Daniel Juvé is an Emeritus Professor at the École Centrale de Lyon, France, in the Fluid Mechanics and Acoustics Laboratory. His main research interests are noise generation by turbulent flows and sound propagation in the atmosphere.Marie-Annick Galland is an Emeritus Professor at the École Centrale de Lyon, France, in the Fluid Mechanics and Acoustics Laboratory. She conducts research in noise control using active control systems and/or passive acoustic materials with an application to aircraft’s nacelle liners.Vincent Clair is an Assistant Professor at the École Centrale de Lyon, France, in the Fluid Mechanics and Acoustics Laboratory. He specializes in the numerical simulation of turbomachinery noise and acoustic propagation through turbulent flows.

• List of Abbreviations, Acronyms and Symbols xiPreface xvChapter 1 Equations of Linear Acoustics 11.1. Validity of the assumptions of linear acoustics and a perfect fluid 11.2. Linearized equations of fluid dynamics 31.3. The wave equation 51.3.1. The special case of ideal gases 61.3.2. The velocity potential 71.3.3. Validity conditions for the linearization of equations 81.4. Acoustic energy, acoustic intensity and source power 91.4.1. Definition of acoustic energy and acoustic intensity 91.4.2. Acoustic sources 101.5. Harmonic waves 121.5.1. Definition of harmonic waves 121.5.2. Average acoustic energy and acoustic intensity 151.6. Boundary conditions 161.6.1. Fluid–solid and fluid–fluid interfaces 161.6.2. Specific acoustic impedance 181.7. Exercises 19Chapter 2 Plane Waves and Spherical Waves 212.1. Plane waves 212.1.1. Plane waves in the time domain 212.1.2. Harmonic plane waves 252.1.3. Evanescent plane waves 282.1.4. Angular spectrum of plane waves 282.1.5. Near-field acoustic holography 292.2. Spherical waves 312.2.1. Time-averaged intensity and power 332.2.2. Harmonic spherical waves 342.3. Cylindrical waves 362.4. Exercises 37Chapter 3 Sound Levels, Spectral Analysis and Notions on Human Sound Perception 433.1. Energy and average power 443.2. Sound levels 453.3. Energy and power spectral densities 463.4. Correlation functions 473.5. Random signals 483.6. Random signals and correlations, some examples 503.7. Frequency bands 523.8. Loudness, equal loudness contours and frequency weightings 553.9. Characterization of non-stationary acoustic signals 583.9.1. Statistical levels 593.9.2. Equivalent level, “Day ”, “Evening” and “Night” levels 603.9.3. Transient signals: sound exposure level and energy spectral density 613.10. Exercises 63Chapter 4 Reflection and Transmission Phenomena 674.1. Reflection and transmission of normally incident plane waves 684.2. Reflection of a harmonic plane wave on an impedance surface 694.3. Multilayer media 724.3.1. Impedance transfer 724.3.2. Transmission through three media 734.3.3. Transmission of a harmonic plane wave through a thin wall 744.4. Reflection and transmission of plane waves at the interface between two fluids: oblique incidence 764.5. Plane wave transmission through a thin wall: oblique incidence 814.6. Piston-tube coupling 854.7. Reflection of spherical waves and image sources 874.8. Exercises 92Chapter 5 Sound Sources and Green’s Functions 975.1. Volume sources 985.2. Green’s functions for the wave equation 995.3. General solution of the wave equation in free-space 1005.3.1. Monopole sources: far-field and compact source region 1015.3.2. Dipole sources 1045.3.3. Quadrupole sources 1075.4. Green’s functions and general solutions of the Helmholtz equation 1085.4.1. Monopole sources 1095.4.2. Dipole and quadrupole sources 1105.5. One-dimensional and two-dimensional Green’s functions 1115.5.1. Two-dimensional Green’s function of the wave equation 1115.5.2. One-dimensional Green’s function of the wave equation 1135.5.3. Green’s functions of the Helmholtz equation in one- and two-dimensions 1135.6. Reciprocity of Green’s functions 1155.7. Green’s functions for a fluid in uniform subsonic motion 1165.7.1. Green’s function of the convected Helmholtz equation 1195.8. Moving sources and the Doppler