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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:
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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!
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