A method of weighted residuals with trigonometric basis functions for sound transmission in circular ducts

Abstract

A modified Galerkin method is employed to formulate the problem of transmission of sound in a uniform circular duct. The basis functions used are trigonometric and are derived from the equivalent problem in a two-dimensional duct. In the case when flow is present basis functions from the case without flow are used. It is found that the success of the method is dependent on the choice of basis functions within the class of functions discussed, particularly when flow is present. Results for axial wave numbers are generally of accuracy similar to the results achievable by a similar approach in the two-dimensional case.