Engineering Noise Control

Transcription

1

2 Engineering Noise Control The practice of engineering noise control demands a solid understanding of the fundamentals of acoustics, the practical application of current noise control technology and the underlying theoretical concepts. This fully revised and updated fourth edition provides a comprehensive explanation of these key areas clearly, yet without oversimplification. Written by experts of their field, the practical focus echoes advances in the discipline, reflected in the fourth edition s new material, including: completely updated coverage of sound transmission loss, mufflers and exhaust stack directivity a new chapter on practical numerical acoustics thorough explanation of the latest instruments for measurements and analysis. Essential reading for advanced students or those already well versed in the art and science of noise control, this distinctive text can be used to solve real world problems encountered by noise and vibration consultants as well as engineers and occupational hygienists. David A. Bies is now retired having served as a Reader and then Visiting Research Fellow at the University of Adelaide s School of Mechanical Engineering. He is an expert and widely published acoustics physicist who has also worked as a senior consultant in industry. Colin H. Hansen is Professor and Head of the School of Mechanical Engineering at the University of Adelaide. With a wealth of experience in consultanting, research and teaching in acoustics, he has authored numerous books, journal articles and conference proceedings on the topic.

3

4 Engineering Noise Control Theory and practice Fourth edition David A. Bies and Colin H. Hansen

5 This book is dedicated to Susan, to Carrie, to Kristy and to Laura. First published 1988 by E & FN Spon, an imprint of Routledge Second edition 1996 Third edition 2003 by Spon Press Fourth edition 2009 by Spon Press 2 Park Square, Milton Park, Abingdon, OX14 4RN Simultaneously published in the USA and Canada by Taylor & Francis 270 Madison Avenue, New York, NY 10016, USA Spon Press is an imprint of the Taylor & Francis Group, an informa business This edition published in the Taylor & Francis e-library, To purchase your own copy of this or any of Taylor & Francis or Routledge s collection of thousands of ebooks please go to David A. Bies and Colin H. Hansen All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. This publication presents material of a broad scope and applicability. Despite stringent efforts by all concerned in the publishing process, some typographical or editorial errors may occur, and readers are encouraged to bring these to our attention where they represent errors of substance. The publisher and author disclaim any liability, in whole or in part, arising from information contained in this publication. The reader is urged to consult with an appropriate licensed professional prior to taking any action or making any interpretation that is within the realm of a licensed professional practice. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Bies, David A., Engineering noise control: theory and pratice / David A. Bies and Colin H. Hansen. 4th ed. p. cm. Includes bibliographical references. 1. Noise control. 2. Machinery Noise. I. Hansen, Colin H., 1951-II. Title. TD892.B dc ISBN Master e-book ISBN ISBN 13: (hbk) ISBN 13: (pbk) ISBN 13: (ebk) ISBN 10: (hbk) ISBN 10: (pbk) ISBN 10: (ebk)

6 CONTENTS PREFACE...xviii ACKNOWLEDGMENTS...xxi CHAPTER 1 FUNDAMENTALS AND BASIC TERMINOLOGY INTRODUCTION NOISE-CONTROL STRATEGIES Sound Source Modification Control of the Transmission Path Modification of the Receiver Existing Facilities Facilities in the Design Stage Airborne versus Structure-borne Noise ACOUSTIC FIELD VARIABLES Variables The Acoustic Field Magnitudes The Speed of Sound Dispersion Acoustic Potential Function WAVE EQUATION Plane and Spherical Waves Plane Wave Propagation Spherical Wave Propagation Wave Summation Plane Standing Waves Spherical Standing Waves MEAN SQUARE QUANTITIES ENERGY DENSITY SOUND INTENSITY Definitions Plane Wave and Far Field Intensity Spherical Wave Intensity SOUND POWER UNITS SPECTRA Frequency Analysis COMBINING SOUND PRESSURES Coherent and Incoherent Sounds Addition of Coherent Sound Pressures... 46

