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
. PMID 3323515.
"Tuning Fork". Collier's New Encyclopedia. 1921.
