Application of Method of Separation of Variables to Find Wave Motion in Waveguides with Variable Boundaries and Medium

Abstract

Perturbation methods were used to study the sound wave propagation in several acoustic wave guides with weak surface undulations. These methods are highly complicated and applicable only in a very narrow domain of the wave guide. Moreover, such solutions create singularities in the solution. Singularities in solution of physical problems originate due to unrealistic assumptions. Therefore, a much simpler and widely applicable analytical method of solution was developed using separation of variables method and presented recently to such wave guide problems. In this article, application of that solution to find wave propagation in several periodic waveguide structures is enumerated.