Sum rule in quantum mechanics

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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=12πa(3γpAρ)1/2

where a is the radius of the bubble, γ is the polytropic coefficient, pA is the ambient pressure, and ρ 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 ρ the difference between the density of water and the bulk density of the cloud. For a bubble in water at standard pressure (pA=100kPa,ρ=1000kg/m3), this equation reduces to fa3.26m/s, where f is the resonant frequency of the bubble.

References

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