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(b) An earthquake-generated ocean wave may be modelled by considering water of depth h, with the lower boundary condition on the vertical velocity w(-h, 1) = b cos(kx - wt) at z = -h, where b is constant. The surface boundary conditions are unchanged. Consider a pressure disturbance of the form (x,z,1) = Z(z) sin(kx - ot), where is as given in part (a). (i) What does this lower boundary condition become in terms of Z(z)? (ii) What does condition (iv), in part (a), become in terms of Z(z)? (iii) What differential equation does Z(z) satisfy? (iv) By solving for Z(z) obtain the pressure perturbation, Ⓡ(x,z,1). (v) What is the corresponding surface displacement? (vi) For any given wavenumber k of the bottom disturbance there is a speed c = wlk of the disturbance for which the surface displacement is singular. How are w and k related in this case? What is happening?