2.1 Acoustic field in a fluid

The propagation of an acoustic wave in a homogeneous non-viscous fluid medium is governed by the linear wave equation [11]

 

$$\nabla^2 p = \frac{1}{c^2}\frac{\partial^2p}{\partial t^2},$$ (1)

where p is the acoustic pressure and c the sound velocity in the fluid. The scalar velocity potential $\psi$, given by

 

$$p = \rho\frac{\partial\psi}{\partial t},$$ (2)

with $\rho$ denoting the density of the fluid, obviously satisfies the same equation

 

$$\nabla^2\psi = \frac{1}{c^2}\frac{\partial^2\psi}{\partial t^2}.$$ (3)