7 vi Contents Beating Addition of Incoherent Sounds (Logarithmic Addition) Subtraction of Sound Pressure Levels Combining Level Reductions IMPEDANCE Mechanical Impedance, Z m Specific Acoustic Impedance, Z s Acoustic Impedance, Z A FLOW RESISTANCE CHAPTER 2 THE HUMAN EAR BRIEF DESCRIPTION OF THE EAR External Ear Middle Ear Inner Ear Cochlear Duct or Partition Hair Cells Neural Encoding Linear Array of Uncoupled Oscillators MECHANICAL PROPERTIES OF THE CENTRAL PARTITION Basilar Membrane Travelling Wave Energy Transport and Group Speed Undamping The Half Octave Shift Frequency Response Critical Frequency Band Frequency Resolution NOISE INDUCED HEARING LOSS SUBJECTIVE RESPONSE TO SOUND PRESSURE LEVEL Masking Loudness Comparative Loudness and the Phon Relative Loudness and the Sone Pitch CHAPTER 3 INSTRUMENTATION FOR NOISE MEASUREMENT AND ANALYSIS MICROPHONES Condenser Microphone Piezoelectric Microphone Pressure Response Microphone Sensitivity Field Effects and Calibration Microphone Accuracy WEIGHTING NETWORKS

8 Contents vii 3.3 SOUND LEVEL METERS CLASSES OF SOUND LEVEL METER SOUND LEVEL METER CALIBRATION Electrical Calibration Acoustic Calibration Measurement Accuracy NOISE MEASUREMENTS USING SOUND LEVEL METERS Microphone Mishandling Sound Level Meter Amplifier Mishandling Microphone and Sound Level Meter Response Characteristics Background Noise Wind Noise Temperature Humidity and Dust Reflections from Nearby Surfaces TIME-VARYING SOUND NOISE LEVEL MEASUREMENT DATA LOGGERS PERSONAL SOUND EXPOSURE METER RECORDING OF NOISE SPECTRUM ANALYSERS INTENSITY METERS Sound Intensity by the pbu Method Accuracy of the pbu Method Sound Intensity by the pbp Method Accuracy of the pbp Method Frequency Decomposition of the Intensity Direct Frequency Decomposition Indirect Frequency Decomposition ENERGY DENSITY SENSORS SOUND SOURCE LOCALISATION Nearfield Acoustic Holography (NAH) Summary of the Underlying Theory Statistically Optimised Nearfield Acoustic Holography (SONAH) Helmholtz Equation Least Squares Method (HELS) Beamforming Summary of the Underlying Theory Direct Sound Intensity measurement CHAPTER 4 CRITERIA INTRODUCTION Noise Measures A-weighted Equivalent Continuous Noise Level, L Aeq A-weighted Sound Exposure

9 viii Contents A-weighted Sound Exposure Level, L AE or SEL DayBNight Average Sound Level, L dn or DNL Community Noise Equivalent Level, L den or CNEL Effective Perceived Noise Level, L PNE Other Descriptors HEARING LOSS Threshold Shift Presbyacusis Hearing Damage HEARING DAMAGE RISK Requirements for Speech Recognition Quantifying Hearing Damage Risk International Standards Organisation Formulation Alternative Formulations Bies and Hansen Formulation Dresden Group Formulation Observed Hearing Loss Some Alternative Interpretations HEARING DAMAGE RISK CRITERIA Continuous Noise Impulse Noise Impact Noise IMPLEMENTING A HEARING CONSERVATION PROGRAM SPEECH INTERFERENCE CRITERIA Broadband Background Noise Intense Tones PSYCHOLOGICAL EFFECTS OF NOISE Noise as a Cause of Stress Effect on Behaviour and Work Efficiency AMBIENT NOISE LEVEL SPECIFICATION Noise Weighting Curves NR Curves NC Curves RC Curves NCB Curves RNC Curves Comparison of Noise Weighting Curves with db(a) Specifications Speech Privacy ENVIRONMENTAL NOISE LEVEL CRITERIA A-weighting Criteria ENVIRONMENTAL NOISE SURVEYS Measurement Locations Duration of the Measurement Survey Measurement Parameters Noise Impact

