurate, the tuner must process a number of cycles and use the pitch average to drive its display. Background noise from other musicians or harmonic overtones from the instrument can impede the electronic tuner from locking onto the input frequency. This is why the needle or display on regular electronic tuners tends to waver when a pitch is played, small movements of the needle, or LED, usually represent a tuning error of 1 cent
35.
Electromagnet
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An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. The magnetic field disappears when the current is turned off, electromagnets usually consist of insulated wire wound into a coil. A current through the wire creates a field which is concentrated in the hole in the center of the coil. The main advantage of an electromagnet over a permanent magnet is that the field can be quickly changed by controlling the amount of electric current in the winding. However, unlike a permanent magnet that needs no power, an electromagnet requires a supply of current to maintain the magnetic field. Electromagnets are also employed in industry for picking up and moving heavy objects such as scrap iron. Danish scientist Hans Christian Ørsted discovered in 1820 that electric currents create magnetic fields, british scientist William Sturgeon invented the electromagnet in 1824. His first electromagnet was a piece of iron that was wrapped with about 18 turns of bare copper wire. The iron was varnished to insulate it from the windings, when a current was passed through the coil, the iron became magnetized and attracted other pieces of iron, when the current was stopped, it lost magnetization. Sturgeon displayed its power by showing that although it only weighed seven ounces, however, Sturgeons magnets were weak because the uninsulated wire he used could only be wrapped in a single spaced out layer around the core, limiting the number of turns. Beginning in 1830, US scientist Joseph Henry systematically improved and popularized the electromagnet, the first major use for electromagnets was in telegraph sounders. A portative electromagnet is one designed to just hold material in place, a tractive electromagnet applies a force and moves something. The solenoid is a coil of wire, and the plunger is made of a such as soft iron. Applying a current to the solenoid applies a force to the plunger, the plunger stops moving when the forces upon it are balanced. For example, the forces are balanced when the plunger is centered in the solenoid, the maximum uniform pull happens when one end of the plunger is at the middle of the solenoid. For units using inches, pounds force, and amperes with long, slender, solenoids, for example, a 12-inch long coil with a long plunger of 1-square inch cross section and 11,200 ampere-turns had a maximum pull of 8.75 pounds. The maximum pull is increased when a stop is inserted into the solenoid. The stop becomes a magnet that will attract the plunger, it adds little to the pull when the plunger is far away
36.
Electronic oscillator
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An electronic oscillator is an electronic circuit that produces a periodic, oscillating electronic signal, often a sine wave or a square wave. Oscillators convert direct current from a supply to an alternating current signal. They are widely used in electronic devices. Oscillators are often characterized by the frequency of their output signal and this term is typically used in the field of audio synthesizers, to distinguish it from an audio frequency oscillator. An audio oscillator produces frequencies in the range, about 16 Hz to 20 kHz. An RF oscillator produces signals in the frequency range of about 100 kHz to 100 GHz. Oscillators designed to produce a high-power AC output from a DC supply are usually called inverters, there are two main types of electronic oscillator, the linear or harmonic oscillator and the nonlinear or relaxation oscillator. The harmonic, or linear, oscillator produces a sinusoidal output, when the power supply to the amplifier is first switched on, electronic noise in the circuit provides a non-zero signal to get oscillations started. The noise travels around the loop and is amplified and filtered until very quickly it converges on a wave at a single frequency. RC oscillators are used to generate lower frequencies, for example in the audio range. Common types of RC oscillator circuits are the phase shift oscillator, in an LC oscillator circuit, the filter is a tuned circuit consisting of an inductor and capacitor connected together. Charge flows back and forth between the plates through the inductor, so the tuned circuit can store electrical energy oscillating at its resonant frequency. There are small losses in the circuit, but the amplifier compensates for those losses and supplies the power for the output signal. Typical LC oscillator circuits are the Hartley, Colpitts and Clapp circuits, in a crystal oscillator circuit the filter is a piezoelectric crystal. The crystal mechanically vibrates as a resonator, and its frequency of vibration determines the oscillation frequency, crystals have very high Q-factor and also better temperature stability than tuned circuits, so crystal oscillators have much better frequency stability than LC or RC oscillators. Crystal oscillators are the most common type of linear oscillator, used to stabilize the frequency of most radio transmitters, crystal oscillators often use the same circuits as LC oscillators, with the crystal replacing the tuned circuit, the Pierce oscillator circuit is also commonly used. Quartz crystals are generally limited to frequencies of 30 MHz or below, other types of resonator, dielectric resonators and surface acoustic wave devices, are used to control higher frequency oscillators, up into the microwave range. For example, SAW oscillators are used to generate the signal in cell phones
37.