effect 1195.8.1. Point mass source in arbitrary motion 1195.8.2. Arbitrarily moving point forces 1225.8.3. Sources in uniform rectilinear motion 1245.9. Exercises 126Chapter 6 Integral Formulations for Sound Radiation and Diffraction 1296.1. Radially oscillating sphere 1306.1.1. Harmonic vibrations: radiation impedance 1316.2. Acoustic radiation from bending vibrations 1346.2.1. Radiated power and radiation impedance 1386.2.2. Acoustic radiation from a finite plate 1406.3. Kirchhoff–Helmholtz integral 1416.3.1. Irregular frequencies 1456.3.2. Expressing the surface integral in terms of pressure and velocity 1466.3.3. Kirchhoff–Helmholtz formula and acoustic field extrapolation 1476.4. Adapted Green’s functions 1486.5. Integral formulation associated with the wave equation 1496.5.1. Bursting balloon 1506.6. Radiation from planar structures: Rayleigh integral 1526.6.1. Radiation from a circular piston 1556.7. Rayleigh integral in the time domain 1606.8. Exercises 161Chapter 7 Diffraction and Scattering 1637.1. Diffraction by a semi-infinite screen 1637.2. Scattering by a rigid cylinder 1697.2.1. Scattering cross-sections 1737.3. Rayleigh scattering by a generic obstacle 1777.4. Scattering by non-rigid obstacles and the Born approximation 1807.4.1. Scattering by inhomogeneities 1807.4.2. The Born approximation 1837.4.3. Validity of the Born approximation 1857.5. Exercises 186Chapter 8 Guided Waves 1898.1. Sound propagation in a duct of constant cross-section 1898.1.1. Propagating modes and evanescent modes 1918.2. Duct of rectangular cross-section 1928.2.1. Phase and group velocities: dispersion of higher modes 1938.2.2. Modes and pairs of plane waves 1958.3. Ducts of circular cross-section 1968.4. Point source in a duct and Green’s function 1988.5. Propagation in a duct with absorbing walls 2018.6. Influence of a uniform flow on modal propagation 2048.7. Exercises 208Chapter 9 One-dimensional Propagation in Ducts 2119.1. Ducts of piecewise constant cross-section: transfer matrices 2119.1.1. Impedance transfer 2129.1.2. Cross-sectional area discontinuities 2129.1.3. Expansion chambers 2159.1.4. Bifurcations and acoustic filters 2179.1.5. Transmission loss and insertion loss 2209.1.6. End corrections 2219.1.7. Helmholtz resonators 2229.2. Webster horn equation 2269.2.1. Propagation in ducts with a slowly varying cross-section 2269.2.2. Horn families: exponential horns 2279.3. Exercises 231Chapter 10 Acoustics of Enclosures: Room Acoustics 23310.1. Simple-shaped cavities 23410.2. Modal approach 23510.2.1. Distribution of the natural frequencies 23810.2.2. Room acoustic response to a point source 24010.3. Energy approach: Sabine’s theory 24110.3.1. Global energy balance 24210.3.2. Diffuse field 24210.3.3. Steady-state level: reverberation time 24410.3.4. Eyring’s formula 24610.4. Influence of the atmospheric absorption 24710.5. Random incidence absorption coefficient 24710.6. Schröder frequency 24810.7. Room critical distance 24910.8. Coupled rooms: transmission loss of a panel 25010.9. Measurements in the reverberation room of École Centrale de Lyon 25110.10. Geometric room acoustics 25310.11. Subjective effects 25610.12. Exercises 261Appendices 267Appendix 1 Basic Fluid Mechanics and Thermodynamics 269Appendix 2 Math Refresher 281References 293Index 297

Daniel Juvé is an Emeritus Professor at the École Centrale de Lyon, France, in the Fluid Mechanics and Acoustics Laboratory. His main research interests are noise generation by turbulent flows and sound propagation in the atmosphere.Marie-Annick Galland is an Emeritus Professor at the École Centrale de Lyon, France, in the Fluid Mechanics and Acoustics Laboratory. She conducts research in noise control using active control systems and/or passive acoustic materials with an application to aircraft’s nacelle liners.Vincent Clair is an Assistant Professor at the École Centrale de Lyon, France, in the Fluid Mechanics and Acoustics Laboratory. He specializes in the numerical simulation of turbomachinery noise and acoustic propagation through turbulent flows.

