Acoustic radiation from two opposed semi-infinite coaxial cylindrical waveguides. I: Overlapping edges (Q1329879)

This paper is the first part of an investigation into the axisymmetric radiation of sound waves from two semi-infinite circular cylinders. Both pipes have a common axis, measured by the Cartesian variable \(z\), but the smaller cylinder extends to infinity in the direction \(z \to -\infty\) whilst the larger extends in the direction \(z \to \infty\). The boundary value problem is formulated as a matrix Wiener-Hopf equation, and a solution is obtained for the case when the ducts overlap. The reflected, transmitted, and radiated far-field waves are determined for a range of values of the inner and outer pipe diameters, and the overlap spacing.