Keyboard instrument
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A keyboard instrument is a musical instrument played using a keyboard. The most common of these are the piano, organ, and various keyboards, including synthesizers. Other keyboard instruments include celestas, which are struck idiophones operated by a keyboard, and carillons, today, the term keyboard often refers to keyboard-style synthesizers. Another important use of the keyboard is in historical musicology. Particularly in the 18th century, the harpsichord, the clavichord, and the piano were in competition. Hence in a phrase like Mozart excelled as a player the word keyboard is usefully noncommittal. The earliest known keyboard instrument was the Ancient Greek hydraulis, a type of pipe organ, the keys were likely balanced and could be played with a light touch, as is clear from the reference in a Latin poem by Claudian, who says magna levi detrudens murmura tactu. Intent, that is “let him thunder forth as he presses out mighty roarings with a light touch”, from its invention until the fourteenth century, the organ remained the only keyboard instrument. Often, the organ did not feature a keyboard at all, almost every keyboard until the fifteenth century had seven naturals to each octave. The clavichord and the harpsichord appeared during the 14th century—the clavichord probably being earlier, the harpsichord and clavichord were both common until widespread adoption of the piano in the 18th century, after which their popularity decreased. The piano was revolutionary, because a pianist could vary the volume of the sound by varying the vigor with which each key was struck. The pianos full name is gravicèmbalo con piano e forte meaning harpsichord with soft and loud but can be shortened to piano-forte, which means soft-loud in Italian. In its current form, the piano is a product of the late 19th century, in fact, the modern piano is significantly different from even the 19th-century pianos used by Liszt, Chopin, and Brahms. See Piano history and musical performance, keyboard instruments were further developed in the early twentieth century. Early electromechanical instruments, such as the Ondes Martenot, appeared early in the century and this was a very important contribution to the keyboards history. Much effort has gone into creating an instrument that sounds like the piano but lacks its size, the electric piano and electronic piano were early efforts that, while useful instruments in their own right, did not convincingly reproduce the timbre of the piano. Electric and electronic organs were developed during the same period, more recent electronic keyboard designs strive to emulate the sound of specific make and model pianos using digital samples and computer models. Concerns celebrated keyboard players and the various instruments used over the centuries
38.
Rhodes piano
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The Rhodes piano is an electric piano invented by Harold Rhodes, which became particularly popular throughout the 1970s. The instrument evolved from Rhodes attempt to manufacture pianos to teach recovering soldiers during World War II under a strict budget, Fender started marketing the Piano Bass, a cut-down version of the piano, but the full-size instrument did not appear until after the sale to CBS in 1965. CBS oversaw mass production of the Rhodes piano in the 1970s, and it was used extensively through the decade, particularly in jazz, pop, the company was eventually sold to Roland, who manufactured digital versions of the Rhodes without authorization or approval from its inventor. In the 1990s, the instrument enjoyed a resurgence in popularity, although Harold Rhodes died in 2000, the instrument has since been reissued, and his teaching methods are still receiving active use. The Rhodes piano features a keyboard with a layout to a traditional acoustic piano. The touch and action of the keyboard is designed to be as close to a piano as possible, pressing a key results in a hammer striking a thin metal rod called a tine, connected to a larger tone bar. The whole tone generator assembly acts as a fork, the tone bar reinforcing and extending the vibrations of the tine. A pickup sits opposite the tine, picking up its vibrations, the Suitcase model Rhodes includes a built-in power amplifier and a tremolo feature that bounces the output signal from the piano in stereo across two speakers. This feature is mistakenly labeled vibrato on some models to be consistent with the labelling on Fender amplifiers, although the Rhodes has the same mechanical operation as a piano, its sound is very different. The sound produced by the tines has a mellow timbre. Putting the two close together gives a bell sound. The instruments sound has been compared with the Wurlitzer electric piano, which uses a similar technology. The Rhodes has a sustain, while the Wurlitzer produces significant harmonics when the keys are played hard. Rhodes started teaching piano when he was 19 and he dropped out of studying at the University of Southern California in 1929 to support his family through the Great Depression by full-time teaching. As a teacher, he designed a method that combined classical and jazz music, which became popular across the United States, Rhodes continued to teach the piano through his lifetime, and the piano method continues to be taught today by a team led by Joseph Brandsetter. By 1942, Rhodes was working for the Army Air Corps and he was unable to supply enough acoustic pianos, so decided to develop a miniature electric model that could be made from surplus army parts. Rhodes won a award for his piano design and subsequently put the model into production for piano teachers during the 1950s. These were retrospectively known as the Pre-Piano, in 1959, Rhodes entered a joint venture with Leo Fender to manufacture the instruments
39.
