Analytical/numerical description of sound field in irregular waveguides

Abstract

The problems of the harmonic wave propagation in waveguides with varying cross sections and sound radiation from open ends of ones are considered. The main attention gives to development method of complete analytical description of the sound fields in both cases. This gives a basis to get accurate quantitative and qualitative description of the fields near the junctions of the waveguide cross sections and open ends. Numerical implementation of the general analytical formulas requires special procedures to be adequate the local singularities in vicinities of corner points. The approach is based on the introduction of the idea of the general solution of the acoustical boundary problem. The idea gives a way to construct analytical solutions for the problems under consideration and can be extended to a broad spectrum of radiation and scattering problems. The well known solutions for regular waveguides in the form of normal waves are used as important part of the general solutions. Numerical data for concrete waveguides demonstrate the accuracy and convergence rate of the method. Analysis of the data shows interesting physical properties of propagating waves, flows of energy, and local structure of sound field at the juncture of waveguide parts.