# Foundations of Engineering Acoustics

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Foundations of Engineering Acoustics takes the reader on a journey from a qualitative introduction to the physical nature of sound, explained in terms of common experience, to mathematical models and analytical results which underlie the techniques applied by the engineering industry to improve the acoustic performance of their products. The book is distinguished by extensive descriptions and explanations of audio-frequency acoustic phenomena and their relevance to engineering, supported by a wealth of diagrams, and by a guide for teachers of tried and tested class demonstrations and laboratory-based experiments. Foundations of Engineering Acoustics is a textbook suitable for both senior undergraduate and postgraduate courses in mechanical, aerospace, marine, and possibly electrical and civil engineering schools at universities. It will be a valuable reference for academic teachers and researchers and will also assist Industrial Acoustic Group staff and Consultants.

## Key Features

- Comprehensive and up-to-date: broad coverage, many illustrations, questions, elaborated answers, references and a bibliography
- Introductory chapter on the importance of sound in technology and the role of the engineering acoustician
- Deals with the fundamental concepts, principles, theories and forms of mathematical representation, rather than methodology
- Frequent reference to practical applications and contemporary technology
- Emphasizes qualitative, physical introductions to each principal as an entrée to mathematical analysis for the less theoretically oriented readers and courses
- Provides a 'cook book' of demonstrations and laboratory-based experiments for teachers
- Useful for discussing acoustical problems with non-expert clients/managers because the descriptive sections are couched in largely non-technical language and any jargon is explained
- Draws on the vast pedagogic experience of the writer

## Readership

Undergraduate, postgraduate, engineers in acoustics

## Table of Contents

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

## Product details

- No. of pages: 443
- Language: English
- Copyright: © Academic Press 2000
- Published: September 12, 2000
- Imprint: Academic Press
- Hardcover ISBN: 9780122476655
- eBook ISBN: 9780080506838

## About the Author

### Frank Fahy

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.

#### Affiliations and Expertise

Institute of Sound and Vibration Research, University of Southampton, UK

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