Question

Consider three dimensional wave equation

where ψ is a function of r and t. Find solutions representing spherical waves i.e. solutions of the form ψ = ψ (r, t).

Answer 1

where ƒ and g are arbitrary functions. Hence we get

The first term represents a spherical wave diverging from the origin, the second a spherical wave converging towards the origin. The velocity of propagation in both cases is v.