Sound Beams
摘要
Diffraction in sound beams is analyzed using the KZK nonlinear parabolic wave equation. General integral solutions are presented for generation of the second harmonic, sum, and difference frequencies in weakly nonlinear axisymmetric sound beams. Analytical solutions are obtained for sources with Gaussian amplitude distributions, both unfocused and focused. Asymptotic solutions are presented for far-field radiation from circular pistons, and the appearance of additional sidelobes is explained. Solutions for difference-frequency radiation in the far field of a parametric array, and the associated self-demodulation of narrowband waveforms, are derived. Numerical simulations are presented for strongly nonlinear sound beams with shocks.