Scattering of acoustic waves in a waveguide

The problem of scattering from boundary discontinuity in a waveguide is discussed. The relationship between the static and dynamic representations of the scattered pressure field will be investigated for those frequencies falling below the first cross mode of the duct. Special attention is paid to the influence of cutoff cross modes to the solution of the pressure field. It is shown that the method of matched asymptotic expansions can be successfully used to determine globally valid pressure field junction conditions near a boundary discontinuity. The matching of exponentially decaying terms of the inner solution is shown to, in turn, contribute to the junction impedance and extend the frequency range of the solution's validity.