Phase relationships of finite amplitude ultrasound waves and its application in determining nonlinear acoustical parameters

Abstract

Compared with second harmonics, phase relation contains more comprehensive nonlinear characteristics, and is proposed to determine the nonlinear acoustical parameter. Based on perturbation theory, the previous 16 harmonic solutions are solved automatically. Hilbert transform is employed to evaluate the phase of nonlinear signal, and phase shift is obtained by subtracting the phase of a nonlinear signal from that of a reference linear signal. Meanwhile, thermodynamic method is also analyzed and which make it easier to calculate phase shift. Then, nonlinear ultrasound experiments are performed in distilled water to verify the theoretical results. It shows that the simulated phase and phase shift are consistent with experiments. With experimental phase shift data collected at different propagation distances and of different excitation levels, the nonlinear parameter of water is calculated ($\stackrel{\sim }{\beta }$ = 3.44 at 18℃) with an optimization method. It shows that determining nonlinear parameter with phase shift not only avoids the use of inaccurate second harmonic perturbation solution, but also eliminates the need for extracting fundamental and harmonic amplitudes. This work enriches the propagation theory of finite amplitude waves and provides a new method for nonlinear ultrasonic detection and evaluation.