The wave equation(∂tt−c2∆x)u(x, t) =e−tf(x, t) in the cone{(x, t) :‖x‖ ≤t, x∈Rd, t∈R+}is shown to have a unique solution if u and its partial derivatives in x are in L2(e−t) on the cone, and the solution can be explicit given in the Fourier series of orthogonal polynomials on the cone. This provides a particular solution for the boundary value problems of the non-homogeneous wave equation on the cone, which can be combined with a solution to the homogeneous wave equation in the cone to obtain the full solution.