Sound Cavities
Open/closed tube resonances. Builds on Standing Waves & Harmonics.
You have two organ pipes of the same length L. One is open at both ends; the other is closed at one end. Both resonate at their fundamental frequency.
Which pipe produces the LOWER fundamental note?
The closed pipe produces a note one OCTAVE lower! Its fundamental wavelength is 4L (fitting just one quarter-wavelength inside), while the open pipe’s fundamental wavelength is 2L (fitting one half-wavelength). Since f = v/λ, the closed pipe’s frequency is half that of the open pipe. Same length, but very different sound!
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Toggle between open-open and closed-open pipes. Watch the standing wave patterns form inside. Notice the closed pipe’s fundamental fits only 1/4 wavelength, while the open pipe fits 1/2. Listen to the pitch difference!
fₙ = nv/(2L) (open) fₙ = nv/(4L) (closed, odd n)
A closed pipe’s missing even harmonics give it a very different tone color from an open pipe, even at the same pitch. This is why a clarinet (closed) sounds different from a flute (open).
Church organs use both open and closed (stopped) pipes. A stopped pipe sounds an octave lower than an open pipe of the same length, saving space and materials for the lowest bass notes.
A clarinet is acoustically a closed-open pipe (reed end is closed). A flute is open-open. That’s why a clarinet of similar length plays nearly an octave lower and has a different, richer tone.
Car exhaust systems use tuned pipe lengths to cancel specific sound frequencies via destructive interference. Quarter-wave resonators absorb noise at their resonant frequency.
Trumpets and trombones use their tube length plus valves or slides to access different harmonics. The bugle (no valves) can only play the natural harmonic series of its fixed tube.
“Same pipe, different ends, different music. Boundary conditions determine which waves fit — and that determines what you hear.”
Sound Cavity Lab
Explore resonance in open and closed pipes. Adjust pipe length, drive frequency, and end conditions. Visualize pressure and displacement standing waves, and hear the resulting tones.
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Start with an open-open pipe and sweep the frequency to find the first three harmonics. Note they’re evenly spaced (f, 2f, 3f). Now switch to closed-open and sweep again — only odd harmonics appear (f, 3f, 5f). Compare the fundamental frequencies: the closed pipe’s is exactly half. Toggle between pressure and displacement views to see how the node patterns differ.
Open ends force displacement antinodes; closed ends force displacement nodes. This simple boundary condition determines the entire harmonic series — all harmonics for open pipes, odd only for closed pipes.