10 Contents ix CHAPTER 5 SOUND SOURCES AND OUTDOOR SOUND PROPAGATION INTRODUCTION SIMPLE SOURCE Pulsating Sphere Fluid Mechanical Monopole Source DIPOLE SOURCE Pulsating Doublet or Dipole (Far-field Approximation) Pulsating Doublet or Dipole (Near-field) Oscillating Sphere Fluid Mechanical Dipole Source QUADRUPOLE SOURCE (FAR-FIELD APPROXIMATION) Lateral Quadrupole Longitudinal Quadrupole Fluid Mechanical Quadrupole Source LINE SOURCE Infinite Line Source Finite Line Source PISTON IN AN INFINITE BAFFLE Far Field Near Field On-axis Radiation Load of the Near Field INCOHERENT PLANE RADIATOR Single Wall Several Walls of a Building or Enclosure DIRECTIVITY REFLECTION EFFECTS Simple Source Near a Reflecting Surface Observer Near a Reflecting Surface Observer and Source Both Close to a Reflecting Surface REFLECTION AND TRANSMISSION AT A PLANE / TWO MEDIA INTERFACE Porous Earth Plane Wave Reflection and Transmission Spherical Wave Reflection at a Plane Interface Effects of Turbulence SOUND PROPAGATION OUTDOORS, GENERAL CONCEPTS Methodology Limits to Accuracy of Prediction Outdoor Sound Propagation Prediction Schemes Geometrical Spreading, K Directivity Index, DI M Excess Attenuation Factor, A E Air Absorption, A a Shielding by Barriers, Houses and Process Equipment/Industrial Buildings, A bhp

11 x Contents Attenuation due to Forests and Dense Foliage, A f Ground Effects CONCAWE Method Simple Method (Hard or Soft Ground) Plane Wave Method ISO (1996) Method Detailed, Accurate and Complex Method Image Inversion and Increased Attenuation at Large Distance Meteorological Effects Attenuation in the Shadow Zone (Negative Sonic Gradient) Meteorological Attenuation Calculated according to Tonin (1985) Meteorological Attenuation Calculated according to CONCAWE Meteorological Attenuation Calculated according to ISO (1996) Combined Excess Attenuation Model Accuracy of Outdoor Sound Predictions CHAPTER 6 SOUND POWER, ITS USE AND MEASUREMENT INTRODUCTION RADIATION IMPEDANCE RELATION BETWEEN SOUND POWER AND SOUND PRESSURE RADIATION FIELD OF A SOUND SOURCE Free-field Simulation in an Anechoic Room Sound Field Produced in an Enclosure DETERMINATION OF SOUND POWER USING INTENSITY MEASUREMENTS DETERMINATION OF SOUND POWER USING CONVENTIONAL PRESSURE MEASUREMENTS Measurement in Free or Semi-free Field Measurement in a Diffuse Field Substitution Method Absolute Method Field Measurement Semi-reverberant Field Measurements by Method One Semi-reverberant Field Measurements by Method Two Semi-reverberant Field Measurements by Method Three Near-field Measurements DETERMINATION OF SOUND POWER USING SURFACE VIBRATION MEASUREMENTS SOME USES OF SOUND POWER INFORMATION The Far Free Field The Near Free Field

12 Contents xi CHAPTER 7 SOUND IN ENCLOSED SPACES INTRODUCTION Wall-interior Modal Coupling Sabine Rooms Flat and Long Rooms LOW FREQUENCIES Rectangular rooms Cylindrical Rooms BOUND BETWEEN LOW-FREQUENCY AND HIGH-FREQUENCY BEHAVIOUR Modal Density Modal Damping and Bandwidth Modal Overlap Cross-over Frequency HIGH FREQUENCIES, STATISTICAL ANALYSIS Effective Intensity in a Diffuse Field Energy Absorption at Boundaries Air Absorption Steady-state Response TRANSIENT RESPONSE Classical Description Modal Description Empirical Description Mean Free Path MEASUREMENT OF THE ROOM CONSTANT Reference Sound Source Method Reverberation Time Method POROUS SOUND ABSORBERS Measurement of Absorption Coefficients Noise Reduction Coefficient (NRC) Porous Liners Porous Liners with Perforated Panel Facings Sound Absorption Coefficients of Materials in Combination PANEL SOUND ABSORBERS Empirical Method Analytical Method FLAT AND LONG ROOMS Flat Room with Specularly Reflecting Floor and Ceiling Flat Room with Diffusely Reflecting Floor and Ceiling Flat Room with Specularly and Diffusely Reflecting Boundaries Long Room with Specularly Reflecting Walls Long Room with Circular Cross-section and Diffusely Reflecting Wall Long Room with Rectangular Cross-section APPLICATIONS OF SOUND ABSORPTION Relative Importance of the Reverberant Field

