Basic physics of the violin
Encyclopedia
The distinctive sound of a violin
is the result of interactions between its many parts. Drawing a bow across the strings causes them to vibrate. This vibration is transmitted through the bridge and sound post to the body of the violin (mainly the top and back), which allows the sound to effectively radiate into the air. The tension and type of strings, the bow, and the construction of the body all contribute to the loudness and tonal quality of the sound.
of a violin are stretched across the bridge
and nut of the violin so that the ends are essentially stationary, allowing for the creation of standing waves. The fundamental frequency
and harmonic
overtone
s of the resulting sound depend on the material properties of the string, such as the tension, length, mass
, elasticity
and damping
factor.
affects the sound a violin produces in an obvious way. Increasing the tension on a string results in a higher frequency note. The strings of a violin are wrapped around adjustable tuning peg
s. By turning its associated peg, each string may be loosened or tightened until it produces the desired pitch
, which may be described in terms of frequency
. The playing tension of a violin string ranges from about 9 lbf (40 N) to 20 lbf (89 N).
, but in some cases fingertip contact alone is enough to stop the string at the desired sounding length. Stopping the string at a shorter length has the effect of raising its pitch.
. String material influences the overtone mix. Response and ease of articulation are also affected by choice of string materials.
Violin strings were originally made from catgut
which is still available, although its market niche is limited, due to its cost and tuning sensitivity to humidity and temperature. Modern strings are made of steel, stranded steel, or a variety of synthetic materials. Violin strings, with the exception of most E strings and some "historically informed" gut strings are wound (or overspun) with metal, to keep their thickness within comfortable limits, as well as to manage their surface friction properties. Some stranded steel strings have an inner winding under the surface winding.
supports one end of the strings' playing length. It must stand up under a combined down force of about 20 lbf (89 N). Down force preloads the violin's top, or table, affecting the sound of a sensitive instrument. String break angle across the bridge affects the down force, and is typically 158°.
More importantly, the bridge transfers vibration from the strings to the top of the violin. The most significant bridge motion is side-to-side rocking, coming from the transverse component of the strings' vibration. The bridge may be usefully viewed as a mechanical filter, or an arrangement of masses and "springs" that filters and shapes the timbre of the sound. Often the bridge is shaped to emphasize the singers' formant at about 3000 Hz.
consisting of a flat ribbon of parallel horse hairs stretched between the ends of a stick, which may be made of wood or synthetic material such as fiberglass
or carbon-fiber composite
. 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
.
The hair is coated with rosin
to provide controlled stick-slip as it moves transversely to the string. Different types of rosin are available, providing varying amounts of "grip" or static friction.
In bowing, the three most prominent factors under the player's immediate control are bow speed, downward force, and location of the sounding point where hair crosses string. The desired sounding point will generally move closer to the bridge as the string is stopped to a shorter sounding length. The player may also vary the amount of hair in contact with the string by tilting the bow stick more or less away from the bridge. Violinists are trained to keep the bow perpendicular to the string in most cases, as other angles may adversely affect the sound.
is used to fasten the parts together, since it is capable of making tightly fitted joints which do not damp vibrations nor add reflective discontinuities to the vibrating structure.
An internal sound post
helps transmit sound to the back of the violin and serves as structural support.
The body of the violin acts as a "sound box" to couple the vibration of strings to the surrounding air, making it audible. The construction of this sound box, and especially the arching of the top and back, have a profound effect on the overall sound quality of the instrument. The sound-producing system of the violin body includes the top and back (and to some degree the sides, or ribs), the bass bar that is glued to the underside of the top, and the bridge and sound post. In addition to the resonant
modes
of the body structure, the enclosed air volume exhibits Helmholtz resonance
modes.
Violin
The violin is a string instrument, usually with four strings tuned in perfect fifths. It is the smallest, highest-pitched member of the violin family of string instruments, which includes the viola and cello....
is the result of interactions between its many parts. Drawing a bow across the strings causes them to vibrate. This vibration is transmitted through the bridge and sound post to the body of the violin (mainly the top and back), which allows the sound to effectively radiate into the air. The tension and type of strings, the bow, and the construction of the body all contribute to the loudness and tonal quality of the sound.
