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

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

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 ${\displaystyle (p_{A}=100~{\rm {kPa}},~\rho =1000~{\rm {kg/m^{3}}})}$, this equation reduces to ${\displaystyle fa\approx 3.26~{\rm {m/s}}}$, where ${\displaystyle f~}$ 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.