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Helmholtz Resonator Frequency Calculator

Find the resonant frequency of a cavity-and-neck resonator (a bottle, a speaker port, a tuned enclosure) from its neck dimensions and cavity volume.

Resonant frequency
238.9 Hz
Effective neck length (physical length + end correction)
5.125 cm
End correction added
2.125 cm

How it works

A Helmholtz resonator — a bottle, a speaker enclosure's tuning port, any cavity with a narrow neck — resonates because the plug of air sitting in the neck behaves like a mass, while the air trapped in the larger cavity behaves like a spring, the same mass-spring physics as mechanical oscillation realized acoustically. The resonant frequency is f = (c ÷ 2π) × √(S ÷ (V × Leff)), where S is the neck's cross-sectional area, V is the cavity volume, c is the speed of sound, and Leff is the neck's effective length.

Leff isn't just the neck's physical length: air just outside the open end also moves with the oscillation, adding extra effective mass. The standard correction is Leff = L + k×d, where d is the neck's diameter and k is 0.85 for an unflanged opening (a neck that protrudes freely into open air, like a bottle) or 0.61 for a flanged opening (a neck's mouth sitting flush with a larger flat panel, like a port drilled through a speaker-box wall) — this model assumes a single open neck end, the common real-world case, not a tube open to free air at both ends.

Speed of sound defaults to 343 m/s (dry air at roughly 20°C) but is left editable, since it genuinely shifts the resonant frequency a few percent across realistic temperature ranges — pair with this site's own Speed of Sound in Air calculator to get a more precise value for your actual conditions.

FAQ

Why does a flanged neck resonate at a higher frequency than an unflanged one?

A flanged mounting (flush with a panel) only lets air radiate outward into a half-space, which adds less effective mass to the neck than an unflanged opening radiating into free space on all sides — a smaller end correction means a shorter effective neck, and a shorter, lighter acoustic mass resonates faster for the same cavity 'spring.'

Does a bigger cavity always lower the pitch?

Yes — a larger cavity volume is a 'softer' acoustic spring (it takes a smaller pressure change to displace the same volume of air), and frequency falls as the square root of volume. This is the same principle behind why blowing across a nearly-empty bottle produces a lower note than blowing across one that's mostly full: the empty bottle has more effective air volume acting as the spring.

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