String Vibration Calculator

About this calculator

This calculator applies two results from the physics of a stretched string: the wave speed v = √(T/μ), where T is the tension and μ is the linear mass density (mass per unit length), and the fundamental frequency f = v/2L for a string of length L fixed at both ends — the lowest standing-wave mode, whose wavelength is exactly twice the string's length. Raising tension or shortening the string raises pitch, while a heavier (thicker or denser) string lowers it for the same tension.

Instrument builders and luthiers use these relationships to choose string gauges and tunings for guitars, pianos, and violins, since a given pitch can be reached by trading off tension against mass per unit length. Physics students studying standing waves and resonance, and audio engineers working with string instrument acoustics, use the same equations to predict how a string will behave before it's ever put under load.