• List of Abbreviations, Acronyms and Symbols xiPreface xvChapter 1 Equations of Linear Acoustics 11.1. Validity of the assumptions of linear acoustics and a perfect fluid 11.2. Linearized equations of fluid dynamics 31.3. The wave equation 51.3.1. The special case of ideal gases 61.3.2. The velocity potential 71.3.3. Validity conditions for the linearization of equations 81.4. Acoustic energy, acoustic intensity and source power 91.4.1. Definition of acoustic energy and acoustic intensity 91.4.2. Acoustic sources 101.5. Harmonic waves 121.5.1. Definition of harmonic waves 121.5.2. Average acoustic energy and acoustic intensity 151.6. Boundary conditions 161.6.1. Fluid–solid and fluid–fluid interfaces 161.6.2. Specific acoustic impedance 181.7. Exercises 19Chapter 2 Plane Waves and Spherical Waves 212.1. Plane waves 212.1.1. Plane waves in the time domain 212.1.2. Harmonic plane waves 252.1.3. Evanescent plane waves 282.1.4. Angular spectrum of plane waves 282.1.5. Near-field acoustic holography 292.2. Spherical waves 312.2.1. Time-averaged intensity and power 332.2.2. Harmonic spherical waves 342.3. Cylindrical waves 362.4. Exercises 37Chapter 3 Sound Levels, Spectral Analysis and Notions on Human Sound Perception 433.1. Energy and average power 443.2. Sound levels 453.3. Energy and power spectral densities 463.4. Correlation functions 473.5. Random signals 483.6. Random signals and correlations, some examples 503.7. Frequency bands 523.8. Loudness, equal loudness contours and frequency weightings 553.9. Characterization of non-stationary acoustic signals 583.9.1. Statistical levels 593.9.2. Equivalent level, “Day ”, “Evening” and “Night” levels 603.9.3. Transient signals: sound exposure level and energy spectral density 613.10. Exercises 63Chapter 4 Reflection and Transmission Phenomena 674.1. Reflection and transmission of normally incident plane waves 684.2. Reflection of a harmonic plane wave on an impedance surface 694.3. Multilayer media 724.3.1. Impedance transfer 724.3.2. Transmission through three media 734.3.3. Transmission of a harmonic plane wave through a thin wall 744.4. Reflection and transmission of plane waves at the interface between two fluids: oblique incidence 764.5. Plane wave transmission through a thin wall: oblique incidence 814.6. Piston-tube coupling 854.7. Reflection of spherical waves and image sources 874.8. Exercises 92Chapter 5 Sound Sources and Green’s Functions 975.1. Volume sources 985.2. Green’s functions for the wave equation 995.3. General solution of the wave equation in free-space 1005.3.1. Monopole sources: far-field and compact source region 1015.3.2. Dipole sources 1045.3.3. Quadrupole sources 1075.4. Green’s functions and general solutions of the Helmholtz equation 1085.4.1. Monopole sources 1095.4.2. Dipole and quadrupole sources 1105.5. One-dimensional and two-dimensional Green’s functions 1115.5.1. Two-dimensional Green’s function of the wave equation 1115.5.2. One-dimensional Green’s function of the wave equation 1135.5.3. Green’s functions of the Helmholtz equation in one- and two-dimensions 1135.6. Reciprocity of Green’s functions 1155.7. Green’s functions for a fluid in uniform subsonic motion 1165.7.1. Green’s function of the convected Helmholtz equation 1195.8. Moving sources and the Doppler effect 1195.8.1. Point mass source in arbitrary motion 1195.8.2. Arbitrarily moving point forces 1225.8.3. Sources in uniform rectilinear motion 1245.9. Exercises 126Chapter 6 Integral Formulations for Sound Radiation and Diffraction 1296.1. Radially oscillating sphere 1306.1.1. Harmonic vibrations: radiation impedance 1316.2. Acoustic radiation from bending vibrations 1346.2.1. Radiated