Foundations of Engineering Acoustics

Frank Fahy has been teaching and researching at the Institute of Sound and Vibration Research, Southampton, England, for nearly forty years. He is Emeritus Professor of Engineering Acoustics, signifying both his training and professionalmotivation. He is a Rayleigh Medal holder and Honorary Fellow of the Institute of Acoustics.

Preface
Acknowledgments
Chapter 1 Sound Engineering
1.1 The Importance of Sound
1.2 Acoustics and the Engineer
1.3 Sound the Servant
Chapter 2 The Nature of Sound and Some Sound Wave Phenomena
2.1 Introduction
2.2 What Is Sound?
2.3 Sound and Vibration
2.4 Sound in Solids
2.5 a Qualitative Introduction to Wave Phenomena
2.5.1 Wavefronts
2.5.2 Interference
2.5.3 Reflection
2.5.4 Scattering
2.5.5 Diffraction
2.5.6 Refraction
2.5.7 The Doppler Effect
2.5.8 Convection
2.6 Some More Common Examples of the Behavior of Sound Waves
Chapter 3 Sound in Fluids
3.1 Introduction
3.2 The Physical Characteristics of Fluids
3.3 Molecules and Particles
3.4 Fluid Pressure
3.5 Fluid Temperature
3.6 Pressure, Density and Temperature in Sound Waves in a Gas
3.7 Particle Motion
3.8 Sound in Liquids
3.9 Mathematical Models of Sound Waves
3.9.1 The Plane Sound Wave Equation
3.9.2 Solutions of the Plane Wave Equation
3.9.3 Harmonic Plane Waves: Sound Pressure
3.9.4 Plane Waves: Particle Velocity
3.9.5 The Wave Equation in Three Dimensions
3.9.6 Plane Waves in Three Dimensions
3.9.7 The Wave Equation in Spherical Coordinates
3.9.8 The Spherically Symmetric Sound Field
3.9.9 Particle Velocity in the Spherically Symmetric Sound Field
3.9.10 Other Forms of Sound Field
Chapter 4 Impedance
4.1 Introduction
4.2 Some Simple Examples of the Utility of Impedance
4.3 Mechanical Impedance
4.3.1 Impedance of Lumped Structural Elements
4.4 Forms of Acoustic Impedance
4.4.1 Impedances of Lumped Acoustic Elements
4.4.2 Specific Acoustic Impedance of Fluid in a Tube at Low Frequency
4.4.3 Normal Specific Acoustic Impedance
4.4.4 Radiation Impedance
4.4.5 Acoustic Impedance
4.4.6 Line and Surface Wave Impedance
4.4.7 Modal Radiation Impedance
4.5 an Application of Radiation Impedance of a Uniformly Pulsating Sphere
4.6 Radiation Efficiency
Chapter 5 Sound Energy and Intensity
5.1 The Practical Importance of Sound Energy
5.2 Sound Energy
5.3 Transport of Sound Energy: Sound Intensity
5.4 Sound Intensity in Plane Wave Fields
5.5 Intensity and Mean Square Pressure
5.6 Examples of Ideal Sound Intensity Fields
5.6.1 The Point Monopole
5.6.2 The Compact Dipole
5.6.3 Interfering Monopoles
5.6.4 Intensity Distributions in Orthogonally Directed Harmonic Plane Wave Fields
5.7 Sound Intensity Measurement
5.8 Determination of Source Sound Power Using Sound Intensity Measurement
5.9 Other Applications of Sound Intensity Measurement
Chapter 6 Sources of Sound
6.1 Introduction
6.2 Qualitative Categorization of Sources
6.2.1 Category 1 Sources
6.2.2 Category 2 Sources
6.2.3 Category 3 Sources
6.3 The Inhomogeneous Wave Equation
6.3.1 Sound Radiation by Foreign Bodies
6.3.2 Boundary 'Sources' Can Reflect or Absorb Energy
6.4 Ideal Elementary Source Models
6.4.1 The Dirac Delta Function
6.4.2 The Point Monopole and the Pulsating Sphere
6.4.3 Acoustic Reciprocity
6.4.4 External Forces on a Fluid and the Compact Dipole
6.4.5 The Oscillating Sphere
