Reciprocity theorems for two‐way and one‐way wave vectors: A comparison

For acoustic applications in which there is a ‘‘preferred direction of propagation’’ (the axial direction) it is useful to arrange the two‐way and one‐way wave equations into the same matrix‐vector formalism. In this formalism, axial variations of the wave vector are expressed in terms of lateral variations of the same wave vector. The two‐way wave vector contains the field quantities pressure and velocity (axial component only), whereas the one‐way wave vector contains waves propagating in the positive and negative axial direction. By exploiting the equivalent form of the two‐way and one‐way matrix‐vector equations, it appears to be possible to derive two‐way and one‐way reciprocity theorems that have an equivalent form but a different interpretation. The main differences appear in the boundary integrals for unbounded media, in the contrast terms, and (for the correlation‐type theorems) in the handling of evanescent waves.

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