Formula - Resonant frequencies for pipes closed at one end

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 = 3 is the third harmonic, the oscillation mode with n = 5 is the fifth harmonic, and so on.
Note that the even harmonics are missing in pipes with one
closed end.

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 end and a node across the closed end of the pipe. Thus, we can find the wavelength of an oscillation mode by
requiring that there is an antinode across the open end and a node across the
closed 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 closed at one end

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