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.

“...a masterpiece of thoroughness, organization, and clarity...sure to become a classic in acoustical literature and should be on the shelves of every acoustics library.” --Jorge P. Arenas, Auburn University, International Journal of Acoustics and Vibration, Vol. 6, No. 1, 2001“essentially a text book aimed at senior undergraduate, and post graduate engineering students, and their tutors ... However, the scope and format are also suitable for professional engineers with no formal training in acoustics...Foundations of Engineering Acoustics does great service to the field of acoustics by providing an appropriate introduction to the practical implications of noise and vibration in engineering and everyday life in general.” --Donald Quinn, Institute of Acoustics Bulletin“...there are very few textbooks that present Engineering Acoustics at a fairly basic, though higher than elementary, level. Professor Fahy's book therefore meets a need on the part of many engineers who may lack a formal background in acoustics but nonetheless are faced with acquiring some knowledge of the subject...Questions are occasionally interposed in the text, and these should help to stimulate the thought processes of the reader. The occasional flashes of humor are welcome...One feels that Professor Fahy has succeeded in his purpose,"...to assist readers to acquire an understanding of those concepts and principles, physical phenomena, theoretical models and mathematical representations that form the foundations of the practice of engineering acoustics"...the reader who carefully reads and works his way through this text will acquire a very good understanding of the physics involved in a wide range of engineering acoustics and vibration applications, as well as the mathematical basis for tackling more advanced problems...Overall, Frank Fahy has written a book that is up to the standard of erudition, authoritativeness and pedagogical excellence that we have come to expect from him on the basis of his other publications.” --Applied Acoustics, Vol. 66, Issue 1, January 2005“I found that this book serves its purpose as a comprehensive introduction to acoustics for the upper level engineering student. I can also recommend the text as a refresher for the practicing engineer.” --Stephen M. Jaeger, Colin Gordon & Associates, San Bruno, CA, USA

• PrefaceAcknowledgmentsChapter 1 Sound Engineering1.1 The Importance of Sound1.2 Acoustics and the Engineer1.3 Sound the ServantChapter 2 The Nature of Sound and Some Sound Wave Phenomena2.1 Introduction2.2 What Is Sound?2.3 Sound and Vibration2.4 Sound in Solids2.5 a Qualitative Introduction to Wave Phenomena2.5.1 Wavefronts2.5.2 Interference2.5.3 Reflection2.5.4 Scattering2.5.5 Diffraction2.5.6 Refraction2.5.7 The Doppler Effect2.5.8 Convection2.6 Some More Common Examples of the Behavior of Sound WavesChapter 3 Sound in Fluids3.1 Introduction3.2 The Physical Characteristics of Fluids3.3 Molecules and Particles3.4 Fluid Pressure3.5 Fluid Temperature3.6 Pressure, Density and Temperature in Sound Waves in a Gas3.7 Particle Motion3.8 Sound in Liquids3.9 Mathematical Models of Sound Waves3.9.1 The Plane Sound Wave Equation3.9.2 Solutions of the Plane Wave Equation3.9.3 Harmonic Plane Waves: Sound Pressure3.9.4 Plane Waves: Particle Velocity3.9.5 The Wave Equation in Three Dimensions3.9.6 Plane Waves in Three Dimensions3.9.7 The Wave Equation in Spherical Coordinates3.9.8 The Spherically Symmetric Sound Field3.9.9 Particle Velocity in the Spherically Symmetric Sound Field3.9.10 Other Forms of Sound FieldChapter 4 Impedance4.1 Introduction4.2 Some Simple Examples of the Utility of Impedance4.3 Mechanical Impedance4.3.1 Impedance of