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
where h is the thickness of the bubble layer, and
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?
