Scattering matrices in non-uniformly lined ducts

Sudden area expansion and sudden area contraction in an infinitely long duct with discontinuous locally reacting lining are defined by respective mixed boundary value problems. In the absence of a sudden area change, a separate problem with an infinite duct having bifid lining on its wall is described. Introducing Fourier transform along the duct axis boundary value problems is solved by the well-known Wiener–Hopf technique, and then, corresponding scattering matrices are constructed. To show the proper use of scattering matrices in the case of several discontinuities and also validation and comparison purposes, transmitted field in a duct with an inserted expansion chamber whose walls are treated by acoustically absorbent material is derived by the help of the relevant scattering matrices. A perfect agreement is observed when the transmitted fields are compared numerically with a similar work exists in the literature.