Dulcitone
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A dulcitone is a keyboard instrument in which sound is produced by a range of tuning forks, which vibrate when struck by felt-covered hammers activated by the keyboard. The dulcitone is an instrument of the idiophone class, it sounds an octave higher than the standard written pitch. It has a five octave written range from AA to a3, a significant feature of the dulcitone was its portability, a product of its lightweight and compact construction and the fact that the tuning forks were not prone to going out of tune. However, the volume produced is limited, and the dulcitones part is frequently substituted by a glockenspiel. Two pieces scored for the dulcitone is Vincent dIndys Song of the Bells and Percy Graingers The Power of Rome, surviving examples exist as far afield as New Zealand, where one is preserved in the Whittakers Musical Museum. The dulcitone continues to play a role in popular music, arthur Jeffes of Penguin Cafe plays a dulcitone on several tracks of his 2012 album Insofar. Greg Cook of the Vagaband also plays dulcitone on their 2012 album Town and Country, rhodes piano, technically an electrically amplified dulcitone. Celesta, similar to the dulcitone in that bars are struck by hammers
40.
Quartz clock
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A quartz clock is a clock that uses an electronic oscillator that is regulated by a quartz crystal to keep time. This crystal oscillator creates a signal with very precise frequency, so that quartz clocks are at least an order of more accurate than mechanical clocks. Generally, some form of digital logic counts the cycles of this signal and provides a numeric display, usually in units of hours, minutes. The first quartz clock was built in 1927 by Warren Marrison, chemically, quartz is a compound called silicon dioxide. Many materials can be formed into plates that will resonate, however, quartz is also a piezoelectric material, that is, when a quartz crystal is subject to mechanical stress, such as bending, it accumulates electrical charge across some planes. In a reverse effect, if charges are placed across the crystal plane, since quartz can be directly driven by an electric signal, no additional speaker or microphone is required to use it in a resonator. Similar crystals are used in low-end phonograph cartridges, The movement of the stylus flexes a quartz crystal, which produces a small voltage, Quartz microphones are still available, though not common. Quartz has an advantage in that its size does not change much as temperature fluctuates. Fused quartz is used for laboratory equipment that must not change shape along with the temperature. A quartz plates resonance frequency, based on its size, will not significantly rise or fall, similarly, since its resonator does not change shape, a quartz clock will remain relatively accurate as the temperature changes. In the early 20th century, radio engineers sought a precise, stable source of radio frequencies, however, when Walter Guyton Cady found that quartz can resonate with less equipment and better temperature stability, steel resonators disappeared within a few years. Later, scientists at NIST discovered that a crystal oscillator could be accurate than a pendulum clock. The electronic circuit is an oscillator, an amplifier whose output passes through the quartz resonator, the resonator acts as an electronic filter, eliminating all but the single frequency of interest. The output of the resonator feeds back to the input of the amplifier, when the circuit starts up, even a single shot can cascade to bringing the oscillator at the desired frequency. If the amplifier is too perfect, the oscillator will not start, the frequency at which the crystal oscillates depends on its shape, size, and the crystal plane on which the quartz is cut. The positions at which electrodes are placed can slightly change the tuning, if the crystal is accurately shaped and positioned, it will oscillate at a desired frequency. In nearly all quartz watches, the frequency is 32,768 Hz, and this frequency is a power of two, just high enough so most people cannot hear it, yet low enough to permit inexpensive counters to derive a 1-second pulse. A 15-bit binary digital counter driven by the frequency will overflow once per second, the pulse-per-second output can be used to drive many kinds of clocks
41.
