Minnaert resonance

The Minnaert resonance^[1] is the acoustic resonance frequency of a single bubble in an infinite domain of water (neglecting the effects of surface tension and viscous attenuation). The resonant frequency is given by

$f = \cfrac{1}{2\pi a}\left(\cfrac{3\gamma~p_A}{\rho}\right)^{1/2}$

where $a$ is the radius of the bubble, $\gamma$ is the polytropic coefficient, $p_A$ is the ambient pressure, and $\rho$ is the density of water. This formula can also be used to find the resonant frequency of a bubble cloud with $a$ as the radius of the cloud and $\rho$ the difference between the density of water and the bulk density of the cloud. For a bubble in water at standard pressure $(p_A=100~ {\rm kPa}, ~ \rho=1000~ {\rm kg/m^3})$, this equation reduces to $f a \approx 3.26~ \rm m/s$, where $f~$ is the resonant frequency of the bubble.

References

1. Minnaert, M. (1933), "On musical air-bubbles and the sound of running water", Philosophical Magazine 16 (104): 235–248, doi:10.1080/14786443309462277

External links

• Low-Frequency Resonant Scattering of Bubble Clouds by Paul A. Hwang and William J. Teague, 2000, Journal of Atmospheric and Oceanic Technology, vol. 17, no. 6, pp. 847-853.