4.1. Introduction

The objective of this chapter and the following ones (with the exception of Chapters 10 and 11) is to introduce the methods used to solve the fundamental equations of linear acoustics in dissipative and homogeneous fluids, and the solutions for the acoustic motion that are most widely used in solving acoustic problems. The term "acoustic motion" implies that the entropic and vortical variables are not among those considered here. However, this does not mean that dissipation is ignored completely as it plays an important and fundamental role in practice (for many reasons detailed in this chapter) and simplifies, to some extent, the modeling process.

The bivariance of the medium (first hypothesis) implies the use of only two independent variables to describe the thermodynamic state of the fluid in motion. However, to limit the problem to two scalar variables among the many involved (pressure, density, temperature, entropy, etc.) would be to overlook the vectorial nature of an acoustic field: the particle velocity. The knowledge of this vectorial quantity leads directly to the knowledge of one of the scalar quantity (i.e. the density variation p' via the mass conservation law) so that one can substitute the scalar quantity for the particle velocity. Moreover, the "pressure variation" plays a major and unique role in acoustic problems simply because most acoustic sensors are only sensitive to this quantity. It is therefore clear that the most convenient couple of variables to represent an acoustic field are the pressure variation and the particle velocity.