6.4.6 Boundary Sources
6.4.7 Free-Field and Other Green's Functions
6.4.8 The Rayleigh Integrals
6.5 Sound Radiation from Vibrating Plane Surfaces
6.6 The Vibrating Circular Piston and the Cone Loudspeaker
6.7 Directivity and Sound Power of Distributed Sources
6.7.1 Sound Power of a Source in the Presence of a Second Source
6.8 Zones of a Sound Field Radiated by a Spatially Extended Source
6.9 Experimental Methods for Source Sound Power Determination
6.10 Source Characterization
Chapter 7 Sound Absorption and Sound Absorbers
7.1 Introduction
7.2 The Effects of Viscosity, Thermal Diffusion and Relaxation Processes on Sound in Gases
7.2.1 The Origin of Gas Viscosity
7.2.2 The Effects of Thermal Diffusion
7.2.3 The Effect of Molecular Relaxation
7.2.4 Sound Energy Dissipation at the Rigid Boundary of a Gas
7.2.5 Acoustically Induced Boundary Layers in a Gas-Filled Tube
7.3 Forms of Porous Sound Absorbent Material
7.4 Macroscopic Physical Properties of Porous Sound-Absorbing Materials
7.4.1 Porosity
7.4.2 Flow Resistance and Resistivity
7.4.3 Structure Factor
7.5 The Modified Equation for Plane Wave Sound Propagation in Gases Contained within Rigid Porous Materials
7.5.1 Equation of Mass Conservation
7.5.2 Momentum Equation
7.5.3 The Modified Plane Wave Equation
7.5.4 Harmonic Solution of the Modified Plane Wave Equation
7.6 Sound Absorption by a Plane Surface of Uniform Impedance
7.6.1 The Local Reaction Model
7.6.2 Sound Power Absorption Coefficient of a Locally Reactive Surface
7.6.3 Wave Impedance
7.7 Sound Absorption by Thin Porous Sheets
7.7.1 The Immobile Sheet in Free Field
7.7.2 The Limp Sheet in Free Field
7.7.3 The Effect of a Rigid Wall Parallel to a Thin Sheet
7.8 Sound Absorption by Thick Sheets of Rigid Porous Material
7.8.1 The Infinitely Thick 'Sheet'
7.8.2 The Sheet of Finite Thickness
7.8.3 The Effect of a Backing Cavity on the Sound Absorption of a Sheet of Porous Material
7.9 Sound Absorption by Flexible Cellular and Fibrous Materials
7.10 The Effect of Perforated Cover Sheets on Sound Absorption by Porous Materials
7.11 Non-Porous Sound Absorbers
7.11.1 Helmholtz Resonators
7.11.2 Panel Absorbers
7.12 Methods of Measurement of Boundary Impedance and Absorption Coefficient
7.12.1 The Impedance Tube
7.12.2 Reverberation Room Method
Chapter 8 Sound in Waveguides
8.1 Introduction
8.2 Plane Wave Pulses in a Uniform Tube
8.3 Plane Wave Modes and Natural Frequencies of Fluid in Uniform Waveguides
8.3.1 Conservative Terminations
8.3.2 Non-Conservative Terminations
8.4 Response to Harmonic Excitation
8.4.1 Impedance Model
8.4.2 Harmonic Response in Terms of Green'S Functions
8.5 a Simple Case of Structure-Fluid Interaction
8.6 Plane Waves in Ducts that Incorporate Impedance Discontinuities
8.6.1 Insertion Loss and Transmission Loss
8.6.2 Transmission of Plane Waves through an Abrupt Change of Crosssectional Area and an Expansion Chamber
8.6.3 Series Networks of Acoustic Transmission Lines
8.6.4 Side Branch Connections to Uniform Acoustic Waveguides
8.6.5 The Side Branch Tube
8.6.6 The Side Branch Orifice
8.6.7 The Helmholtz Resonator Side Branch
8.6.8 Bends in Otherwise Straight Uniform Waveguides
8.7 Transverse Modes of Uniform Acoustic Waveguides
8.7.1 The Uniform Two-Dimensional Waveguide with Rigid Walls
8.7.2 The Uniform Two-Dimensional Waveguide with Finite Impedance Boundaries
