1. Sound

Sound is a wave characterised by over-pressure - i.e. an excess of particles - at one point and a lack of particles at another point. It is a longitudinal vibration of the air that is propagated step by step.

Propagation of a sound emitted in the air by a bell.

The sound perceived depends on two main things:

- The tension and the length of the string that determines the fundamental frequency at which the string vibrates. By "stopping" a string, i.e. placing a finger on it and thus changing its length, the violinist can modify the vibrating frequency. If the finger is placed at a whole fraction of the length of the string, the vibration produces a note in harmony with the fundamental note. This principle was discovered by Pythagoras already two thousand years ago.

The various harmonics of a string.

- The way in which the violist rubs the string with the bow. The string not only undergoes a transversal and a longitudinal vibration by being tightened and then released, it also undergoes a torsion according to the force behind the rubbing, which modifies the timbre of the instrument.

Example of a transversal vibration.

Example of a longitudinal vibration.

Of course the sound perceived by the listener depends on the timbre of the instrument itself which in turn depends on the form of the resonant box (the main part of the violin) as well as on the type of wood and varnish used.

The violin is capable of generating a great variety of sounds. It can produce very sharp sounds when the length of a string is reduced by pressing a finger down on it. Moreover, as it is up to the violinist to create the sound - rather than to select a predefined sound as with the piano - the range is unlimited. All the charm of the violin lies therein - but so does the difficulty in playing it!

Acoustics

Let us have a look at the principles involved in the formation of sound. They may be defined as follows:

Curve representing a 3 Hz frequency.

- The period expresses the distance between two crests of a wave thus determining the pitch of the sound perceived.

- The frequency represents the number of oscillations per second, generally expressed in hertz (Hz). The higher the frequency, the sharper the sound. The human ear perceives those sounds whose frequency lies between the infrasounds (< 20 Hz) and the ultrasounds (> 20 kHz); the latter is reduced with age. Only certain animals, such as bats, are sensitive to ultrasounds.

- The amplitude determines the power of the sound. It is the maximum elongation of the sound wave. The greater the amplitude, the louder the sound.

It should be noted that the amplitude of the vibration decreases with the distance, for the energy of the wave is distributed in an increasing volume. It should also be noted that when a wave is canalised in a cylindrical tube (as in the flute) or by a reflector (such as the belly of the violin) the amplitude is scarcely diminished. This explains why we can hear sound in a tunnel or in a subway station so well. It is the principle used by the violin to amplify the sound and direct it to the listeners!

Chords and noise

The sounds produced by musical instruments are not pure sounds but composite sounds. A composite sound is the result of the superimposing of several waves.

- One is the fundamental note, which has the same frequency as the vibration of the string and determines the pitch of the sound perceived.

- The others are harmonic and determine the timbre of the instrument. Two different instruments, such as a flute and a violin, playing the same note have a different timbre and therefore a different spectrum.

This is the sound intensity with respect to the frequency for two composite sounds of a like pitch but of a different timbre.

A sound at A pitch contains approximately 40 audible harmonics whose respective intensities can vary! It is easy to understand, then, the immense range of possibilities in the variations of timbre. Such variations allow one to individualise not only musical instruments, but the human voice as well.

The superimposing of various pure or composite sounds is a chord. A chord may be consonant or dissonant according to whether or not it is pleasing to the ear - a rather subjective criterion!

The spectrum represents a three-note chord ~ G3, B3, D4 and its harmonics.

If there are too many fundamentals in a chord - for instance, when one bangs simultaneously on all the keys of a piano - the ear perceives noise rather than a chord. Noise is defined as any wave which has no periodic element (i.e. no repetitive cycle) and is therefore composed of an infinite number of pure sounds. An explosion is a good example!

Non-periodic curves of different sounds.

Let us conclude by pointing out that the manner in which sounds and harmonies are perceived vary from one person to another and according to time periods, cultures, countries and civilisations. This also explains why classical harmonies are not always appreciated.

For more information on sound in general, we highly recommend The Soundry (ThinkQuest 1998) site