Ultrasound
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Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Ultrasound is no different from normal sound in its physical properties and this limit varies from person to person and is approximately 20 kilohertz in healthy, young adults. Ultrasound devices operate with frequencies from 20 kHz up to several gigahertz, Ultrasound is used in many different fields. Ultrasonic devices are used to detect objects and measure distances, Ultrasound imaging or sonography is often used in medicine. In the nondestructive testing of products and structures, ultrasound is used to detect invisible flaws, industrially, ultrasound is used for cleaning, mixing, and to accelerate chemical processes. Animals such as bats and porpoises use ultrasound for locating prey, scientist are also studying ultrasound using graphene diaphragms as a method of communication. Acoustics, the science of sound, starts as far back as Pythagoras in the 6th century BC, echolocation in bats was discovered by Lazzaro Spallanzani in 1794, when he demonstrated that bats hunted and navigated by inaudible sound and not vision. The first technological application of ultrasound was an attempt to detect submarines by Paul Langevin in 1917, the piezoelectric effect, discovered by Jacques and Pierre Curie in 1880, was useful in transducers to generate and detect ultrasonic waves in air and water. Ultrasound is defined by the American National Standards Institute as sound at frequencies greater than 20 kHz, in air at atmospheric pressure ultrasonic waves have wavelengths of 1.9 cm or less. The upper frequency limit in humans is due to limitations of the middle ear, auditory sensation can occur if high‐intensity ultrasound is fed directly into the human skull and reaches the cochlea through bone conduction, without passing through the middle ear. Children can hear some high-pitched sounds that older adults cannot hear, the Mosquito is an electronic device that uses a high pitched frequency to deter loitering by young people. Bats use a variety of ultrasonic ranging techniques to detect their prey and they can detect frequencies beyond 100 kHz, possibly up to 200 kHz. Many insects have good hearing and most of these are nocturnal insects listening for echolocating bats. This includes many groups of moths, beetles, praying mantids, upon hearing a bat, some insects will make evasive manoeuvres to escape being caught. Ultrasonic frequencies trigger an action in the noctuid moth that cause it to drop slightly in its flight to evade attack. Tiger moths also emit clicks which may disturb bats echolocation, dogs and cats hearing range extends into the ultrasound, the top end of a dogs hearing range is about 45 kHz, while a cats is 64 kHz. The wild ancestors of cats and dogs evolved this higher hearing range to hear sounds made by their preferred prey. A dog whistle is a whistle that emits ultrasound, used for training and calling dogs, porpoises have the highest known upper hearing limit, at around 160 kHz
42.
