Solve the 2d wave equation of a rectangular vibrating

Question

Solve the 2D wave equation of a rectangular vibrating membrane

∂²u/∂t² = c² (∂²u/∂x² + ∂²u/∂y²), 0 < x < L, 0 < y < H,

with initial conditions

u(x, y, 0) = 0, ∂u/∂t (x, y, 0) = g(x, y),

and boundary conditions

u(0, y, t) = 0, u(L, y, t) = 0, ∂u/∂y (x, 0, t) = 0,  ∂u/∂y (x, H, t) = 0,