Propagation of localized pulse trains in a circular acoustic waveguide

Abstract

A brief overview of a novel approach to the synthesis of wave signals [cf. I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, J. Math. Phys. 30, 1254 (1989)] will be presented. This approach, referred to as the bidirectional method, was originally introduced in order to understand the salient features of Brittingham-like solutions. Its scope is broader, however, and encompasses classes of problems altogether different from wave propagation in an unbounded homogeneous domain. The efficacy of the bidirectional method in geometrics involving boundaries has already been demonstrated [cf. A. M. Shaarawi, I. M. Besieris, and R. W. Ziolkowski, J. Appl. Phys. 65, 805 (1989)]. In this presentation, the propagation of localized pulse trains in an infinitely long, circular, acoustic waveguide will be examined in detail. The farfields radiated out of a semi-infinite, circular, acoustic waveguide, excited by a localized initial pulse, will also be studied. These approximate solutions, which are computed using Kirchhoff's integral formula with a retarded Green's function, are causal, have finite energy, and exhibit a slow energy decay.