Minnaert resonance

The Minnaert resonance 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

where ${\displaystyle a}$ is the radius of the bubble, ${\displaystyle \gamma }$ is the polytropic coefficient, ${\displaystyle p_{A}}$ is the ambient pressure, and ${\displaystyle \rho }$ is the density of water. This formula can also be used to find the resonant frequency of a bubble cloud with ${\displaystyle a}$ as the radius of the cloud and ${\displaystyle \rho }$ 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.

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