Simple discontinuities in acoustic waveguides at low frequencies: Critical analysis and formulae

The variational method of Schwinger is applied to reach qualitative conclusions regarding the effects of symmetrical discontinuities (change in cross-section, diaphragm of zero thickness) in acoustic waveguides. For bidimensional geometry the exact results from an analytical solution are used to discuss the convergence of the solutions of the modal theory when the number of modes taken into account increases. The variation of the discontinuity inductances with frequency and the difference between radiation into infinite space and into a large waveguide are discussed. Finally, by a fitting procedure a set of formulae is provided for the engineer for both the case of the radiation of a plane piston into an infinite waveguide and the case of a change in cross-section in a circular guide.

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