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Closed organ pipe
Intermediate
Closed at one end supports only odd harmonics.
f_n = (2n−1)v/4LClosed at one end: node at the closed end and antinode at the open end, so only odd harmonics: fₙ = (2n − 1)v/4L; fundamental v/4L is half of an open pipe's.
L = 0.5 m: f₁ = 171 Hz, then 514, 857.
Sounds an octave lower than an open pipe of the same length.
In more detail
A closed organ pipe has a node at the closed end and an antinode at the open end. It supports only odd harmonics, with frequencies f_n = n v / 4L, for n odd.
Real-world uses
- Clarinets and stopped organ pipes produce a hollow sound from odd harmonics.
- Some bottles produce a tone when blown across, behaving as closed pipes.
- A clarinet acts like a pipe closed at one end, which gives only odd harmonics and a hollow sound.
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Frequently asked questions
Why only odd harmonics?
Because the closed end forces a node, which only allows wavelengths that fit a quarter-cycle pattern.
How long is the fundamental?
The pipe length is a quarter of the wavelength.
Why does a closed pipe only give odd harmonics?
The closed end must be a node, and only odd multiples of a quarter wavelength fit the length of the pipe.
Related topics in Waves & Sound
Modes of a stretched string · Harmonics and overtones · Open organ pipe · End correction · Kundt's tube · Resonance tube experiment