Helmholtz number#
Named after: Hermann von Helmholtz (1821-1894).
$$\text{He} \stackrel{\text{def}}{=} \frac{f L}{c} \sim \frac{\text{acoustic length scale}}{\text{sound speed}}$$
Description#
Measures acoustic length scale relative to wavelength through frequency and sound speed. It indicates whether a body or domain is acoustically compact.
Quantities#
| Name | Symbol | SI units | Dimension |
|---|---|---|---|
| frequency | \(f\) | \(\mathrm{Hz}\) | \(\text T^{-1}\) |
| characteristic length | \(L\) | \(\mathrm{m}\) | \(\text L\) |
| speed of sound | \(c\) | \(\mathrm{m}\,\mathrm{s}^{-1}\) | \(\text L\,\text T^{-1}\) |
Regimes#
Acoustics
| Range | Regime | Description |
|---|---|---|
| 0 – 0.1 | compact | The object or domain is small relative to the acoustic wavelength and can often be treated as acoustically compact. |
| 0.1 – 1 | finite wavelength | Wavelength effects are noticeable and spatial phase variation matters. |
| 1 – ∞ | wave dominated | The acoustic wavelength is comparable to or smaller than the characteristic length. Resonance and wave structure dominate. |