GENERATION OF CUMULATIVE SUM FREQUENCY AND DIFFERENCE FREQUENCY ACOUSTIC WAVES IN A TWO-DIMENSIONAL HARD-WALLED WAVEGUIDE

An approach based on second-order approximation technique and partial wave analysis method has been proposed for analyzing the generation of the cumulative sum frequency (SF) and difference frequency (DF) acoustic waves in a two-dimensional hard-walled waveguide. There are two or more sets of fundamental modes with different frequencies, in the waveguide, if an excitation source is of multi-frequency. The cross-interaction between two partial waves of the fundamental modes with different frequencies causes the generation of the driven SF and DF waves. The driven SF and DF waves may have the cumulative growth effect once the two fundamental modes with different frequencies have the same phase velocities. With appropriate boundary and initial conditions of excitation, the physical process of generation of the cumulative SF and DF waves has been clearly shown, and the analytical solution of the cumulative SF and DF waves has also been determined. The solution shows that the cumulative SF and DF acoustic fields may be symmetrical or antisymmetrical. The numerical results clearly reveal the distortion and the symmetry of the field patterns of the cumulative SF and DF waves.