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Violin acoustics is an area of study within musical acoustics concerned with how the sound of a violin is created as the result of interactions between its many parts. These acoustic qualities are similar to those of other members of the violin family, such as the viola.
The energy of a String vibration is transmitted through the bridge to the body of the violin, which allows the sound to radiate into the surrounding air. Both ends of a violin string are effectively stationary, allowing for the creation of standing waves. A range of simultaneously produced harmonics each affect the timbre, but only the fundamental frequency is heard. The frequency of a note can be raised by the increasing the string's tension, or decreasing its length or mass. The number of harmonics present in the tone can be reduced, for instance by the using the left hand to shorten the string length. The loudness and timbre of each of the strings is not the same, and the material used affects sound quality and ease of articulation. Violin strings were originally made from catgut but are now usually made of steel or a synthetic material. Most strings are wound with metal to increase their mass while avoiding excess thickness.
During a bow stroke, the string is pulled until the string's tension causes it to return, after which it receives energy again from the bow. Violin players can control bow speed, the force used, the position of the bow on the string, and the amount of hair in contact with the string. The static forces acting on the bridge, which supports one end of the strings' playing length, are large: dynamic forces acting on the bridge force it to rock back and forth, which causes the vibrations from the strings to be transmitted. A violin's body is strong enough to resist the tension from the strings, but also light enough to vibrate properly. It is made of two arched wooden plates with ribs around the sides and has two Sound hole on either side of the bridge. It acts as a sound box to couple the vibration of strings to the surrounding air, with the different parts of the body all respond differently to the notes that are played, and every part (including the bass bar concealed inside) contributing to the violin's characteristic sound. In comparison to when a string is bowed, a pizzicato string Damping ratio more quickly.
The other members of the violin family have different, but similar timbres. The viola and the double bass’s characteristics contribute to them being used less in the orchestra as solo instruments, in contrast to the Violoncello (violoncello), which is not adversely affected by having the optimum dimensions to correspond with the pitch of its open strings.
During the nineteenth century, the harmonic sound from a Bow stroke string was first studied in detail by the French physicist Félix Savart. The German physicist Hermann von Helmholtz investigated the physics of the Pizzicato string, and showed that the bowed string travelled in a triangular shape with the apex moving at a constant speed.
The violin's Normal mode were researched in Germany during the 1930s by Hermann Backhaus and his student Hermann Meinel, whose work included the investigation of frequency responses of violins. Understanding of the acoustical properties of violins was developed by F.A. Saunders in the 1930s and 40s, work that was continued over the following decades by Saunders and his assistant Carleen Hutchins, and also Werner Lottermoser, Jürgen Meyer, and Simone Sacconi. Hutchins' work dominated the field of violin acoustics for twenty years from the 1960s onwards, until it was superseded by the use of modal analysis, a technique that was, according to the acoustician George Bissinger, "of enormous importance for understanding the acoustics of the violin".
A vibrating string does not produce a single frequency. The sound may be described as a combination of a fundamental frequency and its overtones, which cause the sound to have a quality that is individual to the instrument, known as the timbre. The timbre is affected by the number and comparative strength of the overtones (harmonics) present in a tone. Even though they are produced at the same time, only the fundamental frequency—which has the greatest amplitude—is heard. The violin is unusual in that it produces frequencies Ultrasound.
The fundamental frequency and overtones of the resulting sound depend on the material properties of the string: tension, length, and mass, as well as Damping ratio effects and the stiffness of the string. Violinists stop a string with a left-hand fingertip, shortening its playing length. Most often the string is stopped against the violin's fingerboard, but in some cases a string lightly touched with the fingertip is enough, causing an artificial harmonic to be produced. Stopping the string at a shorter length has the effect of raising its pitch, and since the fingerboard is Fret, any frequency on the length of the string is possible. There is a difference in timbre between notes made on an 'open' string and those produced by placing the left hand fingers on the string, as the finger acts to reduce the number of harmonics present. Additionally, the loudness and timbre of the four strings is not the same.
The fingering positions for a particular interval vary according to the length of the vibrating part of the string. For a violin, the Major second interval on an open string is about —at the other end of the string, the same interval is less than a third of this size. The equivalent numbers are successively larger for a viola, a Violoncello (violoncello) and a double bass.
When the violinist is directed to pluck a string (Italian language pizzicato), the sound produced dies away, or dampens, quickly: the dampening is more striking for a violin compared with the other members of the violin family because of its smaller dimensions, and the effect is greater if an open string is plucked. During a pizzicato note, the decaying higher harmonics diminish more quickly than the lower ones.
