Fundamental of a Closed Pipe
Worked example: 25 cm closed pipe (v = 343) → f = 343 Hz — press Try an example to run it live, then adjust anything.
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Grade 11Grade 11 Physics
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Fundamental of a Closed Pipe explained
A pipe sealed at one end must have a node (no air motion) at the closed end and an antinode (maximum motion) at the open mouth. The longest wave satisfying both fits just a quarter of a wavelength inside, so the fundamental is v/4L — an octave lower than an open pipe of the same length. Blow across a 20 cm test tube and you get roughly 343/(4 × 0.20) ≈ 429 Hz, close to concert A.
This quarter-wave trick is why a clarinet plays nearly an octave deeper than a flute of the same length: the reed end acts closed while the flute is open at both ends. It also explains the closed pipe's hollow timbre — the boundary conditions only permit odd harmonics (f, 3f, 5f...), stripping out every even overtone. Your own ear canal is a closed pipe about 2.5 cm deep, resonating near 3400 Hz, which is precisely where human hearing is most sensitive — and where audiologists find the most noise damage.
Fundamental of a Closed Pipe formula
- = Fundamental frequency (Hz)
- = Speed of sound (m/s)
- = Pipe length (m)
Missing one of these? Work it out first, then come back
- Fundamental frequency — Fundamental Frequency of a String, Fundamental of an Open Pipe
- Speed of sound — Doppler Effect (Approaching Source), Doppler Effect (Approaching Observer)
- Pipe length — Fundamental of an Open Pipe, Poiseuille's Law