power and radiation impedance 1386.2.2. Acoustic radiation from a finite plate 1406.3. Kirchhoff–Helmholtz integral 1416.3.1. Irregular frequencies 1456.3.2. Expressing the surface integral in terms of pressure and velocity 1466.3.3. Kirchhoff–Helmholtz formula and acoustic field extrapolation 1476.4. Adapted Green’s functions 1486.5. Integral formulation associated with the wave equation 1496.5.1. Bursting balloon 1506.6. Radiation from planar structures: Rayleigh integral 1526.6.1. Radiation from a circular piston 1556.7. Rayleigh integral in the time domain 1606.8. Exercises 161Chapter 7 Diffraction and Scattering 1637.1. Diffraction by a semi-infinite screen 1637.2. Scattering by a rigid cylinder 1697.2.1. Scattering cross-sections 1737.3. Rayleigh scattering by a generic obstacle 1777.4. Scattering by non-rigid obstacles and the Born approximation 1807.4.1. Scattering by inhomogeneities 1807.4.2. The Born approximation 1837.4.3. Validity of the Born approximation 1857.5. Exercises 186Chapter 8 Guided Waves 1898.1. Sound propagation in a duct of constant cross-section 1898.1.1. Propagating modes and evanescent modes 1918.2. Duct of rectangular cross-section 1928.2.1. Phase and group velocities: dispersion of higher modes 1938.2.2. Modes and pairs of plane waves 1958.3. Ducts of circular cross-section 1968.4. Point source in a duct and Green’s function 1988.5. Propagation in a duct with absorbing walls 2018.6. Influence of a uniform flow on modal propagation 2048.7. Exercises 208Chapter 9 One-dimensional Propagation in Ducts 2119.1. Ducts of piecewise constant cross-section: transfer matrices 2119.1.1. Impedance transfer 2129.1.2. Cross-sectional area discontinuities 2129.1.3. Expansion chambers 2159.1.4. Bifurcations and acoustic filters 2179.1.5. Transmission loss and insertion loss 2209.1.6. End corrections 2219.1.7. Helmholtz resonators 2229.2. Webster horn equation 2269.2.1. Propagation in ducts with a slowly varying cross-section 2269.2.2. Horn families: exponential horns 2279.3. Exercises 231Chapter 10 Acoustics of Enclosures: Room Acoustics 23310.1. Simple-shaped cavities 23410.2. Modal approach 23510.2.1. Distribution of the natural frequencies 23810.2.2. Room acoustic response to a point source 24010.3. Energy approach: Sabine’s theory 24110.3.1. Global energy balance 24210.3.2. Diffuse field 24210.3.3. Steady-state level: reverberation time 24410.3.4. Eyring’s formula 24610.4. Influence of the atmospheric absorption 24710.5. Random incidence absorption coefficient 24710.6. Schröder frequency 24810.7. Room critical distance 24910.8. Coupled rooms: transmission loss of a panel 25010.9. Measurements in the reverberation room of École Centrale de Lyon 25110.10. Geometric room acoustics 25310.11. Subjective effects 25610.12. Exercises 261Appendices 267Appendix 1 Basic Fluid Mechanics and Thermodynamics 269Appendix 2 Math Refresher 281References 293Index 297

Daniel Juvé is an Emeritus Professor at the École Centrale de Lyon, France, in the Fluid Mechanics and Acoustics Laboratory. His main research interests are noise generation by turbulent flows and sound propagation in the atmosphere.Marie-Annick Galland is an Emeritus Professor at the École Centrale de Lyon, France, in the Fluid Mechanics and Acoustics Laboratory. She conducts research in noise control using active control systems and/or passive acoustic materials with an application to aircraft’s nacelle liners.Vincent Clair is an Assistant Professor at the École Centrale de Lyon, France, in the Fluid Mechanics and Acoustics Laboratory. He specializes in the numerical simulation of turbomachinery noise and acoustic propagation through turbulent flows.

