Fundamentals of Acoustics

The central theme of the chapters is acoustic propagation in fluid media, dissipative or non-dissipative, homogeneous or nonhomogeneous, infinite or limited, placing particular emphasis on the theoretical formulation of the problems considered.

Auteur
Michel Bruneau is Emeritus Professor at the University of Maine in France. He is the founder of the Laboratoire d'Acoustique from University of Maine (LAUM) affiliated to the Centre National de la Recherche Scientifique (CNRS) where he was the director of the postgraduate studies in acoustics. This book results mainly from his lectures and publications.

Contenu

Preface 13

Chapter 1. Equations of Motion in Non-dissipative Fluid 15

1.1. Introduction 15

1.1.1. Basic elements 15

1.1.2. Mechanisms of transmission 16

1.1.3. Acoustic motion and driving motion 17

1.1.4. Notion of frequency 17

1.1.5. Acoustic amplitude and intensity 18

1.1.6. Viscous and thermal phenomena 19

1.2. Fundamental laws of propagation in non-dissipative fluids 20

1.2.1. Basis of thermodynamics 20

1.2.2. Lagrangian and Eulerian descriptions of fluid motion 25

1.2.3. Expression of the fluid compressibility: mass conservation law 27

1.2.4. Expression of the fundamental law of dynamics: Euler's equation 29

1.2.5. Law of fluid behavior: law of conservation of thermomechanic energy 30

1.2.6. Summary of the fundamental laws 31

1.2.7. Equation of equilibrium of moments 32

1.3. Equation of acoustic propagation 33

1.3.1. Equation of propagation 33

1.3.2. Linear acoustic approximation 34

1.3.3. Velocity potential 38

1.3.4. Problems at the boundaries 40

1.4. Density of energy and energy flow, energy conservation law 42

1.4.1. Complex representation in the Fourier domain 42

1.4.2. Energy density in an ideal fluid 43

1.4.3. Energy flow and acoustic intensity 45

1.4.4. Energy conservation law 48

Chapter 1: Appendix. Some General Comments on Thermodynamics 50

A.1. Thermodynamic equilibrium and equation of state 50

A.2. Digression on functions of multiple variables (study case of two variables) 51

A.2.1. Implicit functions 51

A.2.2. Total exact differential form 53

Chapter 2. Equations of Motion in Dissipative Fluid 55

2.1. Introduction 55

2.2. Propagation in viscous fluid: Navier-Stokes equation 56

2.2.1. Deformation and strain tensor 57

2.2.2. Stress tensor 62

2.2.3. Expression of the fundamental law of dynamics 64

2.3. Heat propagation: Fourier equation 70

2.4. Molecular thermal relaxation 72

2.4.1. Nature of the phenomenon 72

2.4.2. Internal energy, energy of translation, of rotation and of vibration of molecules 74

2.4.3. Molecular relaxation: delay of molecular vibrations 75

2.5. Problems of linear acoustics in dissipative fluid at rest 77

2.5.1. Propagation equations in linear acoustics 77

2.5.2. Approach to determine the solutions 81

2.5.3. Approach of the solutions in presence of acoustic sources 84

2.5.4. Boundary conditions 85

Chapter 2: Appendix. Equations of continuity and equations at the thermomechanic discontinuities in continuous media 93

A.1. Introduction 93

A.1.1. Material derivative of volume integrals 93

A.1.2. Generalization 96

A.2. Equations of continuity 97

A.2.1. Mass conservation equation 97

A.2.2. Equation of impulse continuity 98

A.2.3. Equation of entropy continuity 99

A.2.4. Equation of energy continuity 99

A.3. Equations at discontinuities in mechanics 102

A.3.1. Introduction 102

A.3.2. Application to the equation of impulse conservation 103

A.3.3. Other conditions at discontinuities 106

A.4. Examples of application of the equations at discontinuities in mechanics: interface conditions 106

A.4.1. Interface solid viscous fluid 107

A.4.2. Interface between perfect fluids 108

A.4.3 Interface between two non-miscible fluids in motion 109

Chapter 3. Problems of Acoustics in Dissipative Fluids 111

3.1. Introduction 111

3.2. Reflection of a harmonic wave from a rigid plane 111

3.2.1. Reflection of an incident harmonic plane wave 111

3.2.2. Reflection of a harmonic acoustic wave 115

3.3. Spherical wave in infinite space: Green's function 118

3.3.1. Impulse spherical source 118 3.3.2. Green's function in three-dimensional ...