13 xii Contents Reverberation Control AUDITORIUM DESIGN Reverberation Time Early Decay Time (EDT) Clarity (C 80) Envelopment Interaural Cross Correlation Coefficient, IACC Background Noise Level Total Sound Level or Loudness, G Diffusion Speech Intelligibility RASTI Articulation Loss Signal to Noise Ratio Sound Reinforcement Direction Perception Feedback Control Estimation of Parameters for Occupied Concert Halls Optimum Volumes for Auditoria CHAPTER 8 PARTITIONS, ENCLOSURES AND BARRIERS INTRODUCTION SOUND TRANSMISSION THROUGH PARTITIONS Bending Waves Transmission Loss Impact Isolation Panel Transmission Loss (or Sound Reduction Index) Behaviour Sharp s Prediction Scheme for Isotropic Panels Davy s Prediction Scheme for Isotropic Panels Thickness Correction for Isotropic Panels Orthotropic Panels Sandwich Panels Double Wall Transmission Loss Sharp Model for Double Wall TL Davy Model for Double Wall TL Staggered Studs Panel Damping Effect of the Flow Resistance of the Sound Absorbing Material in the Cavity Multi-leaf and Composite Panels Triple Wall Sound Transmission Loss Common Building Materials Sound-absorptive Linings NOISE REDUCTION vs TRANSMISSION LOSS Composite Transmission Loss Flanking Transmission Loss

14 Contents xiii 8.4 ENCLOSURES Noise Inside Enclosures Noise Outside Enclosures Personnel Enclosures Enclosure Windows Enclosure Leakages Access and Ventilation Enclosure Vibration Isolation Enclosure Resonances Close-fitting Enclosures Partial Enclosures BARRIERS Diffraction at the Edge of a Thin Sheet Outdoor Barriers Thick Barriers Shielding by Terrain Effects of Wind and Temperature Gradients on Barrier Attenuation ISO Approach to Barrier Insertion Loss Calculations Indoor Barriers PIPE LAGGING Porous Material Lagging Impermeable Jacket and Porous Blanket Lagging CHAPTER 9 MUFFLING DEVICES INTRODUCTION MEASURES OF PERFORMANCE DIFFUSERS AS MUFFLING DEVICES CLASSIFICATION OF MUFFLING DEVICES ACOUSTIC IMPEDANCE LUMPED ELEMENT DEVICES Impedance of an Orifice or a Short Narrow Duct End Correction Acoustic Resistance Impedance of a Volume REACTIVE DEVICES Acoustical Analogs of Kirchhoff's Laws Side Branch Resonator End Corrections for a Helmholtz Resonator Neck and Quarter Wave Tube Quality Factor of a Helmholtz Resonator and Quarter Wave Tube Insertion Loss due to Side Branch Transmission Loss due to Side Branch Resonator Mufflers

15 xiv Contents Expansion Chamber Insertion Loss Transmission Loss Small Engine Exhaust Lowpass Filter Pressure Drop Calculations for Reactive Muffling Devices Flow-generated Noise LINED DUCTS Locally Reacting and Bulk Reacting Liners Liner Specification Lined Duct Silencers Flow Effects Higher Order Mode Propagation Cross-sectional Discontinuities Pressure Drop Calculations for Dissipative Mufflers DUCT BENDS OR ELBOWS UNLINED DUCTS EFFECT OF DUCT END REFLECTIONS DUCT BREAK-OUT NOISE Break-out Sound Transmission Break-in Sound Transmission LINED PLENUM ATTENUATOR Wells Method ASHRAE Method More Complex Methods (Cummings and Ih) WATER INJECTION DIRECTIVITY OF EXHAUST DUCTS CHAPTER 10 VIBRATION CONTROL INTRODUCTION VIBRATION ISOLATION Single-degree-of-freedom Systems Surging in Coil Springs Four-isolator Systems Two-stage Vibration Isolation Practical Isolator Considerations Lack of Stiffness of Equipment Mounted on Isolators Lack of Stiffness of Foundations Superimposed Loads on Isolators TYPES OF ISOLATORS Rubber Metal Springs Cork Felt Air Springs VIBRATION ABSORBERS