Lumped Structural Elements4.4 Forms of Acoustic Impedance4.4.1 Impedances of Lumped Acoustic Elements4.4.2 Specific Acoustic Impedance of Fluid in a Tube at Low Frequency4.4.3 Normal Specific Acoustic Impedance4.4.4 Radiation Impedance4.4.5 Acoustic Impedance4.4.6 Line and Surface Wave Impedance4.4.7 Modal Radiation Impedance4.5 an Application of Radiation Impedance of a Uniformly Pulsating Sphere4.6 Radiation EfficiencyChapter 5 Sound Energy and Intensity5.1 The Practical Importance of Sound Energy5.2 Sound Energy5.3 Transport of Sound Energy: Sound Intensity5.4 Sound Intensity in Plane Wave Fields5.5 Intensity and Mean Square Pressure5.6 Examples of Ideal Sound Intensity Fields5.6.1 The Point Monopole5.6.2 The Compact Dipole5.6.3 Interfering Monopoles5.6.4 Intensity Distributions in Orthogonally Directed Harmonic Plane Wave Fields5.7 Sound Intensity Measurement5.8 Determination of Source Sound Power Using Sound Intensity Measurement 5.9 Other Applications of Sound Intensity MeasurementChapter 6 Sources of Sound6.1 Introduction6.2 Qualitative Categorization of Sources6.2.1 Category 1 Sources 6.2.2 Category 2 Sources6.2.3 Category 3 Sources6.3 The Inhomogeneous Wave Equation6.3.1 Sound Radiation by Foreign Bodies6.3.2 Boundary 'Sources' Can Reflect or Absorb Energy6.4 Ideal Elementary Source Models6.4.1 The Dirac Delta Function6.4.2 The Point Monopole and the Pulsating Sphere6.4.3 Acoustic Reciprocity6.4.4 External Forces on a Fluid and the Compact Dipole6.4.5 The Oscillating Sphere6.4.6 Boundary Sources6.4.7 Free-Field and Other Green's Functions6.4.8 The Rayleigh Integrals6.5 Sound Radiation from Vibrating Plane Surfaces6.6 The Vibrating Circular Piston and the Cone Loudspeaker6.7 Directivity and Sound Power of Distributed Sources6.7.1 Sound Power of a Source in the Presence of a Second Source6.8 Zones of a Sound Field Radiated by a Spatially Extended Source6.9 Experimental Methods for Source Sound Power Determination6.10 Source CharacterizationChapter 7 Sound Absorption and Sound Absorbers7.1 Introduction7.2 The Effects of Viscosity, Thermal Diffusion and Relaxation Processes on Sound in Gases7.2.1 The Origin of Gas Viscosity7.2.2 The Effects of Thermal Diffusion7.2.3 The Effect of Molecular Relaxation7.2.4 Sound Energy Dissipation at the Rigid Boundary of a Gas7.2.5 Acoustically Induced Boundary Layers in a Gas-Filled Tube7.3 Forms of Porous Sound Absorbent Material7.4 Macroscopic Physical Properties of Porous Sound-Absorbing Materials7.4.1 Porosity7.4.2 Flow Resistance and Resistivity7.4.3 Structure Factor7.5 The Modified Equation for Plane Wave Sound Propagation in Gases Contained within Rigid Porous Materials7.5.1 Equation of Mass Conservation7.5.2 Momentum Equation7.5.3 The Modified Plane Wave Equation7.5.4 Harmonic Solution of the Modified Plane Wave Equation7.6 Sound Absorption by a Plane Surface of Uniform Impedance7.6.1 The Local Reaction Model7.6.2 Sound Power Absorption Coefficient of a Locally Reactive Surface7.6.3 Wave Impedance7.7 Sound Absorption by Thin Porous Sheets7.7.1 The Immobile Sheet in Free Field7.7.2 The Limp Sheet in Free Field 7.7.3 The Effect of a Rigid Wall Parallel to a Thin Sheet7.8 Sound Absorption by Thick Sheets of Rigid Porous Material7.8.1 The Infinitely Thick 'Sheet'7.8.2 The Sheet of Finite Thickness7.8.3 The Effect of a Backing Cavity on the Sound Absorption of a Sheet of Porous Material7.9 Sound Absorption by Flexible Cellular and Fibrous Materials7.10 The Effect of Perforated Cover Sheets on Sound Absorption by Porous Materials7.11 Non-Porous Sound Absorbers7.11.1 Helmholtz Resonators7.11.2 Panel Absorbers7.12 Methods of Measurement of Boundary Impedance and Absorption Coefficient7.12.1 The Impedance Tube7.12.2 Reverberation Room MethodChapter 