Fundamentals of Acoustics

Chapter 1: Equations of Motion in Non-Dissipative Fluid

Overview

The objective of the two first chapters of this book is to present the fundamental equations of acoustics in fluids resulting from the thermodynamics of continuous media, stressing the fact that thermal and mechanical effects in compressible fluids are absolutely indissociable.

This chapter presents the fundamental phenomena and the partial differential equations of motion in non-dissipative fluids (viscosity and thermal conduction are introduced in Chapter 2). These equations are widely applicable as they can deal with non-linear motions and media, non-homogeneities, flows and various types of acoustic sources. Phenomena such as cavitation and chemical reactions induced by acoustic waves are not considered.

Chapter 2 completes the presentation by introducing the basic phenomenon of dissipation associated to viscosity, thermal conduction and even molecular relaxation.

1.1. Introduction

The first paragraph presents, in no particular order, some fundamental notions of thermodynamics.

1.1.1. Basic Elements

The domain of physics acoustics is simply part of the fast science of thermomechanics of continuous media. To ensure acoustic transmission, three fundamental elements are required: one or several emitters or sources, one receiver and a propagation medium. The principle of transmission is based on the existence of "particles" whose position at equilibrium can be modified. All displacements related to any types of excitation other than those related to the transmitted quantity are generally not considered (i.e. the motion associated to Brownian noise in gases).

1.1.2. Mechanisms of Transmission

The waves can either be transverse or longitudinal (the displacement of the particle is respectively perpendicular or parallel to...

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