Acoustics of an obstacle inside a reactive silencer

Abstract

The transmission and reflection of sound in a cylindrical duct containing several discontinuities is investigated. A building-block method, which gives the transmission and reflection matrices for a complex system from those of the parts, is applied to bifurcations, sudden area changes with or without extended inlets, and spherical obstacles (which may be lossy). In some cases the solution can be interpreted in terms of multiple reflections. When the lengths between the discontinuities are small it is important to include also non-propagating modes, and this is especially true when the sudden area change is obtained from the area change with extended inlet in the limit of vanishing inlet. For an expansion chamber (a portion of the duct with larger radius) with or without an obstacle and with or without inlets a number of numerical results with variation in frequency are presented. Numerical results for the various building-block elements of the expansion chamber are also considered.