An underwater monopole source with angular frequency ? = ck is at depth zS below the water’s surface (a pressure-release surface) and is at a distance xS from a large rigid surface occupying the x = 0...

An underwater monopole source with angular frequency ? = ck is at depth zS below the water’s surface (a pressure-release surface) and is at a distance xS from a large rigid surface occupying the x = 0 plane. Otherwise the region occupied by the water is unbounded. (a) Determine the Green’s function Gk(x, y, z|xS, yS, zS) for the Helmholtz equation that satisfies the boundary conditions appropriate to this problem and verify that the Green’s function satisfies the reciprocity condition. (b) Determine the far-field radiation pattern of the source at distances |x| ?? |xS| when k|x| ?? 1. (c) Determine the time-averaged acoustic power of the source and discuss the limiting cases of kxS ? 0 and kzS ? 0.