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Helmholtz Resonator Frequency Calculator — result sheet
Estimate the resonance frequency of a bottle-like Helmholtz resonator from opening area, cavity volume, neck geometry, and sound speed.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Leff = L + αr; f = c/(2π)√[A/(VLeff)].
The opening behaves as an acoustic mass and the cavity as an acoustic compliance. The entered end-correction factor makes the neck-length convention explicit instead of silently assuming a particular opening geometry.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Neck opening area — m²; minimum 1.0E-12; maximum 1000000
- Cavity volume — m³; minimum 1.0E-12; maximum 1000000
- Physical neck length — m; minimum 1.0E-6; maximum 1000000
- Neck radius — m; minimum 1.0E-6; maximum 1000000
- Speed of sound — m/s; minimum 1.0E-6; maximum 1000000
- End-correction factor — minimum 0; maximum 100
Worked example
| Input | Value |
|---|---|
| Neck opening area | 0.0001 |
| Cavity volume | 0.001 |
| Physical neck length | 0.02 |
| Neck radius | 0.005 |
| Speed of sound | 343 |
| End-correction factor | 1.7 |
Effective neck length is 0.0285 m and resonance is about 102.3 Hz.
Assumptions and limits
- The resonator is small compared with the acoustic wavelength and behaves as a lumped low-frequency system.
- Neck area, cavity volume, radius, and length use SI units; the end factor is supplied for the opening geometry.
- Damping, wall compliance, radiation impedance, higher modes, and frequency-dependent losses are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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