Bulova
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Bulova is an American manufacturer of watches and clocks. Its headquarters is located in New York City, bulovas Swiss-Made line is known as Bulova Accu•Swiss or formerly, Bulova Accutron. It is owned by Citizen Watch Co, Bulova was founded and incorporated as the J. Bulova Company in 1875 by Joseph Bulova, an immigrant from Bohemia. It was reincorporated under the name Bulova Watch Company in 1923, in 1912, he launched his first plant dedicated entirely to the production of watches. Manufacturing watches at their factory in Biel, Bulova began a mass production never seen in the world of watchmaking until then. In 1919, Joseph Bulova offered the first complete range of watches for men, the iconic visual style of his first popular advertising made its watches popular with the American public. But beyond the style, precision and technological research also became an endless quest for Bulova. In 1927, he set up an observatory on the roof of a skyscraper located at 580 5th Avenue to make measurements that would enable him to determine very precisely universal time. Bulova established its operations in Woodside, New York, and Flushing, New York, where it made innovations in watchmaking and its horological innovations included the Accutron watch, which used a resonating tuning fork as a means of regulating the time-keeping function. Bulova became a watch company in 1923. In 1927, Charles A. Lindbergh was the first pilot to cross the Atlantic nonstop and his crossing earned him a Bulova Watch and a check for $1000, and it became an emblem for the brand that created the model Lone Eagle in his likeness. Bulova claims to have been the first manufacturer to offer electric clocks beginning in 1931, in the 1930s and 1940s, the brand was a huge success with its rectangular plated watches whose case was strongly curved to better fit the curve of the wrist. Bulova produced the worlds first official television commercial, on July 1,1941, the announcement, for which the company paid anywhere from $4.00 to $9.00, displayed a WNBT test pattern modified to look like a clock with the hands showing the time. The Bulova logo, with the phrase Bulova Watch Time, was shown in the lower quadrant of the test pattern while the second hand swept around the dial for one minute. The Joseph Bulova School of Watchmaking was founded in 1945 by Arde Bulova, Chairman of the Board, the school later became a full-fledged rehabilitation facility, an advocate for disabled people nationwide, and one of the founders of wheelchair sports in the United States. In 1967, Bulova bought the Manufacture des montres Universal Perret Frères SA at Geneva, the factory in Biel was closed in 1983. Bulova’s Accutron watches, first sold in October 1960, use a 360 hertz tuning fork instead of a wheel as the timekeeping element. The inventor, Max Hetzel, was born in Basel, Switzerland, the tuning fork was powered by a one-transistor electronic oscillator circuit, so the Accutron qualifies as the first electronic watch
43.
Crystal oscillator
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A crystal oscillator is an electronic oscillator circuit that uses the mechanical resonance of a vibrating crystal of piezoelectric material to create an electrical signal with a precise frequency. Quartz crystals are manufactured for frequencies from a few tens of kilohertz to hundreds of megahertz, more than two billion crystals are manufactured annually. Most are used for devices such as wristwatches, clocks, radios, computers. Quartz crystals are found inside test and measurement equipment, such as counters, signal generators. A crystal oscillator is an oscillator circuit that uses a piezoelectric resonator. Crystal is the term used in electronics for the frequency-determining component. A more accurate term for it is piezoelectric resonator, Crystals are also used in other types of electronic circuits, such as crystal filters. Piezoelectric resonators are sold as components for use in crystal oscillator circuits. An example is shown in the picture and they are also often incorporated in a single package with the crystal oscillator circuit, shown on the righthand side. Piezoelectricity was discovered by Jacques and Pierre Curie in 1880, paul Langevin first investigated quartz resonators for use in sonar during World War I. Cady built the first quartz oscillator in 1921. Other early innovators in quartz crystal oscillators include G. W. Pierce, Quartz crystal oscillators were developed for high-stability frequency references during the 1920s and 1930s. Prior to crystals, radio stations controlled their frequency with tuned circuits, since broadcast stations were assigned frequencies only 10 kHz apart, interference between adjacent stations due to frequency drift was a common problem. In 1928, Warren Marrison of Bell Telephone Laboratories developed the first quartz-crystal clock, with accuracies of up to 1 second in 30 years, quartz clocks replaced precision pendulum clocks as the worlds most accurate timekeepers until atomic clocks were developed in the 1950s. Using the early work at Bell Labs, AT&T eventually established their Frequency Control Products division, later spun off, a number of firms started producing quartz crystals for electronic use during this time. Using what are now considered primitive methods, about 100,000 crystal units were produced in the United States during 1939, through World War II crystals were made from natural quartz crystal, virtually all from Brazil. By the 1970s virtually all crystals used in electronics were synthetic, although crystal oscillators still most commonly use quartz crystals, devices using other materials are becoming more common, such as ceramic resonators. A crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, almost any object made of an elastic material could be used like a crystal, with appropriate transducers, since all objects have natural resonant frequencies of vibration
44.
