Standing Wave and Harmonics Calculator

Works out the notes a string or pipe can sound.

Frequency of this mode

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Wavelength —

Fundamental frequency —

Wave speed —

First six modes

Assumes —

The formula

string or open pipe: f = n v ÷ 2L pipe closed at one end: f = (2n − 1) v ÷ 4L string speed: v = √(T ÷ μ)

A standing wave fits a whole number of half wavelengths in the length, or an odd number of quarter wavelengths in a pipe closed at one end.

Mass per length is the string’s mass divided by its length. Tightening a string raises the pitch, and shortening it raises it further.

What is the fundamental of a 65 cm string at 70 N and 0.6 g/m?

About 263 Hz.

What about a 1 m closed pipe in air?

85.8 Hz, half that of an open pipe at 172 Hz.