This work includes analysis of basic discontinuities in cylindrical acoustic wave-guide with rigid wall and at condition of axial symmetry. Accurate mathematical models for both basic discontinuities - diameter step and rigid diaphragm with coaxial opening - have been presented for multi-mode case. Accuracy of the models was checked with the energy conservation law and with direct check of accuracy for the boundary conditions at discontinuities.

Presented numerical data for transmission/reflection coefficients were used to test the reciprocity properties of both basic discontinuities. Test results demonstrated, that Rayleigh-Lamb version of the reciprocity theorem properly describes these discontinuities for single traveling mode only - below first radial resonance in the wave-guide. But it fails with these discontinuities in multi-mode case. It was suggested new version of reciprocity relations for basic discontinuities in acoustic wave-guide. The new version describes relations between modes - incident and transmitted and incident and reflected. It is interesting, that new version transforms into old one for case of single traveling mode.

PACS numbers: 43.20.Mv, 43.20.Bi

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