Minnaert resonance
The Minnaert resonance is the acoustic resonance frequency of a single bubble in an infinite domain of water. The resonant frequency is given by
where is the radius of the bubble, is the polytropic coefficient, is the ambient pressure, and is the density of water. This formula can also be used to find the resonant frequency of a bubble cloud with as the radius of the cloud and the difference between the density of water and the bulk density of the cloud. For a bubble in water at standard pressure, this equation reduces to
,
where is the resonant frequency of the bubble. The Minnaert formula assumes an ideal gas, however it can be easily modified to account for deviations from real gas behavior by accounting for the gas compressibility factor , or the gaz Bulk modulus :
and being respectively the density and the speed of sound in the bubble.