Watch
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A watch is a small timepiece intended to be carried or worn by a person. It is designed to keep working despite the motions caused by the persons activities, a wristwatch is designed to be worn around the wrist, attached by a watch strap or other type of bracelet. A pocket watch is designed for a person to carry in a pocket, watches evolved in the 17th century from spring-powered clocks, which appeared as early as the 14th century. During most of its history the watch was a device, driven by clockwork, powered by winding a mainspring. In the 1960s the electronic quartz watch was invented, which was powered by a battery, by the 1980s the quartz watch had taken over most of the market from the mechanical watch. Today most inexpensive and medium-priced watches, used mainly for timekeeping, have quartz movements, various extra features, called complications, such as moon-phase displays and the different types of tourbillon, are sometimes included. Modern watches often display the day, date, month and year, time-related features such as timers, chronographs and alarm functions are common. Some modern designs incorporate calculators, GPS and Bluetooth technology or have heart-rate monitoring capabilities, some watches use radio clock technology to regularly correct the time. Developments in the 2010s include smartwatches, which are elaborate computer-like electronic devices designed to be worn on a wrist and they generally incorporate timekeeping functions, but these are only small fractions of what the smartwatch can do. The study of timekeeping is known as horology, watches evolved from portable spring-driven clocks, which first appeared in 15th century Europe. Watches werent widely worn in pockets until the 17th century, one account says that the word watch came from the Old English word woecce which meant watchman, because it was used by town watchmen to keep track of their shifts at work. Another says that the term came from 17th century sailors, who used the new mechanisms to time the length of their shipboard watches, the increased accuracy of the balance wheel focused attention on errors caused by other parts of the movement, igniting a two-century wave of watchmaking innovation. The first thing to be improved was the escapement, the verge escapement was replaced in quality watches by the cylinder escapement, invented by Thomas Tompion in 1695 and further developed by George Graham in the 1720s. The British had predominated in watch manufacture for much of the 17th and 18th centuries, aaron Lufkin Dennison started a factory in 1851 in Massachusetts that used interchangeable parts, and by 1861 it was running a successful enterprise incorporated as the Waltham Watch Company. The concept of the wristwatch goes back to the production of the very earliest watches in the 16th century, elizabeth I of England received a wristwatch from Robert Dudley in 1571, described as an arm watch. The oldest surviving wristwatch is one made in 1806 and given to Joséphine de Beauharnais, from the beginning, wrist watches were almost exclusively worn by women, while men used pocket-watches up until the early 20th century. The Garstin Company of London patented a Watch Wristlet design in 1893, officers in the British Army began using wristwatches during colonial military campaigns in the 1880s, such as during the Anglo-Burma War of 1885. In continental Europe Girard-Perregaux and other Swiss watch makers began supplying German naval officers with wrist watches in about 1880 and these early models were essentially standard pocket-watches fitted to a leather strap but, by the early 20th century, manufacturers began producing purpose-built wristwatches
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Piezoelectricity
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Piezoelectricity /piˌeɪzoʊˌilɛkˈtrɪsɪti/ is the electric charge that accumulates in certain solid materials in response to applied mechanical stress. The word piezoelectricity means electricity resulting from pressure and it is derived from the Greek piezō or piezein, which means to squeeze or press, and ēlektron, which means amber, an ancient source of electric charge. Piezoelectricity was discovered in 1880 by French physicists Jacques and Pierre Curie, the piezoelectric effect is understood as the linear electromechanical interaction between the mechanical and the electrical state in crystalline materials with no inversion symmetry. The piezoelectric effect is a process in that materials exhibiting the direct piezoelectric effect also exhibit the reverse piezoelectric effect. For example, lead zirconate titanate crystals will generate measurable piezoelectricity when their structure is deformed by about 0. 1% of the original dimension. Conversely, those same crystals will change about 0. 