Formula - Resonant frequencies for pipes open at both ends

A sinusoidal sound wave

Frequency of the sound source

A sound source

The longitudinal displacements of the particles
along the x-axis can be plotted along the y-axis

The oscillation mode with the harmonic number n = 1
is called the fundamental mode or the first harmonic. It has the longest
resonant wavelength and the lowest resonant frequency. The oscillation mode with n = 2 is the
second harmonic, the oscillation mode with n = 3 is the third harmonic, and so on.

Since the frequency is related to the wavelength and
the speed of sound through f = v/l, the resonant
frequencies are given by

At resonance, there is always an antinode across the
open side of the pipe. Thus, we can find the wavelength of an oscillation mode by
requiring that there is an antinode across each open end of the pipe. This
requirement is satisfied if the wavelength is given by

Air particles

The fundamental mode (first harmonic) is set up in the pipe

A pipe open at both ends

Click and drag the blue line to change the frequency of the sound source