Horns and Stepped Ducts

Abstract

The wave equations derived in the preceding chapter allow for calculation of arbitrary sound fields with any possible, physically meaningful boundary conditions. We had restricted ourselves to one-dimensional waves so far. These can, for instance, be observed in tubes with a diameter being small compared to the wavelength, that is d ≪ λ. This condition guarantees that no other waveforms than axial ones can propagate in the tube. One-dimensional propagation also means that all wave planes perpendicular to the axial direction are planes of constant phase.

In the following, ducts shall be considered where the diameter varies with x. In other words, the area function A = f(x) is no longer constant. Nevertheless, the condition d ≪ λ shall still holds. Two cases – depicted in Fig.8.1 – will be discussed.