16 Contents xv 10.5 VIBRATION NEUTRALISERS VIBRATION MEASUREMENT Acceleration Transducers Sources of Measurement Error Sources of Error in the Measurement of Transients Accelerometer Calibration Accelerometer Mounting Piezo-resistive Accelerometers Velocity Transducers Laser Vibrometers Instrumentation Systems Units of Vibration DAMPING OF VIBRATING SURFACES When Damping is Effective and Ineffective Damping Methods MEASUREMENT OF DAMPING CHAPTER 11 SOUND POWER AND SOUND PRESSURE LEVEL ESTIMATION PROCEDURES INTRODUCTION FAN NOISE AIR COMPRESSORS Small Compressors Large Compressors (Noise Levels within the Inlet and Exit Piping) Centrifugal Compressors (Interior Noise Levels) Rotary or Axial Compressors (Interior Noise Levels) Reciprocating Compressors (Interior Noise) Large Compressors (Exterior Noise Levels) COMPRESSORS FOR CHILLERS AND REFRIGERATION UNITS COOLING TOWERS PUMPS JETS General Estimation Procedures Gas and Steam Vents General Jet Noise Control CONTROL VALVES Internal Sound Power Generation Internal Sound Pressure Level External Sound Pressure Level High Exit Velocities Control Valve Noise Reduction Control Valves for Liquids Control Valves for Steam PIPE FLOW

17 xvi Contents BOILERS TURBINES DIESEL AND GAS-DRIVEN ENGINES Exhaust Noise Casing Noise Inlet Noise FURNACE NOISE ELECTRIC MOTORS Small Electric Motors (below 300 kw) Large Electric Motors (above 300 kw) GENERATORS TRANSFORMERS GEARS TRANSPORTATION NOISE Road Traffic Noise UK DoT model (CoRTN) United States FHWA Traffic Noise Model (TNM) Other Models Rail Traffic Noise Aircraft Noise CHAPTER 12 PRACTICAL NUMERICAL ACOUSTICS by Carl Howard INTRODUCTION LOW-FREQUENCY REGION Helmholtz Method Boundary Element Method (BEM) Direct Method Indirect Method Meshing Problem Formulation Rayleigh Integral Method Finite Element Analysis (FEA) Pressure Formulated Acoustic Elements Displacement Formulated Acoustic Elements Practical Aspects of Modelling Acoustic Systems with FEA Numerical Modal Analysis Modal Coupling using MATLAB Acoustic Potential Energy HIGH-FREQUENCY REGION: STATISTICAL ENERGY ANALYSIS Coupling Loss Factors Amplitude Responses

18 Contents xvii APPENDIX A WAVE EQUATION DERIVATION A.1 CONSERVATION OF MASS A.2EULER'S EQUATION A.3EQUATION OF STATE A.4WAVE EQUATION (LINEARISED) APPENDIX B PROPERTIES OF MATERIALS APPENDIX C ACOUSTICAL PROPERTIES OF POROUS MATERIALS C.l FLOW RESISTANCE AND RESISTIVITY C.2 SOUND PROPAGATION IN POROUS MEDIA C.3 SOUND REDUCTION DUE TO PROPAGATION THROUGH A POROUS MATERIAL C.4 MEASUREMENT AND CALCULATION OF ABSORPTION COEFFICIENTS C.4.1 Porous Materials with a Backing Cavity C.4.2 Multiple Layers of Porous Liner backed by an Impedance Z L C.4.3 Porous Liner Covered with a Limp Impervious Layer C.4.4 Porous Liner Covered with a Perforated Sheet C.4.5 Porous Liner Covered with a Limp Impervious Layer and a Perforated Sheet APPENDIX D FREQUENCY ANALYSIS D.1 DIGITAL FILTERING D.2 DISCRETE FOURIER ANALYSIS D.2.1 Power Spectrum D.2.2 Sampling Frequency and Aliasing D.2.3 Uncertainty Principle D.2.4 Real-time Frequency D.2.5 Weighting Functions D.2.6 Zoom Analysis D.3 IMPORTANT FUNCTIONS D.3.1 Cross-spectrum D.3.2 Coherence D.3.3 Frequency Response (or Transfer) Function REFERENCES LIST OF ACOUSTICAL STANDARDS INDEX

