A method is presented for the efficient calculation of radiated acoustic fields from a radially symmetric source in a rigid baffle excited by an arbitrary time excitation. The technique is a modal analysis based on the series expansion of the source velocity excitation in terms of either of two basis functions. Each mode is propagated by the technique with rapid convergence of the solution evident in 30 or less terms, allowing rapid and efficient computer-based solutions to be obtained. Several numerical field simulations are given.