Chapter 5: The Finite-Amplitude Acoustic Wave

In the previous chapters, we assumed the following: (1) when an acoustic wave propagates in a medium, the medium particles vibrate with velocity amplitudes much smaller than the propagation velocity; (2) the vibration displacement amplitude of a particle is much smaller than the wavelength of the acoustic wave; (3) the density variation amplitude is much smaller than the equilibrium density. Based on these conditions, we were able to linearize the nonlinear fluid dynamic equation to obtain a linear wave equation. The theory of acoustics based on the aforementioned assumptions is called the linear acoustics. However, the fluid dynamics itself, on which the acoustics is based on, is nonlinear. If the above assumptions are no longer valid in some cases, we must keep the nonlinear terms in the fluid dynamic equations, this is the origin of the nonlinear acoustics. The wave equation which is developed to describe the nonlinear acoustic wave propagation is called the nonlinear wave equation. The most evident difference between the linear and nonlinear acoustic wave equations is the superposition principle which works so well in the linear acoustics is no longer valid in nonlinear acoustics. For example, the frequency spectrum analysis, Fourier analysis and Green's theorem which are widely used in linear acoustics, are no longer applicable in nonlinear acoustics.