The analysis of plane discontinuities in offset cylindrical waveguides

This paper applies the re-expansion method for analyzing the effects on the sound field due to planar discontinuities at the junction of two offset circular acoustic waveguides. The normal modes in the two waveguides are expanded at the junction plane into a system of functions accounting for velocity singularities at the corner points. As the new expansion has a high convergence order, only a few terms have to be considered for obtaining the solution of most practical problems. This paper gives the equivalent impedance accounting for nonplanar waves into a plane-wave analysis. The last section of the paper applies the re-expansion technique to the case of two offset pipes (step discontinuity) and to that of an offset aperture in a cylindrical pipe (diaphragm-type discontinuity). The plots of the discontinuity inductance, characterized by Karal's factor, are quite similar but the values in the second case are 1.5-2 times larger, showing that the diaphragm-type discontinuity excites much more nonplanar evanescent modes than the step discontinuity.