Blowing across a bottle produces a tone: the air in the neck bounces like a mass on the spring of the air in the cavity. Loudspeaker ports, guitar sound holes, car intakes and noise silencers are all tuned Helmholtz resonators.
How to use the Helmholtz Resonator Calculator
- Cavity shape
- Cavity volume V
- Box length
- Box width
- Box height
- Cavity diameter
- Cylinder height
- Opening shape
- Opening area
- Opening diameter
- Opening width
- Opening height
- Neck length L
- End correction
- Speed of sound
- Custom speed of sound
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the cavity and opening shapes and enter the dimensions. Pick the end correction that matches your neck (a flanged end sits flush with a large surface).
Inputs explained
| Field | What to enter |
|---|---|
| Cavity shape | Choose one: Arbitrary (volume), Box, Sphere, Cylinder |
| Cavity volume V | Units: L, mL, m³, US gal, ft³ |
| Box length | Units: cm, mm, m, in, ft |
| Box width | Units: cm, mm, m, in, ft |
| Box height | Units: cm, mm, m, in, ft |
| Cavity diameter | Units: cm, mm, m, in, ft |
| Cylinder height | Units: cm, mm, m, in, ft |
| Opening shape | Choose one: Arbitrary (area), Circle, Rectangle |
| Opening area | Units: cm², mm², m², in² |
| Opening diameter | Units: cm, mm, m, in, ft |
| Opening width | Units: cm, mm, m, in, ft |
| Opening height | Units: cm, mm, m, in, ft |
| Neck length L | Units: cm, mm, m, in, ft |
| End correction | Choose one: Both ends free (1.2r), One end flanged (1.45r), Both ends flanged (1.7r), None |
| Speed of sound | Choose one: Air at 0 °C, Air at 20 °C, Air at 40 °C, Helium at 20 °C … |
| Custom speed of sound | Units: m/s, km/h, mph, ft/s, knots |
What each result means
- Effective neck length = [Neck length L] + [End correction]×sqrt([Opening area]÷pi)
- Cavity volume = [Cavity volume]
- Resonant frequency f = [c]÷(2×pi)×sqrt([Opening area]÷([Cavity volume]×[Effective neck length]))
Example values
How the main result changes when Cavity volume V changes and everything else stays at the example values above:
| Cavity volume V (L) | Resonant frequency f (Hz) |
|---|---|
| 0.375 | 180.1405 |
| 0.5625 | 147.0841 |
| 0.75 | 127.3786 |
| 0.9375 | 113.9309 |
| 1.13 | 104.0042 |
| 1.5 | 90.0703 |
Formula
f = (c/2π)·√(A / (V·L_eff)), L_eff = L + end correction (0.6r per free end, 0.85r per flanged end)
Worked example
Inputs — Cavity shape: Arbitrary (volume); Cavity volume V: 0.75 L; Opening shape: Circle; Opening diameter: 2.2 cm; Neck length L: 8 cm; End correction: Both ends free (1.2r); Speed of sound: Air at 20 °C.
Results — Effective neck length = 9.32 cm; Cavity volume = 0.75 L; Resonant frequency f = 127.37859 Hz.
Key terms
- Helmholtz resonance
- Air-mass-on-air-spring oscillation of a cavity with a neck.
Frequently asked questions
Why does a half-empty bottle sound higher?
The air volume is smaller, so the resonance rises.
How are loudspeaker ports tuned?
By choosing the port area and length to set the box resonance.
What is the end correction?
Air just outside the neck also moves, making the neck act longer.
Is the formula exact?
It assumes the cavity is much larger than the neck and the wavelength much longer than the resonator.