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). It is the characteristic sound of a drop of water from a tap falling in water underneath. The resonant frequency of the resulting air bubble in the water is given by
where formula_2 is the radius of the bubble, formula_3 is the polytropic coefficient, formula_4 is the ambient pressure, and formula_5 is the density of water. This formula can also be used to find the resonant frequency of a bubble cloud with formula_2 as the radius of the cloud and formula_5 the difference between the density of water and the bulk density of the cloud. For a bubble in water at standard pressure formula_8, this equation reduces to
formula_9, 
where formula_10 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 gas bulk modulus formula_11
formula_13 and formula_14 being respectively the density and the speed of sound in the bubble.