Blow across the top of a bottle and it hums a single clear note — that's a Helmholtz resonator. The trapped air in the bottle's body acts like a soft spring, and the plug of air sitting inside the narrow neck acts like a mass bouncing on that spring. Push the neck-air in and the cavity pressure rises and pushes back; the system oscillates at one dominant frequency, exactly like a mass on a spring in mechanics.
f = c/(2π) · √(A / (V·Leff)), where A is the neck's cross-sectional area, V is the cavity volume, Leff is the neck length plus an "end correction" for the air that moves just outside each opening, and c is the speed of sound.A) means a lighter, easier-to-push air mass → higher pitch.V) is a softer spring → lower pitch.Leff) is a heavier air mass → lower pitch.c, which raises the pitch slightly.Hermann von Helmholtz described this resonance in the 1860s using bottle-shaped brass spheres to isolate individual pitches from complex sounds. The same physics tunes bass-reflex loudspeaker ports, car exhaust mufflers, and the sound of blowing across a drink bottle.
A 3D bottle-shaped cavity where the trapped air acts as a spring and the plug of air in the neck acts as a mass, oscillating at one dominant resonant frequency exactly like blowing across a bottle top.
The resonant frequency depends on the neck's cross-sectional area, the neck's effective length (including end corrections), and the cavity's volume — the same spring-mass-damper physics as a mechanical oscillator.
Adjust neck length, neck radius, cavity volume and air temperature to see the resonant frequency, note and wavelength update live. Click "Puff of air" to excite the resonator and watch the air mass oscillate and sound-wave rings spread from the neck.
Hermann von Helmholtz used bottle-shaped brass resonators in the 1860s to isolate single pitches from complex sounds — the same principle now tunes bass-reflex speaker ports and car mufflers.