8.7.3 The Uniform Waveguide of Rectangular Cross-Section with Rigid Walls
8.7.4 The Uniform Waveguide of Circular Cross-Section with Rigid Walls
8.8 Harmonic Excitation of Waveguide Modes
8.9 Energy Flux in a Waveguide of Rectangular Cross-Section with Rigid Walls
8.10 Examples of the Sound Attenuation Characteristics of Lined Ducts and Splitter Attenuators
8.11 Acoustic Horns
8.11.1 Applications
8.11.2 The Horn Equation
Chapter 9 Sound in Enclosures
9.1 Introduction
9.2 Some General Features of Sound Fields in Enclosures
9.3 Apology for the Rectangular Enclosure
9.4 The Impulse Response of Fluid in a Reverberant Rectangular Enclosure
9.5 Acoustic Natural Frequencies and Modes of Fluid in a Rigid-Walled Rectangular Enclosure
9.6 Modal Energy
9.7 The Effects of Finite Wall Impedance on Modal Energy-Time Dependence in Free Vibration
9.8 The Response of Fluid in a Rectangular Enclosure to Harmonic Excitation by a Point Monopole Source
9.9 The Sound Power of a Point Monopole in a Reverberant Enclosure
9.10 Sound Radiation into an Enclosure by the Vibration of a Boundary
9.11 Probabilistic Wave Field Models for Enclosed Sound Fields at High Frequency
9.11.1 The Modal Overlap Factor and Response Uncertainty
9.11.2 High-Frequency Sound Field Statistics
9.11.3 The Diffuse Field Model
9.12 Applications of The Diffuse Field Model
9.12.1 Steady State Diffuse Field Energy, Intensity and Enclosure Absorption
9.12.2 Reverberation Time
9.12.3 Steady State Source Sound Power and Reverberant Field Energy
9.13 a Brief Introduction to Geometric (Ray) Acoustics
Chapter 10 Structure-Borne Sound
10.1 The Nature and Practical Importance of Structure-Borne Sound
10.2 Emphasis and Content of the Chapter
10.3 The Energy Approach to Modeling Structure-Borne Sound
10.4 Quasi-Longitudinal Waves in Uniform Rods and Plates
10.5 The Bending Wave in Uniform Homogeneous Beams
10.5.1 A Review of the Roles of Direct and Shear Stresses
10.5.2 Shear Force and Bending Moment
10.5.3 The Beam Bending Wave Equation
10.5.4 Harmonic Solutions of the Bending Wave Equation
10.6 The Bending Wave in Thin Uniform Homogeneous Plates
10.7 Transverse Plane Waves in Flat Plates
10.8 Dispersion Curves, Wavenumber Vector Diagrams and Modal Density
10.9 Structure-Borne Wave Energy and Energy Flux
10.9.1 Quasi-Longitudinal Waves
10.9.2 Bending Waves in Beams
10.9.3 Bending Waves in Plates
10.10 Mechanical Impedances of Infinite, Uniform Rods, Beams and Plates
10.10.1 Impedance of Quasi-Longitudinal Waves in Rods
10.10.2 Impedances of Beams in Bending
10.10.3 Impedances of Thin, Uniform, Flat Plates in Bending
10.10.4 Impedance and Modal Density
10.11 Wave Energy Transmission through Junctions Between Structural Components
10.12 Impedance, Mobility and Vibration Isolation
10.13 Structure-Borne Sound Generated by Impact
10.14 Sound Radiation by Vibrating Flat Plates
10.14.1 The Critical Frequency and Radiation Cancellation
10.14.2 Analysis of Modal Radiation
10.14.3 Physical Interpretations and Practical Implications
Chapter 11 Transmission of Sound through Partitions
11.1 Practical Aspects of Sound Transmission through Partitions
11.2 Transmission of Normally Incident Plane Waves through an Unbounded Partition
11.3 Transmission of Sound through an Unbounded Flexible Partition
