Wave propagation in a waveguide

We shall consider the sound radiation of a surface wave mode which propagates towards the mouth of a semi‐infinite waveguide which supports surface waves. This semi‐infinite waveguide is symmetrically located inside an infinite waveguide whose surface is lined with an absorbent surface. The whole system constitutes a new trifurcated waveguide boundary value problem. This model results in a scalar Wiener‐Hopf problem. An exact closed form solution is obtained with the aid of the Wiener‐Hopf technique. The theoretical problem solved has application in acoustics and electromagnetism.