Sample cylindrical designs at 20°C
| Case | Neck Ø (cm) | Neck L (cm) | Cavity Ø (cm) | Cavity L (cm) | Estimated f (Hz) |
|---|---|---|---|---|---|
| Compact canister | 2.00 | 4.00 | 10.00 | 15.00 | 123.5 |
| Longer port | 2.00 | 8.00 | 10.00 | 15.00 | 92.9 |
| Larger cavity | 2.00 | 4.00 | 14.00 | 20.00 | 76.4 |
Helmholtz resonance for a cylindrical cavity
The classic Helmholtz frequency uses neck cross-sectional area, cavity volume, and an effective neck length:
- A = π(rneck)² (circular neck area)
- V = π(rcav)² · Lcav (cylindrical cavity volume)
- Leff = Lneck + ΔLin + ΔLout
- Typical end corrections use ΔL ≈ k·r with k ≈ 0.61 (unflanged) or k ≈ 0.85 (flanged)
- Temperature-based sound speed: c ≈ 331.4 + 0.6T (m/s), with T in °C
Step-by-step
- Select a mode: frequency, neck length, or cavity length.
- Pick a length unit and enter neck and cavity diameters.
- Enter the remaining dimensions, or a target frequency if required.
- Choose end correction presets, or override coefficients if needed.
- Set temperature (or override sound speed), then click Calculate.
- Use the CSV/PDF buttons to export the computed report.
Cylindrical Helmholtz resonators are tube-friendly devices for targeting a narrow tonal frequency in ducts, enclosures, and noise-control prototypes.
1) What a cylindrical Helmholtz resonator is
A Helmholtz resonator behaves like a spring–mass system: cavity air compresses like a spring and neck air moves like a mass. Cylindrical versions are popular because volume is set by diameter and length, making tube-based prototypes fast to build and repeat.
2) Geometry that drives the result
The inputs are neck diameter/length and cavity diameter/length. Neck area scales with diameter squared, so a small diameter increase can raise frequency quickly. Cavity volume scales with diameter squared too; increasing cavity length or diameter lowers frequency by increasing volume.
3) Frequency equation in one sentence
The calculator uses f = (c/2π)·√(A/(V·Leff)), where A is neck area, V is cavity volume, and Leff is the effective neck length. Intermediate values are shown to help verify inputs and units.
4) Why effective neck length matters
Air motion extends beyond the physical neck, so Leff = L + ΔLin + ΔLout. Corrections depend on how each opening radiates. Ignoring them can shift results, especially with short necks or large neck diameters.
5) Choosing end correction presets
Unflanged is typical for a plain tube opening. Flanged is closer to an opening flush with a large baffle or wall. Confined or “inside cavity” ends can behave differently than free-air ends. If you have measured data, custom coefficients let you match your setup and reuse that calibration.
6) Temperature, sound speed, and tuning drift
Sound speed increases with temperature, so resonance rises as air warms. A change from 0 °C to 20 °C shifts predictions by roughly 3–4%. For HVAC, engine-bay, or outdoor designs, set temperature (or override c) to reduce frequency surprises during testing.
7) A practical design workflow
Pick a target frequency and solve for neck length or cavity length, then confirm the geometry is buildable. Keep ratios sensible: extremely short, wide necks can break the lumped assumption. Iterate by changing one parameter and observing A, V, and Leff.
8) Limits and validation tips
This is an estimate model for a single dominant resonance. Mean flow, high SPL, leaks, porous linings, or complex ports add losses that shift the peak and broaden bandwidth. When performance is critical, prototype and measure, then refine dimensions using the calculator for faster convergence.
Common questions
1) What units does the calculator accept?
Choose mm, cm, m, inches, or feet. All geometry inputs are converted internally to meters before computing volume, area, and effective neck length, then results are displayed with consistent units.
2) Why does “effective neck length” differ from my physical neck?
Air motion extends beyond the neck openings, adding an end correction. The effective length equals physical length plus the selected corrections at the inner and outer neck ends.
3) Should I use flanged or unflanged end correction?
Use unflanged for a simple pipe opening into free space. Use flanged when the neck opens flush to a large baffle or wall. When unsure, compare both and validate with a quick measurement.
4) How does cavity diameter affect resonance?
For a fixed cavity length, increasing cavity diameter increases volume, which lowers resonance. Because volume scales with diameter squared, small diameter changes can noticeably shift frequency.
5) Can I design by solving for cavity length?
Yes. Select the cavity-length mode, enter neck geometry and target frequency, then the tool computes the cavity length required for the needed volume while keeping the cylindrical cavity shape.
6) Does this include losses and damping?
The main output is the ideal resonance frequency. Viscous and thermal losses, leakage, and material absorption are not fully modeled, so real resonators may have a slightly different peak and bandwidth.
7) Why does temperature matter so much?
Resonance scales with sound speed. Warmer air increases sound speed, raising frequency; cooler air lowers it. If your application spans seasons or heated airflow, entering temperature improves estimates.
Disclaimer: This calculator uses a classic lumped-parameter approximation and is for engineering estimates. For high SPL, mean flow, or complex geometries, validate with measurement or detailed simulation.