Propagation of Long Waves in Curved Ducts

Abstract

Propagation of waves in curved ducts and pipes belong to the class of motion which is characterized by wave patterns totally different from those known in straight ducts or in unlimited space. The curvilinear boundaries are responsible for the appearance of a continuous standing radial wave which in turn affects the transmitted tangential waves. The purpose of this paper is to solve the problem of propagation of long acoustic waves in slightly and sharply bend ducts. This problem has been only partially analyzed by various authors. In this study two acoustic systems are considered which allow determination of the basic modes of motion and desribe the transition and distortion of plane waves as they propagate down the curved channel. A detailed study of the behavior of waves in junctions between straight and curved ducts will be given. Solutions and expressions for principal modes of the wave are obtained by using the linearized equation of motion solved for its characteristic values. This original approach required a novel use of Bessel functions to determine the characteristic values of the steady and the decaying fields of motion.