Sonometer
an instrument for determining the laws of sounding strings. It consists usually of two or more piano wires of known weight, stretched over a sounding box, with devices, usually weights, for increasing their tension. The laws of sounding strings are very interesting:
1. The heavier the string, the lower the tone. For strings of the same length and tension, the pitch varies inversely as the square root of the weight. If one string be four times as heavy as another, its pitch will be half as high, that is to say, an octave lower. If a third string be added whose diameter is three times that of the first, and whose weight is consequently nine times as great, it will vibrate one third as many times per second as the first string. 2. If two strings have the same length and size, but carrying unequal weights, the tighter string will give the higher note. For strings of the same length and size, the pitch varies directly as the square root of the tension or stretching weight. If two strings otherwise alike be stretched with weights of one and four, the note of the second will be an octave higher than that of the first. If a third and similar string be added, sustaining a streching weight of nine, it will vibrate three times as frequently as the first string. 3. The shorter the string, the higher the note. If two similar strings be stretched to the same tension, and with lengths of one and two respectively, the note of the first will be an octave higher than that of the second. If a third string be added whose length is three times that of the first, the first will vibrate three times as often as the third. If a sounding string be held motionless at its middle, its half produces a note an octave above that produced by the whole string. By using strings of different weight, and by varying the length of the sounding segment with his fingers, the violin player is able to produce an apparently limitless variety of notes.
Tuning a piano consists in giving each wire its proper tension, so that it will vibrate with desired frequency and produce the tone expected from it.