8 Sound in Waveguides8.1 Introduction8.2 Plane Wave Pulses in a Uniform Tube8.3 Plane Wave Modes and Natural Frequencies of Fluid in Uniform Waveguides8.3.1 Conservative Terminations8.3.2 Non-Conservative Terminations8.4 Response to Harmonic Excitation8.4.1 Impedance Model8.4.2 Harmonic Response in Terms of Green'S Functions8.5 a Simple Case of Structure-Fluid Interaction8.6 Plane Waves in Ducts that Incorporate Impedance Discontinuities8.6.1 Insertion Loss and Transmission Loss8.6.2 Transmission of Plane Waves through an Abrupt Change of Crosssectional Area and an Expansion Chamber8.6.3 Series Networks of Acoustic Transmission Lines8.6.4 Side Branch Connections to Uniform Acoustic Waveguides8.6.5 The Side Branch Tube8.6.6 The Side Branch Orifice8.6.7 The Helmholtz Resonator Side Branch8.6.8 Bends in Otherwise Straight Uniform Waveguides8.7 Transverse Modes of Uniform Acoustic Waveguides8.7.1 The Uniform Two-Dimensional Waveguide with Rigid Walls8.7.2 The Uniform Two-Dimensional Waveguide with Finite Impedance Boundaries8.7.3 The Uniform Waveguide of Rectangular Cross-Section with Rigid Walls8.7.4 The Uniform Waveguide of Circular Cross-Section with Rigid Walls8.8 Harmonic Excitation of Waveguide Modes8.9 Energy Flux in a Waveguide of Rectangular Cross-Section with Rigid Walls8.10 Examples of the Sound Attenuation Characteristics of Lined Ducts and Splitter Attenuators8.11 Acoustic Horns8.11.1 Applications8.11.2 The Horn EquationChapter 9 Sound in Enclosures9.1 Introduction9.2 Some General Features of Sound Fields in Enclosures9.3 Apology for the Rectangular Enclosure9.4 The Impulse Response of Fluid in a Reverberant Rectangular Enclosure9.5 Acoustic Natural Frequencies and Modes of Fluid in a Rigid-Walled Rectangular Enclosure9.6 Modal Energy9.7 The Effects of Finite Wall Impedance on Modal Energy-Time Dependence in Free Vibration9.8 The Response of Fluid in a Rectangular Enclosure to Harmonic Excitation by a Point Monopole Source9.9 The Sound Power of a Point Monopole in a Reverberant Enclosure9.10 Sound Radiation into an Enclosure by the Vibration of a Boundary9.11 Probabilistic Wave Field Models for Enclosed Sound Fields at High Frequency9.11.1 The Modal Overlap Factor and Response Uncertainty9.11.2 High-Frequency Sound Field Statistics9.11.3 The Diffuse Field Model9.12 Applications of The Diffuse Field Model9.12.1 Steady State Diffuse Field Energy, Intensity and Enclosure Absorption9.12.2 Reverberation Time9.12.3 Steady State Source Sound Power and Reverberant Field Energy9.13 a Brief Introduction to Geometric (Ray) AcousticsChapter 10 Structure-Borne Sound10.1 The Nature and Practical Importance of Structure-Borne Sound10.2 Emphasis and Content of the Chapter10.3 The Energy Approach to Modeling Structure-Borne Sound10.4 Quasi-Longitudinal Waves in Uniform Rods and Plates10.5 The Bending Wave in Uniform Homogeneous Beams10.5.1 A Review of the Roles of Direct and Shear Stresses10.5.2 Shear Force and Bending Moment10.5.3 The Beam Bending Wave Equation10.5.4 Harmonic Solutions of the Bending Wave Equation10.6 The Bending Wave in Thin Uniform Homogeneous Plates10.7 Transverse Plane Waves in Flat Plates10.8 Dispersion Curves, Wavenumber Vector Diagrams and Modal Density10.9 Structure-Borne Wave Energy and Energy Flux10.9.1 Quasi-Longitudinal Waves10.9.2 Bending Waves in Beams10.9.3 Bending Waves in Plates10.10 Mechanical Impedances of Infinite, Uniform Rods, Beams and Plates10.10.1 Impedance of Quasi-Longitudinal Waves in Rods10.10.2 Impedances of Beams in Bending10.10.3 Impedances of Thin, Uniform, Flat Plates in Bending10.10.4 Impedance and Modal Density10.11 Wave Energy Transmission through Junctions Between Structural Components10.12 Impedance, Mobility and Vibration Isolation10.13 