Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Students · Helmholtz Resonator

Helmholtz Resonator for an ultrasound

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate an ultrasound live below — adjust the inputs and watch it respond, right in your browser.

Helmholtz ResonatorLive

the resonance of a bottle

Controls

Presets

Cavity volume (cm³)

Neck diameter (cm)

Neck length (cm)

Blow across a bottle and it sings at its Helmholtz frequency. The plug of air in the neck acts as a mass and the air in the cavity as a spring, giving f = (c/2π)√(A/VL). Bigger cavities and longer necks lower the pitch — the principle behind bass ports, mufflers, and ocarinas.

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Data Inspector

Resonant frequency167 Hz

Wavelength2.05 m

Cavity500 cm³

Governing equation

f = \frac{c}{2 π} \frac{A}{V L _{eff}} = \frac{343}{2 π} \frac{3.14 e - 4}{5.00 e - 4 \cdot 0.067} = 167 Hz

Reading this result: This cavity sings near 167 Hz — a 2.05 m wavelength. Enlarge the cavity or lengthen the neck and the pitch drops, because both add to the mass-on-a-spring that sets the tone.

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Frequently asked questions

Is this good for students?: Yes — this version of "Helmholtz Resonator for an ultrasound" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.