Strings
The stringsStrings (music)
A string is the vibrating element that produces sound in string instruments, such as the guitar, harp, piano, and members of the violin family. Strings are lengths of a flexible material kept under tension so that they may vibrate freely, but controllably. Strings may be "plain"...
of a violin are stretched across the bridge
Bridge (instrument)
A bridge is a device for supporting the strings on a stringed instrument and transmitting the vibration of those strings to some other structural component of the instrument in order to transfer the sound to the surrounding air.- Explanation :...
and nut of the violin so that the ends are essentially stationary, allowing for the creation of standing waves. The fundamental frequency
Fundamental frequency
The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the lowest frequency of a periodic waveform. In terms of a superposition of sinusoids The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the...
and harmonic
Harmonic
A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...
overtone
Overtone
An overtone is any frequency higher than the fundamental frequency of a sound. The fundamental and the overtones together are called partials. Harmonics are partials whose frequencies are whole number multiples of the fundamental These overlapping terms are variously used when discussing the...
s of the resulting sound depend on the material properties of the string, such as the tension, length, mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
, elasticity
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....
and damping
Damping
In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator.In mechanics, friction is one such damping effect...
factor.
Tension
String tensionTension (mechanics)
In physics, tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object. It is the opposite of compression. As tension is the magnitude of a force, it is measured in newtons and is always measured parallel to the string on which it applies...
affects the sound a violin produces in an obvious way. Increasing the tension on a string results in a higher frequency note. The strings of a violin are wrapped around adjustable tuning peg
Tuning peg
A tuning peg is used to hold a string in the pegbox of a stringed instrument. It may be made of ebony, rosewood, boxwood or other material. Some tuning pegs are ornamented with shell, metal, or plastic inlays, beads or rings....
s. By turning its associated peg, each string may be loosened or tightened until it produces the desired pitch
Pitch (music)
Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...
, which may be described in terms of frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
. The playing tension of a violin string ranges from about 9 lbf (40 N) to 20 lbf (89 N).
Length
The length of the string also influences its pitch, and is the basis for how a violin is played. Violinists "stop" a string with a left-hand fingertip, shortening its playing length. Most often the string is stopped against the violin's fingerboardFingerboard
The fingerboard is a part of most stringed instruments. It is a thin, long strip of material, usually wood, that is laminated to the front of the neck of an instrument and above which the strings run...
, but in some cases fingertip contact alone is enough to stop the string at the desired sounding length. Stopping the string at a shorter length has the effect of raising its pitch.
Materials
String material affects the quality of the sound. A vibrating string does not produce a single frequency. The sound may be described as a combination of a fundamental frequency and overtones, which form the sound's timbreTimbre
In music, timbre is the quality of a musical note or sound or tone that distinguishes different types of sound production, such as voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. The physical characteristics of sound that determine the...
. String material influences the overtone mix. Response and ease of articulation are also affected by choice of string materials.
Violin strings were originally made from catgut
Catgut
Catgut is a type of cord that is prepared from the natural fibre found in the walls of animal intestines. Usually sheep or goat intestines are used, but it is occasionally made from the intestines of cattle, hogs, horses, mules, or donkeys.-Etymology:...
which is still available, although its market niche is limited, due to its cost and tuning sensitivity to humidity and temperature. Modern strings are made of steel, stranded steel, or a variety of synthetic materials. Violin strings, with the exception of most E strings and some "historically informed" gut strings are wound (or overspun) with metal, to keep their thickness within comfortable limits, as well as to manage their surface friction properties. Some stranded steel strings have an inner winding under the surface winding.
Bridge
The bridgeBridge (music)
In music, especially western popular music, a bridge is a contrasting section which also prepares for the return of the original material section...
supports one end of the strings' playing length. It must stand up under a combined down force of about 20 lbf (89 N). Down force preloads the violin's top, or table, affecting the sound of a sensitive instrument. String break angle across the bridge affects the down force, and is typically 158°.
