A storm has created a 1m thick surface layer with a uniform distribution of small air bubbles. The fraction of the volume occupied by the bubbles is 10_3.

a. What assumption(s) do you have to make to treat the bubble layer as a homogeneous

acoustic medium?

b. Under these assumptions, find the numerical values of the sound speed c and density _ of the bubble layer. The sound speed of water and air are 1500 m/s and ca = 340 m/s, respectively, and the corresponding densities are _w = 1000 kg/m3 and _a = 1:2 kg/m3.

c. Show that the characteristic equation for normal modes in the bubble layer is

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where h is the thickness of the bubble layer, and

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d. Discuss the physical significance of aw and kz.

e. What is the value of the cutoff frequency below which no normal modes can exist in the bubble layer?