Sound Transmission in an Extended Tube Resonator

The transmission of sound in a duct with sudden area expansion and extended inlet is investigated in the case the walls of the duct lying in overlap region lined with different acoustically absorbent materials. By using the series expansion in overlap region and using Fourier transform technique elsewhere we obtain a Wiener-Hopf equation whose solution involve a set of infinitely many unknown expansion coefficients satisfying a system of linear algebraic equations. Numerical solution of this system is obtained by truncating the infinite series and then the variation of transmission coefficient for different values of problem parameters are displayed graphically.