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  and the present mixed method are shown numerically.
2. Idemen, M., "A new method to obtain exact solutions of vector Wiener-Hopf equations," ZAMM, Vol. 59, 656-658, 1979.
3. Abrahams, I. D., "Scattering of sound by two parallel semi-infinite screens," Wave Motion, Vol. 9, 289-300, 1987.
4. Abrahams, I. D. and G. R. Wickham, "The scattering of water waves by two semi-infinite vertical walls," Wave Motion, Vol. 14, 145-168, 1991.
5. Rawlins, A. D., "A bifurcated circular waveguide problem," IMA J. Appl. Math., Vol. 54, 59-81, 1995.
6. Nilsson, B. and O. Brander, "The propagation of sound in cylindrical ducts with mean flow and bulk reacting lining. I. Modes in an infinite duct," IMA J. Appl. Math., Vol. 26, 269-298, 1980.
7. Demir, A. and A. Buyukaksoy, "Radiation of plane sound waves by a rigid circular cylindrical pipe with a partial internal impedance loading," Acustica, Vol. 89, 578-585, 2003.