Helmholtz Resonator Frequency Calculator
A Helmholtz resonator is a cavity with a narrow neck, where the neck air acts as a mass and the cavity air as a spring, giving a single resonant frequency. It is the physics behind a bottle whistle, a ported speaker, and many acoustic absorbers and mufflers. This calculator applies the standard Helmholtz equation with a 1.7-radius neck end correction. Enter the neck diameter and length, the cavity volume, and the speed of sound, which depends on temperature and is editable.
Helmholtz resonance formula
neck area A = pi * (diameter / 2)^2
effective length Leff = length + 1.7 * (diameter / 2)
frequency = (speed of sound / (2 * pi)) * sqrt(A / (volume * Leff))
period (ms) = 1000 / frequency
The neck air mass and the cavity air spring set the resonance. The end correction of about 1.7 radii accounts for air moving just beyond the neck opening, lowering the frequency a little.
Resonator facts
- A wider neck opening raises the resonant frequency.
- A longer neck or larger cavity lowers it.
- The same physics tunes ported speakers and acoustic mufflers.
- A bottle sounds lower as it empties because the air cavity grows.
- The end correction reflects air motion just outside the neck mouth.
Helmholtz resonator: frequently asked questions
What is a Helmholtz resonator?
A Helmholtz resonator is a cavity with a narrow neck, like a bottle. The air in the neck acts as a mass and the air in the cavity as a spring, so the system resonates at one frequency. Blowing across a bottle top excites exactly this resonance.
What is the Helmholtz resonance formula?
The resonant frequency is (speed of sound / 2 pi) times the square root of neck area divided by the product of cavity volume and effective neck length. Effective length adds an end correction of about 1.7 times the neck radius to the physical neck length.
Why add an end correction to the neck?
Air just outside the neck also moves with the oscillation, so the vibrating air column is effectively longer than the physical neck. A standard correction adds roughly 1.7 radii (0.85 diameters) for a flanged opening, lowering the resonant frequency slightly.
What raises or lowers the resonant frequency?
A larger neck opening raises the frequency, while a longer neck or a larger cavity lowers it. This is why a nearly empty bottle (large cavity) sounds lower than a partly full one (small air cavity) when you blow across it.
What units should I use?
Enter the neck diameter and length in metres, the cavity volume in cubic metres, and the speed of sound in metres per second. The result is the resonant frequency in hertz. Use consistent SI units throughout.
Official sources
- National Institute of Standards and Technology: SI units and frequency.
- Acoustical Society of America: resonator acoustics references.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.