• List of Abbreviations, Acronyms and Symbols xiPreface xvChapter 1 Equations of Linear Acoustics 11.1. Validity of the assumptions of linear acoustics and a perfect fluid 11.2. Linearized equations of fluid dynamics 31.3. The wave equation 51.3.1. The special case of ideal gases 61.3.2. The velocity potential 71.3.3. Validity conditions for the linearization of equations 81.4. Acoustic energy, acoustic intensity and source power 91.4.1. Definition of acoustic energy and acoustic intensity 91.4.2. Acoustic sources 101.5. Harmonic waves 121.5.1. Definition of harmonic waves 121.5.2. Average acoustic energy and acoustic intensity 151.6. Boundary conditions 161.6.1. Fluid–solid and fluid–fluid interfaces 161.6.2. Specific acoustic impedance 181.7. Exercises 19Chapter 2 Plane Waves and Spherical Waves 212.1. Plane waves 212.1.1. Plane waves in the time domain 212.1.2. Harmonic plane waves 252.1.3. Evanescent plane waves 282.1.4. Angular spectrum of plane waves 282.1.5. Near-field acoustic holography 292.2. Spherical waves 312.2.1. Time-averaged intensity and power 332.2.2. Harmonic spherical waves 342.3. Cylindrical waves 362.4. Exercises 37Chapter 3 Sound Levels, Spectral Analysis and Notions on Human Sound Perception 433.1. Energy and average power 443.2. Sound levels 453.3. Energy and power spectral densities 463.4. Correlation functions 473.5. Random signals 483.6. Random signals and correlations, some examples 503.7. Frequency bands 523.8. Loudness, equal loudness contours and frequency weightings 553.9. Characterization of non-stationary acoustic signals 583.9.1. Statistical levels 593.9.2. Equivalent level, “Day ”, “Evening” and “Night” levels 603.9.3. Transient signals: sound exposure level and energy spectral density 613.10. Exercises 63Chapter 4 Reflection and Transmission Phenomena 674.1. Reflection and transmission of normally incident plane waves 684.2. Reflection of a harmonic plane wave on an impedance surface 694.3. Multilayer media 724.3.1. Impedance transfer 724.3.2. Transmission through three media 734.3.3. Transmission of a harmonic plane wave through a thin wall 744.4. Reflection and transmission of plane waves at the interface between two fluids: oblique incidence 764.5. Plane wave transmission through a thin wall: oblique incidence 814.6. Piston-tube coupling 854.7. Reflection of spherical waves and image sources 874.8. Exercises 92Chapter 5 Sound Sources and Green’s Functions 975.1. Volume sources 985.2. Green’s functions for the wave equation 995.3. General solution of the wave equation in free-space 1005.3.1. Monopole sources: far-field and compact source region 1015.3.2. Dipole sources 1045.3.3. Quadrupole sources 1075.4. Green’s functions and general solutions of the Helmholtz equation 1085.4.1. Monopole sources 1095.4.2. Dipole and quadrupole sources 1105.5. One-dimensional and two-dimensional Green’s functions 1115.5.1. Two-dimensional Green’s function of the wave equation 1115.5.2. One-dimensional Green’s function of the wave equation 1135.5.3. Green’s functions of the Helmholtz equation in one- and two-dimensions 1135.6. Reciprocity of Green’s functions 1155.7. Green’s functions for a fluid in uniform subsonic motion 1165.7.1. Green’s function of the convected Helmholtz equation 1195.8. Moving sources and the Doppler