Just one guitar string will naturally vibrate at a number of frequencies. These frequencies, otherwise known as harmonics, depend upon the tension, linear density, and length of the string. Each of the natural frequencies is associated with a standing wave pattern.
There is a length-wavelength relationship associated with each harmonic frequency: the wavelength of the standing wave of any given harmonic is related to the length of the string, and visa versa. Therefore, the length-wavelength relationships, as well as the wave equation (speed = frequency * wavelength) together can be used to perform calculations to predict the length of a sting in order to produce a given frequency. Calculations can also be made to predict the natural frequencies produced by a given length of string.
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