More importantly, the bridge transfers vibration from the strings to the top of the violin. The most significant bridge motion is side-to-side rocking, coming from the transverse component of the strings' vibration. The bridge may be usefully viewed as a mechanical filter, or an arrangement of masses and "springs" that filters and shapes the timbre of the sound. Often the bridge is shaped to emphasize the singers' formant at about 3000 Hz.
Bow
Excitation of string vibration is generally provided by a bowBow (music)
In music, a bow is moved across some part of a musical instrument, causing vibration which the instrument emits as sound. The vast majority of bows are used with string instruments, although some bows are used with musical saws and other bowed idiophones....
consisting of a flat ribbon of parallel horse hairs stretched between the ends of a stick, which may be made of wood or synthetic material such as fiberglass
Glass-reinforced plastic
Fiberglass , is a fiber reinforced polymer made of a plastic matrix reinforced by fine fibers of glass. It is also known as GFK ....
or carbon-fiber composite
Composite material
Composite materials, often shortened to composites or called composition materials, are engineered or naturally occurring materials made from two or more constituent materials with significantly different physical or chemical properties which remain separate and distinct at the macroscopic or...
. 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
Moment of inertia
In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass, is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation...
.
The hair is coated with rosin
Rosin
.Rosin, also called colophony or Greek pitch , is a solid form of resin obtained from pines and some other plants, mostly conifers, produced by heating fresh liquid resin to vaporize the volatile liquid terpene components. It is semi-transparent and varies in color from yellow to black...
to provide controlled stick-slip as it moves transversely to the string. Different types of rosin are available, providing varying amounts of "grip" or static friction.
In bowing, the three most prominent factors under the player's immediate control are bow speed, downward force, and location of the sounding point where hair crosses string. The desired sounding point will generally move closer to the bridge as the string is stopped to a shorter sounding length. The player may also vary the amount of hair in contact with the string by tilting the bow stick more or less away from the bridge. Violinists are trained to keep the bow perpendicular to the string in most cases, as other angles may adversely affect the sound.
Body
The body of a violin must be strong enough to support the tension from the strings, but also light and thin enough to vibrate properly. The body of a violin consists of two arched wooden plates as top and bottom of a box, whose sides are formed by thin curved wooden "ribs." The ribs are reinforced at their edges with lining strips, which provide extra gluing surface where the plates are attached. Animal hide glueAnimal glue
An animal glue is an adhesive that is created by prolonged boiling of animal connective tissue.These protein colloid glues are formed through hydrolysis of the collagen from skins, bones, tendons, and other tissues, similar to gelatin. The word "collagen" itself derives from Greek κόλλα kolla, glue...
is used to fasten the parts together, since it is capable of making tightly fitted joints which do not damp vibrations nor add reflective discontinuities to the vibrating structure.
An internal sound post
Sound post
In a string instrument, the sound post is a small dowel inside the instrument under the treble end of the bridge, spanning the space between the top and back plates and held in place by friction...
helps transmit sound to the back of the violin and serves as structural support.
The body of the violin acts as a "sound box" to couple the vibration of strings to the surrounding air, making it audible. The construction of this sound box, and especially the arching of the top and back, have a profound effect on the overall sound quality of the instrument. The sound-producing system of the violin body includes the top and back (and to some degree the sides, or ribs), the bass bar that is glued to the underside of the top, and the bridge and sound post. In addition to the resonant
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
modes
Normal mode
A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies...
of the body structure, the enclosed air volume exhibits Helmholtz resonance
Helmholtz resonance
Helmholtz resonance is the phenomenon of air resonance in a cavity, such as when one blows across the top of an empty bottle. The name comes from a device created in the 1850s by Hermann von Helmholtz, the "Helmholtz resonator", which he, the author of the classic study of acoustic science, used to...
modes.
External links
- Violin acoustics: an introduction
- William F. Fry: A Physicist's Quest for the "Secrets" of Stradivari (Wisconsin academy review)
- Path Through the Woods - The Use of Medical Imaging in Examining Historical Instruments The use of computer aided tomography to examine the dendochronology (wood density) of the great Italian instruments in order to replicate their acoustics in modern instruments.