1% of their static dimension when an electric field is applied to the material. The inverse piezoelectric effect is used in the production of sound waves. The pyroelectric effect, by which a material generates a potential in response to a temperature change, was studied by Carl Linnaeus. Drawing on this knowledge, both René Just Haüy and Antoine César Becquerel posited a relationship between stress and electric charge, however, experiments by both proved inconclusive. The first demonstration of the piezoelectric effect was in 1880 by the brothers Pierre Curie. Quartz and Rochelle salt exhibited the most piezoelectricity, the Curies, however, did not predict the converse piezoelectric effect. The converse effect was mathematically deduced from fundamental principles by Gabriel Lippmann in 1881. For the next few decades, piezoelectricity remained something of a laboratory curiosity, more work was done to explore and define the crystal structures that exhibited piezoelectricity. The first practical application for piezoelectric devices was sonar, first developed during World War I, in France in 1917, Paul Langevin and his coworkers developed an ultrasonic submarine detector. The detector consisted of a transducer, made of quartz crystals carefully glued between two steel plates, and a hydrophone to detect the returned echo. The use of piezoelectricity in sonar, and the success of that project, over the next few decades, new piezoelectric materials and new applications for those materials were explored and developed. Piezoelectric devices found homes in many fields, ceramic phonograph cartridges simplified player design, were cheap and accurate, and made record players cheaper to maintain and easier to build. The development of the ultrasonic transducer allowed for easy measurement of viscosity and elasticity in fluids and solids, ultrasonic time-domain reflectometers could find flaws inside cast metal and stone objects, improving structural safety
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Accutron
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Bulova is an American manufacturer of watches and clocks. Its headquarters is located in New York City, bulovas Swiss-Made line is known as Bulova Accu•Swiss or formerly, Bulova Accutron. It is owned by Citizen Watch Co, Bulova was founded and incorporated as the J. Bulova Company in 1875 by Joseph Bulova, an immigrant from Bohemia. It was reincorporated under the name Bulova Watch Company in 1923, in 1912, he launched his first plant dedicated entirely to the production of watches. Manufacturing watches at their factory in Biel, Bulova began a mass production never seen in the world of watchmaking until then. In 1919, Joseph Bulova offered the first complete range of watches for men, the iconic visual style of his first popular advertising made its watches popular with the American public. But beyond the style, precision and technological research also became an endless quest for Bulova. In 1927, he set up an observatory on the roof of a skyscraper located at 580 5th Avenue to make measurements that would enable him to determine very precisely universal time. Bulova established its operations in Woodside, New York, and Flushing, New York, where it made innovations in watchmaking and its horological innovations included the Accutron watch, which used a resonating tuning fork as a means of regulating the time-keeping function. Bulova became a watch company in 1923. In 1927, Charles A. Lindbergh was the first pilot to cross the Atlantic nonstop and his crossing earned him a Bulova Watch and a check for $1000, and it became an emblem for the brand that created the model Lone Eagle in his likeness. Bulova claims to have been the first manufacturer to offer electric clocks beginning in 1931, in the 1930s and 1940s, the brand was a huge success with its rectangular plated watches whose case was strongly curved to better fit the curve of the wrist. Bulova produced the worlds first official television commercial, on July 1,1941, the announcement, for which the company paid anywhere from $4.00 to $9.00, displayed a WNBT test pattern modified to look like a clock with the hands showing the time. The Bulova logo, with the phrase Bulova Watch Time, was shown in the lower quadrant of the test pattern while the second hand swept around the dial for one minute. The Joseph Bulova School of Watchmaking was founded in 1945 by Arde Bulova, Chairman of the Board, the school later became a full-fledged rehabilitation facility, an advocate for disabled people nationwide, and one of the founders of wheelchair sports in the United States. In 1967, Bulova bought the Manufacture des montres Universal Perret Frères SA at Geneva, the factory in Biel was closed in 1983. Bulova’s Accutron watches, first sold in October 1960, use a 360 hertz tuning fork instead of a wheel as the timekeeping element. The inventor, Max Hetzel, was born in Basel, Switzerland, the tuning fork was powered by a one-transistor electronic oscillator circuit, so the Accutron qualifies as the first electronic watch
. PMID 3323515.
"Tuning Fork". Collier's New Encyclopedia. 1921.
