# Acoustics of the Violin

For detail anatomy of violin, please refer to Atelierla Bussiere.

## How Does A Violin Make Sound?
### General Concept

When a violinist bows a string, which can produce vibrations with abundant harmonics. The vibrations of the strings are structurally transmitted to the bridge and the body of the instrument through the bridge. The bridge transmits the vibrational energy produced by the strings to the body through its feet, further triggering the vibration of body. The vibration of the body determines sound radiation and sound quality, along with the resonance of the cavity.

### String

The vibration pattern of the strings can be easily be observed. To the naked eye, the string appears to move back and forth in a parabolic shape (see figure), which resembles the first mode of free vibration of a stretched string. The vibration of strings was first investigated by Hermann Von Helmholtz, the famous mathematician and physicist in 19th century. A surprising scenario was discovered that the string actually moves in an inverse “V” shape rather than parabolas (see figure). What we see is just an envelope of the motion of the string. To honor his findings, the motion of bowed strings had been called “Helmholtz motion.”

### Bridge

The primary role of the bridge is to transform the motion of vibrating strings into periodic driving forces by its feet to the top plate of the violin body. The configuration of the bridge can be referred to the figure. The bridge stands on the belly between f holes, which have two primary functions: One is to connect the air inside the body with outside air, and the other one is to make the belly between f holes move more easily than other parts of the body. The fundamental frequency of a violin bridge was found to be around 3000 Hz when it is on a rigid support, and it is an effective energy-transmitting medium to transmit the energy from the string to body at frequencies from 1 kHz to 4 kHz, which is in the range of keen sensitivity of human hearing. If a violinist desires a darker sound from the violin, he or she may attach a mute to the top of the bridge. The mute is actually an additional mass which reduces the fundamental frequency of the bridge. As a result, the sound at higher frequencies is diminished since the force transferred to the body has been decreased. On the other hand, the fundamental frequency of the bridge can be raised by attaching an additional stiffness in the form of tiny wedges, and the sound at higher frequencies will be amplified accordingly.
The sound post connects the flexible belly to the much stiffer back plate. The sound post can prevent the collapse of the belly due to high tension force in the string, and, at the same time, couples the vibration of the plate. The bass bar under the belly extends beyond the f holes and transmits the force of the bridge to a larger area of the belly. As can be seen in the figure, the motion of the treble foot is restricted by the sound post, while, conversely, the foot over bass bar can move up and down more easily. As a result, the bridge tends to move up and down, pivoting about the treble foot. The forces appearing at the two feet remain equal and opposite up to 1 kHz. At higher frequencies, the forces become uneven. The force on the soundpost foot predominates at some frequencies, while it is the bass bar foot at some.

### Body

The body includes top plate, back plate, the sides, and the air inside, all of which serve to transmit the vibration of the bridge into the vibration of air surrounding the violin. For this reason, the violin needs a relatively large surface area to push enough amount of air back and forth. Thus, the top and back plates play important roles in the mechanism. Violin makers have traditionally pay much attention on the vibration of the top and back plates of the violin by listening to the tap tones, or, recently, by observing the vibration mode shapes of the body plates. The vibration modes of an assembled violin are, however, much more complicated.
The vibration modes of top and back plates can be easily observed in a similar technique first performed by Ernest Florens Friedrich Chaldni (1756–1827), who is often respectfully referred “the father of acoustics.” First, the fine sand is uniformly sprinkled on the plate. Then, the plate can be resonated, either by a powerful sound wave tuned to the desired frequencies, by being bowed by a violin bow, or by being excited mechanically or electromechanically at desired frequencies. Consequently, the sand disperses randomly due to the vibration of plate. Some of the sand falls outside the region of plate, while some of the sand is collected by the nodal regions, which have relatively small movement, of the plate. Hence, the mode shapes of the plate can be visualized in this manner, which can be referred to the figures in the reference site, Violin Acoustics. The first seven modes of the top and back plates of violin are presented, with nodal lines depicted by using black sands.
The air inside the body is also important, especially in the range of lower frequencies. It is like the air inside a bottle when you blow into the neck, or, as known as Helmholtz resonance, which has its own modes of vibration. The air inside the body can communicate with air outside through the f holes, and the outside air serves as medium carrying waves from the violin.
see www.violinbridges.co.uk for more articles on bridges and acoustics.

### Sound Radiation

A complete description of sound radiation of a violin should include the information about radiation intensity as functions both of frequency and location. The sound radiation can be measured by a microphone connected to a pressure level meter which is rotatably supported on a stand arm around the violin, while the violin is fastened at the neck by a clip. The force is introduced into the violin by using a miniature impact hammer at the upper edge of the bridge in the direction of bowing. The detail can be referred to Martin Schleske, master studio for violinmaking . The radiation intensity of different frequencies at different locations can be represented by directional characteristics, or acoustic maps. The directional characteristics of a violin can be shown in the figure in the website of Martin Schleske, where the radial distance from the center point represents the absolute value of the sound level (re 1Pa/N) in dB, and the angular coordinate of the full circle indicates the measurement point around the instrument. According to the directional characteristics of violins, the principal radiation directions for the violin in the horizontal plane can be established. For more detail about the principal radiation direction for violins at different frequencies, please refer to reference (Meyer 1972).

## References And Other Links

* Violin Acoustics
* Paul Galluzzo's Homepage
* Martin Schleske, master studio for violinmaking
* Atelierla Bussiere
* Fletcher, N. H., and Rossing, T. D., The physics of musical instrument, Springer-Verlag, 1991
* Meyer, J., "Directivity of bowed stringed instruments and its effect on orchestral sound in concert halls", J. Acoustic. Soc. Am., 51, 1972, pp. 1994–2009
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