# Acoustics/Acoustics in Violins

For a detailed anatomy of the violin, please refer to Atelierla
Bussiere.

![](Violin_front_view.jpg "Violin_front_view.jpg")![](backview.jpg "backview.jpg")

## 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.

![](Acoustics_in_violins_procedure.jpg "Acoustics_in_violins_procedure.jpg")

### 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."

![](String.jpg "String.jpg")
![](Helmholtzmotion.jpg "Helmholtzmotion.jpg")

## 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. In order to
darken the sound of violin, the player attaches a mute on 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.

![](crossview.jpg "crossview.jpg")

### 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 paid much attention to 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

