Basic types of discontinuity in circular acoustic wave guide

It is considered the interaction of acoustic waves with two basic discontinuities--"diameter step" and "diaphragm with coaxial opening"--in a cylindrical acoustic waveguide with a rigid wall. The problem is considered and solved in rigorous formulation for the case of axial symmetry and below first radial resonance (f(r1)) in the waveguide. Obtained data demonstrate that a one-dimensional (1-D) model provides good results for the "diameter step" if the frequency does not exceed 18%-50% of f(r1). Calculated data for the "diameter step" demonstrate that this discontinuity follows the reciprocity principle (below f(r1))--the parameter of nonreciprocity does not exceed calculation errors. Data for the "diaphragm" demonstrate good agreement with the Lamb formula for a rigid screen with parallel slots--a 2-D problem in the Cartesian coordinates. Calculation errors for the both discontinuities were evaluated with the energy conservation law. The difference between sum of power fluxes in reflected and transmitted waves and the power flux in the incident wave does not exceed 1%.