The Propagation of Sound in Cylindrical Ducts with Mean Flow and Bulk-reacting Lining IV. Several Interacting Discontinuities

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Abstract
The interaction of several discontinuities in an acoustical waveguide is treated. A scattering matrix technique is derived and applied to bifurcations, sudden area changes and extended inlets and outlets in a cylindrical duct with gas flow, a perforate and a sound-absorbing material. In some cases the solution can be interpreted in terms of multiple reflexions. It is shown that when the length of the extended inlet vanishes the limit of the solution agrees with an earlier theory of Nilsson & Brander and with experimental results of Ronneberger. In this case both propagating and non-propagating modes must be considered. A number of numerical results with variation of frequency and various lengths are presented. The importance of growing modes in the acoustical interaction between nearby discontinuities is stressed, and the application of the presented method to muffler design is discussed.

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