Scattering of Sound Waves in Two Stepped Non-uniformly Lined Duct

Scattering of sound waves in two stepped cylindrical duct which walls are coated with different acoustically absorbent materials is investigated by using Wiener-Hopf technique directly and by determining scattering matrices. First, by using Fourier transform technique we obtain a couple of modified Wiener-Hopf equations whose solutions involve four sets of infinitely many unknown expansion coefficients providing systems of linear algebraic equations. Then we determine scattering matrices of the problem and we state the total transmitted field by using generalized scattering matrix method. Numerical results are compared for different parameters.