Vibrating strings

A vibration in a string is a wave. Resonance causes a vibrating string to produce a sound with constant frequency, i.e. constant pitch. If the length or tension of the string is correctly adjusted, the sound produced is a musical note. Vibrating strings are the basis of string instruments such as guitars, cellos, and pianos.

The velocity of propagation of a wave in a string (${\displaystyle v}$) is proportional to the square root of the force of tension of the string (${\displaystyle T}$) (this relationship for frequency, proportional to wave velocity, was discovered by Vincenzo Galilei in the late 1500s) and inversely proportional to the square root of the linear density (${\displaystyle \mu }$) of the string:

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