Changing The Pitch of A Vibrating String
There are three ways to change the pitch of a vibrating string. String instruments are tuned by varying the strings' tension because adjusting length or mass per unit length is impractical. Instruments with a fingerboard are then played by adjusting the length of the vibrating portion of the strings. The following observations all apply to a string that is infinitely flexible strung between two fixed supports. Real strings have finite curvature at the bridge and nut, and the bridge, because of its motion, are not exactly nodes of vibration. Hence the following statements about proportionality are (usually rather good) approximations.
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