Nonlinear propagation of sum frequency and difference frequency acoustic fields in a two-dimensional rectangular duct

The nonlinear propagation, in a two-dimensional rectangular duct, of sum frequency and difference frequency acoustic field, arising from the cross-interaction of two fundamental modes with different frequencies, has been investigated by using the partial wave theory of acoustic fields and the technique of second-order approximation. It is found that the acoustic fields of sum and difference frequency hold the second-order nonlinearities once two fundamental modes with different frequencies have the same phase velocities, and that the symmetric characteristics of sum frequency and difference frequency acoustic fields depend on that of two fundamental modes. With the initial condition of excitation of the second-order nonlinear acoustic waves, the analytical expressions of sum frequency and difference frequency acoustic fields have also been obtained in the present paper.