19 PREFACE Although this fourth edition follows the same basic style and format as the first, second and third editions, the content has been considerably updated and expanded, yet again. This is partly in response to significant advances in the practice of acoustics and in the associated technology during the six years since the third edition and partly in response to improvements, corrections, suggestions and queries raised by various practitioners and students. The major additions are outlined below. However, there are many other minor additions and corrections that have been made to the text but which are not specifically identified here. The emphasis of this edition is purely on passive means of noise control and the chapter on active noise control that appeared in the second and third editions has been replaced with a chapter on practical numerical acoustics, where it is shown how free, open source software can be used to solve some difficult acoustics problems, which are too complex for theoretical analysis. The removal of Chapter 12 on active noise control is partly due to lack of space and partly because a more comprehensive and a more useful treatment is available in the book, Understanding Active Noise Cancellation by Colin H. Hansen. Chapter 1 includes updated material on the speed of sound in compliant ducts and the entire section on speed of sound has been rewritten with a more unified treatment of solids, liquids and gases. Chapter 2 has been updated to include some recent discoveries regarding the mechanism of hearing damage. Chapter 3 has been considerably updated and expanded to include a discussion of expected measurement precision and errors using the various forms of instrumentation, as well as a discussion of more advanced instrumentation for noise source localisation using near field acoustic holography and beamforming. The discussion on spectrum analysers and recording equipment has been completely rewritten to reflect more modern instrumentation. In Chapter 4, the section on evaluation of environmental noise has been updated and rewritten. Additions in Chapter 5 include a better definition of incoming solar radiation for enabling the excess attenuation due to meteorological influences to be determined. Many parts of Section 5.11 on outdoor sound propagation have been rewritten in an attempt to clarify some ambiguities in the third edition. The treatment of a vibrating sphere dipole source has also been considerably expanded. In Chapter 7, the section on speech intelligibility in auditoria has been considerably expanded and includes some guidance on the design of sound reinforcement systems. In the low frequency analysis of sound fields, cylindrical rooms are now included in addition to rectangular rooms. The section on the measurement of the room constant has been expanded and explained more clearly. In the section on auditoria, a discussion of the optimum reverberation time in classrooms has now been included. In Chapter 8, the discussion on STC and weighted sound reduction index has been revised. The prediction scheme for estimating the transmission loss of single

20 Preface xix isotropic panels has been extended to low frequencies in the resonance and stiffness controlled ranges and the Davy method for estimating the Transmission Loss of double panel walls has been completely revised and corrected. The discussion now explains how to calculate the TL of multi-leaf and composite panels. Multi-leaf panels are described as those made up of different layers (or leaves) of the same material connected together in various ways whereas composite panels are described as those made up of two leaves of different materials bonded rigidly together. A procedure to calculate the transmission loss of very narrow slits such as found around doors with weather seals has also been added. A section on the calculation of flanking transmission has now been included with details provided for the calculation of flanking transmission via suspended ceilings. The section on calculating the Insertion Loss of barriers according to ISO has been rewritten to more clearly reflect the intention of the standard. In addition, expressions are now provided for calculating the path lengths for sound diffracted around the ends of a barrier. Chapter 9 has had a number of additions: Transmission Loss calculations (in addition to Insertion Loss calculations) for side branch resonators and expansion chambers; a much more detailed and accurate analysis of Helmholtz resonators, including better estimates for the effective length of the neck; an expanded discussion of higher order mode propagation, with expressions for modal cut-on frequencies of circular section ducts; a number of new models for calculating the Transmission Loss of plenum chambers; and a more detailed treatment of directivity of exhaust stacks. In Chapter 10, the effect of the mass of the spring on the resonance frequency of isolated systems has been included in addition to the inclusion of a discussion of the surge phenomenon in coil springs. The treatment of vibration absorbers has been revised and expanded to include a discussion of vibration neutralisers, and plots of performance of various configurations are provided. The treatment of two-stage vibration isolation has been expanded and non-dimensional plots provided to allow estimation of the effect of various parameters on the isolation performance. Chapter 11 remains unchanged and chapter 12 has been replaced with Chapter 13, where the previous content of Chapter 13 now serves as an introduction to a much expanded chapter on practical numerical acoustics written by Dr Carl Howard. This chapter covers the analysis of complex acoustics problems using boundary element analysis, finite element analysis and MatLab. Emphasis is not on the theoretical aspects of these analyses but rather on the practical application of various software packages including a free open source boundary element package. Appendix A, which in the first edition contained example problems, has been replaced with a simple derivation of the wave equation. A comprehensive selection of example problems tailored especially for the book are now available on the internet for no charge at: Appendix B has been updated and considerably expanded with many more materials and their properties covered. In Appendix C, the discussion of flow resistance measurement using an impedance tube has been expanded and clarified. Expressions for the acoustic impedance of porous fibreglass and rockwool materials have been extended to include polyester fibrous materials and plastic foams. The impedance expressions towards the end of Appendix C now include a discussion of multi-layered materials.