Violin acoustics

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 Violin strings were originally made from catgut but are now usually made of steel or a synthetic material.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.

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 sixteenth 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 nineteenth 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 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".

The open strings of a violin are of the same length from the bridge to the nut of the violin, but vary in pitch because they have different masses 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.