Structure-Borne Sound Generated by Impact10.14 Sound Radiation by Vibrating Flat Plates10.14.1 The Critical Frequency and Radiation Cancellation10.14.2 Analysis of Modal Radiation10.14.3 Physical Interpretations and Practical ImplicationsChapter 11 Transmission of Sound through Partitions11.1 Practical Aspects of Sound Transmission through Partitions11.2 Transmission of Normally Incident Plane Waves through an Unbounded Partition11.3 Transmission of Sound through an Unbounded Flexible Partition11.4 Transmission of Diffuse Sound through a Bounded Partition in a Baffle11.5 Double-Leaf Partitions11.6 Transmission of Normally Incident Plane Waves through an Unbounded Double-Leaf Partition11.7 The Effect of Cavity Absorption11.8 Transmission of Obliquely Incident Plane Waves through an Unbounded Double-Leaf Partition11.9 Close-Fitting Enclosures11.10 A Simple Model of a Noise Control Enclosure11.11 Measurement of Sound Reduction Index (Transmission Loss)Chapter 12 Reflection, Scattering, Diffraction and Refraction12.1 Introduction12.2 Scattering by a Discrete Body12.3 Scattering by Crowds of Rigid Bodies12.4 Resonant Scattering12.4.1 Discrete Scatterers12.4.2 Diffusors12.5 Diffraction12.5.1 Diffraction by Plane Screens12.5.2 Diffraction by Apertures in Partitions12.6 Reflection by Thin, Plane Rigid Sheets12.7 Refraction12.7.1 Refracted Ray Path through a Uniform, Weak Sound Speed Gradient12.7.2 Refraction of Sound in the AtmosphereAppendix 1 Complex Exponential Representation of Harmonic FunctionsA1.1 Harmonic Functions of TimeA1.2 Harmonic Functions of SpaceA1.3 CER of Traveling Harmonic Plane WavesA1.4 Operations on Harmonically Varying Quantities Represented by CERAppendix 2 Frequency AnalysisA2.1 IntroductionA2.2 Categories of SignalA2.3 Fourier Analysis of SignalsA2.3.1 The Fourier Integral TransformA2.3.2 Fourier Series AnalysisA2.3.3 Practical Fourier AnalysisA2.3.4 Frequency Analysis by FiltersA2.4 Presentation of the Results of Frequency AnalysisA2.5 Frequency Response FunctionsA2.6 Impulse ResponseAppendix 3 Spatial Fourier Analysis of Space-Dependent VariablesA3.1 Wavenumber TransformA3.2 Wave DispersionAppendix 4 Coherence and Cross-CorrelationA4.1 BackgroundA4.2 CorrelationA4.3 CoherenceA4.4 The Relation between the Cross-Correlation and Coherence FunctionsAppendix 5 The Simple OscillatorA5.1 Free Vibration of the Undamped Mass-Spring OscillatorA5.2 Impulse Response of the Undamped OscillatorA5.3 The Viscously Damped OscillatorA5.4 Impulse Response of the Viscously Damped OscillatorA5.5 Response of a Viscously Damped Oscillator to Harmonic ExcitationAppendix 6 Measures of Sound, Frequency Weighting and Noise Rating IndicatorsA6.1 IntroductionA6.2 Pressure-Time HistoryA6.3 Mean Square PressureA6.4 Sound Pressure LevelA6.5 Sound Intensity LevelA6.6 Sound Power LevelA6.7 Standard Reference CurvesAppendix 7 Demonstrations and ExperimentsA7.1 IntroductionA7.2 DemonstrationsA7.2.1 Noise SourcesA7.2.2 Sound Intensity and Surface Acoustic ImpedanceA7.2.3 Room AcousticsA7.2.4 MiscellaneousA7.3 Formal Laboratory Class ExperimentsA7.3.1 Construct a Calibrated Volume Velocity Source (CVVS)A7.3.2 Source Sound Power Determination Using Intensity Scans, Reverberation Time Measurements and Power BalanceA7.3.3 Investigation of Small Room Acoustic ResponseA7.3.4 Determination of Complex Wavenumbers of Porous MaterialsA7.3.5 Measurement of the Specific Acoustic Impedance of a Sheet of Porous MaterialA7.3.6 Measurement of the Impedance of Side Branch and in-Line Reactive AttenuatorsA7.3.7 Sound Pressure Generation by a Monopole in Free Space and in a TubeA7.3.8 Mode Dispersion in a DuctA7.3.9 Scattering by a Rough SurfaceA7.3.10 Radiation by a Vibrating PlateAnswersBibliographyReferencesIndex