The vibrato effect on a violin is achieved when muscles in the arm, hand and wrist act to cause the pitch of a note to oscillate. A typical vibrato has a frequency of 6 Hertz and causes the pitch to vary by a quarter of a tone.
The strings of a violin are attached to adjustable tuning pegs and (with some strings) finer tuners. Tuning each string is done by loosening or tightening it until the desired pitch is reached. The tension of a violin string ranges from .
For the fundamental frequency of a vibrating string on a violin, the string length is λ, where λ is the associated wavelength, so
Violin strings were originally made from catgut, which is still available and used by some professional musicians, although strings made of other materials are less expensive to make and are not as sensitive to temperature. Modern strings are made of steel-core, stranded steel-core, or a synthetic material such as Perlon. Violin strings (with the exception of most E strings) are helix wound with metal chosen for its density and cost. The winding on a string increases the mass of the string, alters the tone (quality of sound produced) to make it sound brighter or warmer, and affects the response. A plucked steel string sounds duller than one made of gut, as the action does not deform steel into a pointed shape as easily, and so does not produce as many higher frequency harmonics.
The bridge transfers energy from the strings to the body of the violin. As a first approximation, it is considered to act as a node, as otherwise the fundamental frequencies and their related harmonics would not be sustained when a note is played, but its motion is critical in determining how energy is transmitted from the strings to the body, and the behaviour of the strings themselves. One component of its motion is side-to-side rocking as it moves with the string. It may be usefully viewed as a mechanical filter, or an arrangement of masses and "springs" that filters and shapes the timbre of the sound. The bridge is shaped to emphasize a singer's formant at about 3000 Hz.
Since the early 1980s it has been known that high quality violins have vibrated better at frequencies around 2–3 kHz because of an effect attributed to the resonance properties of the bridge, and now referred as the 'bridge-hill' effect.
Muting is achieved by fitting a clip onto the bridge, which absorbs a proportion of the energy transmitted to the body of the instrument. Both a reduction in sound intensity and a different timbre are produced, so that using a mute is not seen by musicians as the main method to use when wanting to play more quietly.
The length, weight, and balance point of modern bows are standardized. Players may notice variations in sound and handling from bow to bow, based on these parameters as well as stiffness and moment of inertia. A violinist or violist would naturally tend to play louder when pushing the bow across the string (an 'up-bow'), as the leverage is greater. At its quietest, the instrument has a power of 0.0000038 watts, compared with 0.09 watts for a small orchestra: the range of sound pressure levels of the instrument is from 25 to 30dB.
Bowing directly above the fingerboard (Ital. sulla tastiera) produces what the 20th century American composer and author Walter Piston described as a "very soft, floating quality", caused by the string being forced to vibrate with a greater amplitude. Sul ponticello—when the bow is played close to the bridge—is the opposite technique, and produces what Piston described as a "glassy and metallic" sound, due to normally unheard harmonics becoming able to affect the timbre.
The physicist C. V. Raman was the first to obtain an accurate model for describing the mechanics of the bowed string, publishing his research in 1918. His model was able to predict the motion described by Helmholtz (known nowadays as Helmholtz motion), but he had to assume that the vibrating string was perfectly flexible, and lost energy when the wave was reflected with a reflection coefficient that depended upon the bow speed. Raman's model was later developed by the mathematicians Joseph Keller and F.G. Friedlander.
Helmholtz and Raman produced models that included sharp cornered waves: the study of smoother corners was undertaken by Cremer and Lazarus in 1968, who showed that significant smoothing occurs (i.e. there are fewer harmonics present) only when normal bowing forces are applied. The theory was further developed during the 1970s and 1980s to produce a digital waveguide model, based on the complex relationship behaviour of the bow's velocity and the frictional forces that were present. The model was a success in simulating Helmholtz motion (including the 'flattening' effect of the motion caused by larger forces), and was later extended to take into account the string's bending stiffness, its twisting motion, and the effect on the string of body vibrations and the distortion of the bow hair. However, the model assumed that the coefficient of friction due to the rosin was solely determined by the bow's speed, and ignored the possibility that the coefficient could depend on other variables. By the early 2000s, the importance of variables such as the energy supplied by friction to the rosin on the bow and the player's input into the action of the bow were recognised, showing the need for an improved model.
