Wiener-Hopf approach for predicting the transmission loss of a circular silencer with a locally reacting lining

The propagation of sound in an infinite rigid circular cylindrical duct with an inserted expansion chamber whose walls are treated with an acoustically absorbent, locally-reacting material is investigated rigorously through the Wiener-Hopf technique. The expansion chamber is separated from the central airway which contain a uniform main gas flow by a perforated cylindrical screen which also increases the silencing performance. The influence of the expansion chamber radius, lining impedances, the mean flow and the acoustical impedance of the central perforated tube on the transmission loss are displayed graphically.