AN APPROXIMATE ANALYTICAL SOLUTION FOR PLANE SOUND WAVE TRANSMISSION IN INHOMOGENEOUS DUCTS

Abstract

A general approximate analytical solution is presented for transmission of plane sound waves in subsonic low Mach number ducts with axial ambient gradients and cross-sectional area variations. This is essentially a high frequency approximation and explicit criteria are presented for the estimation of the lower limiting frequency in practical applications. For uniform ducts, the proposed solution is almost exact for the temperature gradients and frequencies that are likely to be encountered in practice. In the case of non-uniform ducts, the lower limiting frequency increases with the cross-sectional area gradient and in applications where low frequencies are important, the utility of the approximate solution will be limited to ducts with a relatively small area ratio.