Standing Wave Calculator
Harmonics on a string or in a pipe, open or stopped.
Work out Standing Wave. Harmonics on a string or in a pipe, open or stopped. Says where the approximation stops holding.
1 is the fundamental, 2 the next available mode, and so on.
Harmonic 1
171.5 Hz
Fundamental 171.5 Hz · wavelength 2 m
A string fixed at both ends, or a pipe open at both ends, supports every harmonic — 1, 2, 3, 4. A pipe closed at one end supports only the odd ones, and its fundamental is a full octave lower for the same length. That is why a stopped organ pipe sounds an octave below an open pipe of equal length, and why a clarinet — closed at the reed — plays about an octave lower than a flute of similar size and skips to the twelfth rather than the octave when overblown. The harmonic series is also why two instruments playing the same note sound different. The fundamental sets the pitch; the relative strength of the harmonics above it is the timbre.
How the Standing Wave Calculator works
Enter a length and wave speed for the frequency of any harmonic. A pipe closed at one end supports only the odd harmonics and sounds an octave below an open pipe of the same length, which the page handles rather than leaving to you.
Also known as: harmonic frequency calculator · fundamental frequency calculator · open and closed pipe harmonics · string harmonics calculator
Frequently asked questions
How do I calculate the fundamental frequency?
For a string or an open pipe, f = v/2L. For a pipe closed at one end, f = v/4L — an octave lower for the same length.
Why does a closed pipe only give odd harmonics?
Because the closed end must be a node and the open end an antinode, and only odd quarter-wavelengths satisfy both. That is why a clarinet overblows to the twelfth rather than the octave.
Why do two instruments playing the same note sound different?
The fundamental sets the pitch; the relative strengths of the harmonics above it are the timbre. Same note, different recipe of overtones.
What is a node?
A point that never moves. On a string fixed at both ends the ends are always nodes, and higher harmonics add more between them — which is what a guitarist touches to play a harmonic.
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