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 vibrating string 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 Violin strings were originally made from catgut but are now usually made of steel or a synthetic material.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 f-holes 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 plucked string dampens 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 cello (violoncello), which is not adversely affected by having the optimum dimensions to correspond with the pitch of its open strings.
Historical background The nature of vibrating strings was studied by the ancient Ionian Greek philosopher Pythagoras, who is thought to have been the first to observe the relationship between the lengths of vibrating strings and the consonant sounds they make. In the 16th century, the Italian lutenist and composer Vincenzo Galilei pioneered the systematic testing and measurement of stretched strings, using lute strings. He discovered that while the ratio of an interval is proportional to the length of the string, it was directly proportional to the square root of the tension. His son Galileo Galilei published the relationship between frequency, length, tension and diameter in Two New Sciences (1638). The earliest violin makers, though highly skilled, did not advance any scientific knowledge of the acoustics of stringed instruments.
During the 19th century, the multi-harmonic sound from a bowed string was first studied in detail by the French physicist Félix Savart. The German physicist Hermann von Helmholtz investigated the physics of the plucked string, and showed that the bowed string travelled in a triangular shape with the apex moving at a constant speed.
The violin's modes of vibration 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 20 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".
Strings
The four open strings of any particular violin have the same length from the bridge to the nut of the instrument, but vary in pitch because each string has a different mass per unit length. Both ends of a violin string are essentially stationary when it vibrates, allowing for the creation of standing waves (eigenmodes), caused by the superposition of two sine waves travelling past each other.
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 beyond the upper audible limit for humans.
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 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 unfretted, 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 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 whole tone 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 cello (violoncello) and a double bass.
When the violinist is directed to pluck a string (Ital. pizzicato), the sound produced rapidly dies away, or dampens: the effect is more striking for a violin compared with the other members of the violin family because of its smaller dimensions, and 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 Hz and causes the pitch to vary by a quarter of a tone.
Tension The tension (T) in a stretched string is given by
where E is the Young's modulus, S is the cross-sectional area, ΔL is the extension, and L is the string length. For vibrations with a large amplitude, the tension is not constant. Increasing the tension on a string results in a higher frequency note: the frequency of the vibrating string, which is directly proportional to the square root of the tension, can be represented by the following equation:
where f is the fundamental frequency of the string, T is the tension force and M is the mass.
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 .
Length
For any wave travelling at a speed v, travelling a distance λ in one period T, .
For a frequency f
For the fundamental frequency of a vibrating string on a violin, the string length is λ, where λ is the associated wavelength, so .
Materials String material influences the overtone mix and affects the quality of the sound. Response and ease of articulation are also affected by choice of string materials.
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 helically 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 The bridge, which is placed on the top of the body of the violin where the soundboard is highest, supports one end of the strings' playing length. The static forces acting on the bridge are large, and dependent on the tension in the strings: passes down through the bridge as a result of a tension in the strings of . The string 'break' angle made by the string across the bridge affects the downward force, and is typically 13 to 15° to the horizontal.
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.
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 bow