Linear inviscid wave propagation in a waveguide having a single boundary discontinuity: Part I: Theory

An examination of wave propagation in waveguides of rectangular cross section having a single boundary discontinuity is presented. Special attention is paid to waveguides with heights that are small compared to an acoustic wavelength. It is shown that the dynamic behavior of the enclosed fluid can be parametrized by the value of a single small parameter ɛ, where ɛ is the ratio of the typical duct height H₀ to the wall wavelength L₀. The influence of planar discontinuities of zero and small but finite thickness on wave propagation is determined using the method of matched asymptotic expansions. Junction conditions, impedance across the junction, and uniformly valid composite expansions for the pressure in the duct are presented.