Abstract
Noncollinear wave interaction in a rectangular duct is investigated both theoretically and experimentally. An inhomogeneous wave equation, exact to second order in the field variables, is derived for the sum and difference frequency pressure waves generated by noncollinear interaction of two finite amplitude plane waves in a lossless fluid. This equation is extended to the interaction of waves in higher-order modes of a rectangular duct. Quasilinear solutions are obtained, and tube wall attenuation is included ad hoc. Experimental results are reported for the interaction of waves in the (0,0) and (1,0) modes of an air-filled rectangular duct. Theory and experiment are in excellent agreement with regard to oscillatory structure of the sum and difference frequency wave fields. Although overall agreement between theory and experiment is reasonable (±2 dB), it is not within estimated experimental error (±1 dB). It is shown that because local rather than cumulative nonlinear effects dominate the interaction, knowledge of the proper second-order source condition is of crucial importance. Discrepancies between the predicted and measured amplitudes are attributed to an inadequate description of the source condition.
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