Calculator Inputs
Example Data Table
| Case | Resonator | Key Inputs | Estimated Result |
|---|---|---|---|
| 1 | Open-Open Tube | L = 1.20 m, Air at 20°C, Mode = 1 | f ≈ 143.8 Hz, λ ≈ 2.39 m |
| 2 | Open-Closed Tube | L = 0.85 m, Air at 25°C, Mode = 2 | f ≈ 302.7 Hz, odd harmonic family |
| 3 | Closed-Closed Tube | L = 2.00 m, Helium, Mode = 3 | f ≈ 755.3 Hz, λ ≈ 1.33 m |
| 4 | Helmholtz Resonator | d = 0.05 m, l = 0.08 m, V = 0.012 m³ | f ≈ 53.9 Hz, depends on effective neck length |
Formula Used
1) Speed of sound in air: c = 331.3 + 0.606T
2) Open-Open or Closed-Closed tube: fₙ = n c / (2L)
3) Open-Closed tube: fₘ = (2m - 1) c / (4L)
4) Helmholtz resonator: f = (c / 2π) √(A / (V L_eff))
5) Neck area: A = πr²
6) Effective neck length: L_eff = L_n + k r
7) Wavelength: λ = c / f
8) Period: T = 1 / f
9) Angular frequency: ω = 2πf
10) Quality factor relation: Q = f₀ / Δf
Here, L is tube length, V is cavity volume, r is neck radius, and k is the end-correction multiplier.
How to Use This Calculator
- Select the resonator model that matches your system.
- Choose the medium or enter a custom sound speed.
- For tube resonators, provide length and desired mode index.
- For Helmholtz models, enter neck diameter, neck length, cavity volume, and end correction.
- Optionally enter a known Q factor or measured bandwidth.
- Press Calculate Resonance to display the result above the form.
- Review the plotted trend to compare frequency behavior across modes or volume changes.
- Use the CSV or PDF buttons to export the displayed results.
FAQs
1) What does this calculator estimate?
It estimates resonant frequency, wavelength, period, angular frequency, and optional Q-related values for tube and Helmholtz resonators using user-provided geometry and medium settings.
2) Why are only odd harmonics allowed in open-closed tubes?
An open-closed tube must have a pressure node at the open end and an antinode at the closed end. That boundary condition supports only odd multiples of the quarter-wave fundamental.
3) What is the difference between mode index and harmonic number?
For open-open and closed-closed tubes, they match directly. For open-closed tubes, mode index 1, 2, 3 maps to harmonic numbers 1, 3, and 5.
4) What does the end correction factor do?
It adjusts the effective neck length of a Helmholtz resonator because vibrating air extends slightly beyond the physical neck opening. That changes the final resonant frequency.
5) Why does the medium matter?
Resonant frequency depends on the speed of sound. Air, helium, water, and custom media can produce very different resonant values even with identical geometry.
6) How is Q factor used here?
Q relates resonant frequency to bandwidth. If you know one, the calculator can estimate the other. Higher Q usually means a sharper, narrower resonance peak.
7) Can I use this for loudspeaker enclosures?
Yes. The Helmholtz mode is useful for vented cavities and enclosure ports, provided your dimensions and effective neck assumptions reasonably represent the real geometry.
8) What does the plot show?
For tube resonators, it shows modal frequencies across several resonance orders. For Helmholtz resonators, it shows how resonant frequency changes as cavity volume varies.