Transmission of sound waves in a cylindrical duct with an acoustically lined muffler

The propagation of sound in an infinite rigid cylindrical duct with an inserted expansion chamber whose walls are treated with an acoustically absorbent material is investigated rigorously through the Wiener–Hopf technique. By introducing the Fourier transform for the scattered field and applying the boundary conditions in the transform domain, the problem is reduced into a modified Wiener–Hopf equation. The solution involves four sets of infinitely many constants satisfying four infinite systems of linear algebraic equations. An approximate solution of these systems is obtained by means of numerical procedures.