Propagation of Waves in a Bifurcated Cylindrical Waveguide with Wall Impedance Discontinuity

In the present work the radiation of sound from a bifurcated circular waveguide formed by a semi-infinite rigid duct inserted axially into a larger infinite tube with discontinuous wall impedance is reconsidered through an alternative approach which consists of using the mode matching technique in conjunction with the Wiener-Hopf method. By expressing the total field in the appropriate waveguide region in terms of normal modes and using the Fourier transform technique elsewhere, we end up with a single modified Wiener-Hopf equation whose solution involves an infinite system of algebraic equations. This system is solved numerically and the influence of some parameters on the radiation phenomenon is shown graphically. The equivalence of the direct method described in (1) and the present mixed method are shown numerically.