Helmholtz Resonator Calculator

Find the resonant frequency of an acoustic cavity with out Helmholtz resonator calculator!

Helmholtz resonator frequency118.03 Hz(c/2π)√(A/VL) — the note a bottle sounds when you blow across it

Reverberation time2.576 sSabine T₆₀ — the time for sound to decay by 60 dB

Room volume144 m³

Total surface area180 m²

Absorption9 sabinsα = 0.05 — Plastered wall

Suitabilityvery live — speech will be hard to understandspeech intelligibility falls off badly above about 1 second

Average absorption coefficient0.05total absorption divided by total surface — the single figure that characterises how absorptive the room is, regardless of how it is distributed

Absorption coefficient needed0.2147the average coefficient every surface would need to reach 0.6 s

Absorption needed for the target38.64 sabins29.64 sabins more than you have — about 34.9 m² of acoustic foam at α = 0.85

Eyring reverberation time2.511 s2.6% below Sabine's figure — the two converge at low absorption and diverge as it rises

Which formula applies hereSabine is fineaverage α is 0.05, low enough that the field stays diffuse and the two formulas agree closely

Room mode 1,0,021.44 Hzthe lowest axial mode, set by the longest dimension — below this the room cannot support a standing wave at all

Room mode 0,1,028.58 Hz

Room mode 0,0,157.17 Hz

Room mode 1,1,035.73 Hz

Room mode 2,0,042.88 Hz

Schroeder frequency267.5 Hzabove this modes overlap enough to treat the field statistically; below it individual modes dominate and the room colours the sound

Effective neck length6.417 cmthe machined 5 cm plus an end correction of 1.45× the neck radius — the air that oscillates spills out past both ends

Without the end correction133.72 Hz13.3% high — the bare formula always over-predicts, and on a short wide neck it can be out by a whole tone

At half the cavity volume166.93 Hz√2 higher — which is why the pitch rises as you drink from a bottle

The formula

T₆₀ = 0.161V ÷ A; Helmholtz f = (c/2π)√(A ÷ VL)

Volume up, absorption down

Sabine's reverberation time is proportional to room volume and inversely proportional to total absorption. A large hard room rings; a small soft one is dead. Since absorption is area times coefficient, doubling the treated area halves the reverberation time — a linear and predictable relationship, which is why the formula has survived since 1900.

Its assumption is a diffuse field: sound energy uniformly distributed and arriving from all directions. That fails in very absorptive rooms, where sound dies before it can diffuse, and in long narrow ones. Above an average absorption coefficient of about 0.3 Sabine overestimates and Eyring's formula is preferred. Both are computed above, along with which one applies to the room you entered.

Below the Schroeder frequency a room's individual standing-wave modes dominate and reverberation time stops being a useful description. In a domestic room that boundary sits around 100–200 Hz, which is exactly why bass response is so position-dependent and so hard to treat — the lowest axial mode is set by the longest dimension, and below it the room cannot support a standing wave at all.

A Helmholtz resonator is a mass of air in a neck springing against the compliance of a cavity. Its frequency rises as the cavity shrinks, which is audibly why a bottle's note climbs as it empties — and the same principle tunes bass ports and absorbs specific room modes.

The end correction matters

The oscillating air does not stop neatly at the ends of the neck; it spills out past both, so the acoustically effective length exceeds the machined one by roughly 1.45 times the neck radius. Textbook statements of the formula usually leave this out, which over-predicts the frequency — by ten to twenty percent on a bottle-sized neck, enough to be a whole tone sharp. This calculator applies the correction and shows the uncorrected figure alongside it so the size of the effect is visible.