Wiener-Hopf analysis of an acoustic plane wave in a trifurcated waveguide

In this paper, we have made Wiener-Hopf analysis of an acoustic plane wave by a semi-infinite hard duct that is placed symmetrically inside an infinite soft/hard duct. The method of solution is integral transform and Wiener-Hopf technique. The imposition of boundary conditions result in a 2 × 2 matrix Wiener-Hopf equation associated with a new canonical scattering problem which is solved by using the pole removal technique. In the solution, two infinite sets of unknown coefficients are involved that satisfy two infinite systems of linear algebraic equations. These systems of linear algebraic equations are solved numerically. The graphs are plotted for sundry parameters of interest. Kernel functions are also factorized.