The existence of expensive violins is dependent on small differences in their physical behaviour in comparison with cheaper ones. Their construction, and especially the arching of the belly and the backplate, has a profound effect on the overall sound quality of the instrument, and its many different resonant frequencies are caused by the nature of the wooden structure. The different parts all respond differently to the notes that are played, displaying what Carleen Hutchins described as 'wood resonances'. The response of the string can be tested by detecting the motion produced by the Electric current through a metal string when it is placed in an oscillating magnetic field. Such tests have shown that the optimum 'main wood resonance' (the wood resonance with the lowest frequency) occurs between 392 and 494 Hz, equivalent to a tone below and above A4.
The ribs are reinforced at their edges with lining strips, which provide extra gluing surface where the plates are attached. The wooden structure is filled, glued and varnished using materials which all contribute to a violin's characteristic sound. The air in the body also acts to enhance the violin's resonating properties, which are affected by the volume of enclosed air and the size of the f-holes.
The belly and the backplate can display modes of vibration when they are forced to vibrate at particular frequencies. The many modes that exist can be found using fine dust or sand, sprinkled on the surface of a violin-shaped plate. When a mode is found, the dust accumulates at the (stationary) nodes: elsewhere on the plate, where it is oscillating, the dust fails to appear. The patterns produced are named after the German physicist Ernst Chladni, who first developed this experimental technique.
Modern research has used sophisticated techniques such as holographic interferometry, which enables analysis of the motion of the violin surface to be measured, a method first developed by scientists in the 1960s, and the finite element method, where discrete parts of the violin are studied with the aim of constructing an accurate simulation. The British physicist Bernard Richardson has built virtual violins using these techniques. At East Carolina University, the American acoustician George Bissinger has used laser to produce frequency responses that have helped him to determine how the efficiency and damping of the violin's vibrations depend on frequency. Another technique, known as modal analysis, involves the use of 'tonal copies' of old instruments to compare a new instrument with an older one. The effects of changing the new violin in the smallest way can be identified, with the aim of replicating the tonal response of the older model.
When the bridge receives energy from the strings, it rocks, with the sound post acting as a pivot and the bass bar moving with the plate as the result of . This behaviour enhances the violin tone quality: if the sound post's position is adjusted, or if the forces acting on it are changed, the sound produced by the violin can be adversely affected. Together they make the shape of the violin body asymmetrical, which allows different vibrations to occur, which causing the timbre to become more complex.
In addition to the normal modes of the body structure, the enclosed air in the body exhibits Helmholtz resonance modes as it vibrates.
The viola is a larger version of the violin, and has on average a total body length of , with strings tuned a Perfect fifth lower than a violin (with a length of about ). The viola's larger size is not proportionally great enough to correspond to the strings being pitched as they are, which contributes to its different timbre. Violists need to have hands large enough to be able to accomplish fingering comfortably. The C string has been described by Piston as having a timbre that is "powerful and distinctive", but perhaps in part because the sound it produces is easily covered, the viola is not so frequently used in the orchestra as a solo instrument. According to the American physicist John Rigden, the lower notes of the viola (along with the cello and the double bass) suffer from strength and quality. This is because typical resonant frequencies for a viola lie between the natural frequencies of the middle open strings, and are too high to reinforce the frequencies of the lower strings. To correct this problem, Rigden calculated that a viola would need strings that were half as long again as on a violin, which would making the instrument inconvenient to play.
The cello, with an overall length of , is pitched an octave below the viola. The proportionally greater thickness of its body means that its timbre is not adversely affected by having dimensions that do not correspond to its pitch of its open strings, as is the case with the viola.
The double bass, in comparison with the other members of the family, is more pointed where the belly is joined by the neck, possibly to compensate for the strain caused by the tension of the strings, and is fitted with cogs for tuning the strings. The average overall length of an orchestral bass is . The back can be arched or flat. The bassist's fingers have to stretch twice as far as a cellist's, and greater force is required to press them against the finger-board. The pizzicato tone, which is 'rich' sounding due to the slow speed of vibrations, is changeable according to which of the associated harmonies are more dominant. The technical capabilities of the double bass are limited. Quick passages are seldom written for it; they lack clarity because of the time required for the strings to vibrate. The double bass is the foundation of the whole orchestra and therefore musically of great importance. According to John Rigden, a double bass would need to be twice as large as its present size for its bowed notes to sound powerful enough to be heard over an orchestra.
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