Helmholtz Resonator Calculator

A Helmholtz resonator is a cavity of trapped air connected to the outside through a narrow neck. The air in the neck moves as a lump of mass and the air in the cavity acts as a spring, so the device is a mechanical mass-spring oscillator built entirely out of air. Blowing across the top of a bottle is the everyday demonstration: the bottle is the cavity, the mouth is the neck, and the note you get is the resonant frequency this calculator predicts.

The air that moves does not stop neatly at the ends of the neck. A slug of air just outside each opening is dragged along too, so the neck behaves acoustically longer than it measures physically. This calculator adds 0.85 times the neck radius as an effective extra length, the standard flanged-end correction. It is not a rounding detail: for a 5 cm diameter port that is 10 cm long, the correction adds 2.1 cm — over 20 percent — and lowers the predicted frequency by roughly 10 percent. A calculator that omits it will send you a port that tunes high.

Because the model assumes the cavity is acoustically small — every dimension much shorter than a wavelength at the resonant frequency — so the pressure inside it is uniform and only the volume matters. The default here, a 30 litre cavity resonating near 40 Hz, has a wavelength of 8.6 metres against a box roughly 0.31 metres across: about 15 percent of a quarter wavelength, so the assumption holds comfortably. It stops holding as the cavity approaches a quarter wavelength, at which point the box has standing waves of its own and you need a full modal treatment rather than a lumped-element one. The calculator prints that ratio for your geometry.

Sharper than most people want. An untreated resonator has a high Q, meaning it absorbs strongly over a narrow band and does nothing an octave away. That is the point when you are killing one mode, and a liability when you wanted broadband control. Adding a light layer of fabric or open-cell foam across the neck introduces resistance, lowers Q, and trades peak absorption for bandwidth. Most practical bass traps are deliberately damped this way.

Yes, through the speed of sound, and the calculator exposes temperature for that reason. Frequency scales directly with c, which rises about 0.17 percent per degree Celsius near room temperature. A resonator tuned to 42 Hz at 20 °C sits near 42.7 Hz at 30 °C. That is inaudible in a room but it matters in an engine intake, where air temperatures swing by 60 degrees or more and the tuning moves by several percent.