effect 1195.8.1. Point mass source in arbitrary motion 1195.8.2. Arbitrarily moving point forces 1225.8.3. Sources in uniform rectilinear motion 1245.9. Exercises 126Chapter 6 Integral Formulations for Sound Radiation and Diffraction 1296.1. Radially oscillating sphere 1306.1.1. Harmonic vibrations: radiation impedance 1316.2. Acoustic radiation from bending vibrations 1346.2.1. Radiated power and radiation impedance 1386.2.2. Acoustic radiation from a finite plate 1406.3. Kirchhoff–Helmholtz integral 1416.3.1. Irregular frequencies 1456.3.2. Expressing the surface integral in terms of pressure and velocity 1466.3.3. Kirchhoff–Helmholtz formula and acoustic field extrapolation 1476.4. Adapted Green’s functions 1486.5. Integral formulation associated with the wave equation 1496.5.1. Bursting balloon 1506.6. Radiation from planar structures: Rayleigh integral 1526.6.1. Radiation from a circular piston 1556.7. Rayleigh integral in the time domain 1606.8. Exercises 161Chapter 7 Diffraction and Scattering 1637.1. Diffraction by a semi-infinite screen 1637.2. Scattering by a rigid cylinder 1697.2.1. Scattering cross-sections 1737.3. Rayleigh scattering by a generic obstacle 1777.4. Scattering by non-rigid obstacles and the Born approximation 1807.4.1. Scattering by inhomogeneities 1807.4.2. The Born approximation 1837.4.3. Validity of the Born approximation 1857.5. Exercises 186Chapter 8 Guided Waves 1898.1. Sound propagation in a duct of constant cross-section 1898.1.1. Propagating modes and evanescent modes 1918.2. Duct of rectangular cross-section 1928.2.1. Phase and group velocities: dispersion of higher modes 1938.2.2. Modes and pairs of plane waves 1958.3. Ducts of circular cross-section 1968.4. Point source in a duct and Green’s function 1988.5. Propagation in a duct with absorbing walls 2018.6. Influence of a uniform flow on modal propagation 2048.7. Exercises 208Chapter 9 One-dimensional Propagation in Ducts 2119.1. Ducts of piecewise constant cross-section: transfer matrices 2119.1.1. Impedance transfer 2129.1.2. Cross-sectional area discontinuities 2129.1.3. Expansion chambers 2159.1.4. Bifurcations and acoustic filters 2179.1.5. Transmission loss and insertion loss 2209.1.6. End corrections 2219.1.7. Helmholtz resonators 2229.2. Webster horn equation 2269.2.1. Propagation in ducts with a slowly varying cross-section 2269.2.2. Horn families: exponential horns 2279.3. Exercises 231Chapter 10 Acoustics of Enclosures: Room Acoustics 23310.1. Simple-shaped cavities 23410.2. Modal approach 23510.2.1. Distribution of the natural frequencies 23810.2.2. Room acoustic response to a point source 24010.3. Energy approach: Sabine’s theory 24110.3.1. Global energy balance 24210.3.2. Diffuse field 24210.3.3. Steady-state level: reverberation time 24410.3.4. Eyring’s formula 24610.4. Influence of the atmospheric absorption 24710.5. Random incidence absorption coefficient 24710.6. Schröder frequency 24810.7. Room critical distance 24910.8. Coupled rooms: transmission loss of a panel 25010.9. Measurements in the reverberation room of École Centrale de Lyon 25110.10. Geometric room acoustics 25310.11. Subjective effects 25610.12. Exercises 261Appendices 267Appendix 1 Basic Fluid Mechanics and Thermodynamics 269Appendix 2 Math Refresher 281References 293Index 297