The Propagation of Sound in Cylindrical Ducts with Mean Flow and Bulk-reacting Lining II. Bifurcated Ducts

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Abstract
The transmission and reflexion of sound in a bifurcated coaxial cylindrical duct is investigated. The inner tube carries a uniform flow and consists of two semi-infinite tubes: one is hard and the other is perforated. The space between the coaxial cylinders is filled with a sound-absorbing material. Transmission and reflexion matrices are calculated for the causal solution. It is found that causality and the boundary conditions require an instability wave when the perforated tube is downstream its junction to the hard tube. When the perforate is situated upstream the junction the analysis permits incident waves that are unstable. This is important for applications to multiple reflexions. It follows from the analysis that, in addition to giving rise to the instability wave, the gas flow has several other important effects on the acoustic properties of the junction.

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