11.4 Transmission of Diffuse Sound through a Bounded Partition in a Baffle
11.5 Double-Leaf Partitions
11.6 Transmission of Normally Incident Plane Waves through an Unbounded Double-Leaf Partition
11.7 The Effect of Cavity Absorption
11.8 Transmission of Obliquely Incident Plane Waves through an Unbounded Double-Leaf Partition
11.9 Close-Fitting Enclosures
11.10 A Simple Model of a Noise Control Enclosure
11.11 Measurement of Sound Reduction Index (Transmission Loss)
Chapter 12 Reflection, Scattering, Diffraction and Refraction
12.1 Introduction
12.2 Scattering by a Discrete Body
12.3 Scattering by Crowds of Rigid Bodies
12.4 Resonant Scattering
12.4.1 Discrete Scatterers
12.4.2 Diffusors
12.5 Diffraction
12.5.1 Diffraction by Plane Screens
12.5.2 Diffraction by Apertures in Partitions
12.6 Reflection by Thin, Plane Rigid Sheets
12.7 Refraction
12.7.1 Refracted Ray Path through a Uniform, Weak Sound Speed Gradient
12.7.2 Refraction of Sound in the Atmosphere
Appendix 1 Complex Exponential Representation of Harmonic Functions
A1.1 Harmonic Functions of Time
A1.2 Harmonic Functions of Space
A1.3 CER of Traveling Harmonic Plane Waves
A1.4 Operations on Harmonically Varying Quantities Represented by CER
Appendix 2 Frequency Analysis
A2.1 Introduction
A2.2 Categories of Signal
A2.3 Fourier Analysis of Signals
A2.3.1 The Fourier Integral Transform
A2.3.2 Fourier Series Analysis
A2.3.3 Practical Fourier Analysis
A2.3.4 Frequency Analysis by Filters
A2.4 Presentation of the Results of Frequency Analysis
A2.5 Frequency Response Functions
A2.6 Impulse Response
Appendix 3 Spatial Fourier Analysis of Space-Dependent Variables
A3.1 Wavenumber Transform
A3.2 Wave Dispersion
Appendix 4 Coherence and Cross-Correlation
A4.1 Background
A4.2 Correlation
A4.3 Coherence
A4.4 The Relation between the Cross-Correlation and Coherence Functions
Appendix 5 The Simple Oscillator
A5.1 Free Vibration of the Undamped Mass-Spring Oscillator
A5.2 Impulse Response of the Undamped Oscillator
A5.3 The Viscously Damped Oscillator
A5.4 Impulse Response of the Viscously Damped Oscillator
A5.5 Response of a Viscously Damped Oscillator to Harmonic Excitation
Appendix 6 Measures of Sound, Frequency Weighting and Noise Rating Indicators
A6.1 Introduction
A6.2 Pressure-Time History
A6.3 Mean Square Pressure
A6.4 Sound Pressure Level
A6.5 Sound Intensity Level
A6.6 Sound Power Level
A6.7 Standard Reference Curves
Appendix 7 Demonstrations and Experiments
A7.1 Introduction
A7.2 Demonstrations
A7.2.1 Noise Sources
A7.2.2 Sound Intensity and Surface Acoustic Impedance
A7.2.3 Room Acoustics
A7.2.4 Miscellaneous
A7.3 Formal Laboratory Class Experiments
A7.3.1 Construct a Calibrated Volume Velocity Source (CVVS)
A7.3.2 Source Sound Power Determination Using Intensity Scans, Reverberation Time Measurements and Power Balance
A7.3.3 Investigation of Small Room Acoustic Response
A7.3.4 Determination of Complex Wavenumbers of Porous Materials
A7.3.5 Measurement of the Specific Acoustic Impedance of a Sheet of Porous Material
A7.3.6 Measurement of the Impedance of Side Branch and in-Line Reactive Attenuators
A7.3.7 Sound Pressure Generation by a Monopole in Free Space and in a Tube
A7.3.8 Mode Dispersion in a Duct
A7.3.9 Scattering by a Rough Surface
A7.3.10 Radiation by a Vibrating Plate
Answers
Bibliography
References
Index