Ning Xiang
Jens Blauert
Acoustics
for Engineers
Troy Lectures
Third Edition
Acoustics for Engineers
Ning Xiang • Jens Blauert
Acoustics for Engineers
Troy Lectures
Third Edition
123
Ning Xiang |
Jens Blauert |
Program in Architectural Acoustics |
Institute of Communication Acoustics |
Rensselaer Polytechnic Institute (RPI) |
Ruhr-Universität Bochum (RUB) |
Troy, NY, USA |
Bochum, Germany |
ISBN 978-3-662-63341-0 ISBN 978-3-662-63342-7 (eBook) https://doi.org/10.1007/978-3-662-63342-7
Jointly published with ASA Press
1st & 2nd editions: © Springer-Verlag Berlin Heidelberg 2008, 2009
3rd edition: © Springer-Verlag GmbH Germany, part of Springer Nature 2021
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This Springer imprint is published by the registered company Springer-Verlag GmbH, DE part of Springer Nature.
The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany
The ASA Press
ASA Press, which represents a collaboration between the Acoustical Society of America and Springer Nature, is dedicated to encouraging the publication of important new books as well as the distribution of classic titles in acoustics. These titles, published under a dual ASA Press/Springer imprint, are intended to reflect the full range of research in acoustics. ASA Press titles can include all types of books that Springer publishes, and may appear in any appropriate Springer book series.
Editorial Board
Mark F. Hamilton (Chair), University of Texas at Austin James Cottingham, Coe College
Timothy F. Duda, Woods Hole Oceanographic Institution Robin Glosemeyer Petrone, Threshold Acoustics
William M. Hartmann (Ex Officio), Michigan State University Darlene R. Ketten, Boston University
James F. Lynch (Ex Officio), Woods Hole Oceanographic Institution Philip L. Marston, Washington State University
Arthur N. Popper (Ex Officio), University of Maryland Christine H. Shadle, Haskins Laboratories
G. Christopher Stecker, Boys Town National Research Hospital Stephen C. Thompson, The Pennsylvania State University Ning Xiang, Rensselaer Polytechnic Institute
The Acoustical Society of America
On 27 December 1928 a group of scientists and engineers met at Bell Telephone Laboratories in New York City to discuss organizing a society dedicated to the field of acoustics. Plans developed rapidly, and the Acoustical Society of America (ASA) held its first meeting on 10–11 May 1929 with a charter membership of about 450. Today, ASA has a worldwide membership of about 7000.
The scope of this new society incorporated a broad range of technical areas that continues to be reflected in ASA’s present-day endeavors. Today, ASA serves the interests of its members and the acoustics community in all branches of acoustics, both theoretical and applied. To achieve this goal, ASA has established Technical Committees charged with keeping abreast of the developments and needs of membership in specialized fields, as well as identifying new ones as they develop.
The Technical Committees include acoustical oceanography, animal bioacoustics, architectural acoustics, biomedical acoustics, engineering acoustics, musical acoustics, noise, physical acoustics, psychological and physiological acoustics, signal processing in acoustics, speech communication, structural acoustics and vibration, and underwater acoustics. This diversity is one of the Society’s unique and strongest assets since it so strongly fosters and encourages cross-disciplinary learning, collaboration, and interactions.
ASA publications and meetings incorporate the diversity of these Technical Committees. In particular, publications play a major role in the Society. The Journal of the Acoustical Society of America (JASA) includes contributed papers and patent reviews. JASA Express Letters (JASA-EL) and Proceedings of Meetings on Acoustics (POMA) are online, open-access publications, offering rapid publication. Acoustics Today, published quarterly, is a popular open-access magazine. Other key features of ASA’s publishing program include books, reprints of classic acoustics texts, and videos. ASA’s biannual meetings offer opportunities for attendees to share information, with strong support throughout the career continuum, from students to retirees. Meetings incorporate many opportunities for
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The Acoustical Society of America |
professional and social interactions, and attendees find the personal contacts a rewarding experience. These experiences result in building a robust network of fellow scientists and engineers, many of whom become lifelong friends and colleagues.
From the Society’s inception, members recognized the importance of developing acoustical standards with a focus on terminology, measurement procedures, and criteria for determining the effects of noise and vibration. The ASA Standards Program serves as the Secretariat for four American National Standards Institute Committees and provides administrative support for several international standards committees.
Throughout its history to present day, ASA’s strength resides in attracting the interest and commitment of scholars devoted to promoting the knowledge and practical applications of acoustics. The unselfish activity of these individuals in the development of the Society is largely responsible for ASA’s growth and present stature.
Preface
This book provides the material for an introductory course in engineering acoustics for students with basic knowledge of mathematics. The contents are based on extensive teaching experience at the university level.
Under the guidance of an academic teacher, the book is sufficient as the sole textbook for the subject. Each chapter deals with a well-defined topic and represents the material for a two-hour lecture. The chapters alternate between more theoretical and more application-oriented concepts.
For self-study, we advise our readers to consult complementary introductory material. Chapter 16 lists several textbooks for this purpose.
Thanks go to various colleagues and graduate students who most willingly helped with corrections, proofreading, and stylistic improvement, and last but not the least, to the reviewers of the first edition, in particular, to Profs. Gerhard Sessler and Dominique J. Chéenne. Nevertheless, the authors assume full responsibility for all contents. For the current edition, we reversed the authors’ order. Ning Xiang is now the corresponding author, and Jens Blauert acts as the co-author.
In this (third) edition, we corrected recognized errors and typos, and edited several figures, notations, and equations to increase the clarity of the presentation. Also, we made some appropriate amendments.
At every chapter’s end, we offer exercise problems. Chapter 15 proposes approaches to solving them. The problems provide our readers with the opportunity to explore the underlying mathematical background in more detail. However, the study of the problems and their proposed solutions is no prerequisite for comprehending the material presented in the book’s main body.
Troy, NY, USA |
Ning Xiang |
Bochum, Germany |
Jens Blauert |
April 2021 |
|
ix
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
1 |
|
1.1 |
Definition of Three Basic Terms . . . . . . . . . . . . . . . . . . . . . . |
1 |
1.2 |
Specialized Areas within Acoustics . . . . . . . . . . . . . . . . . . . . |
3 |
1.3 |
About the History of Acoustics . . . . . . . . . . . . . . . . . . . . . . . |
4 |
1.4 |
Relevant Quantities in Acoustics . . . . . . . . . . . . . . . . . . . . . . |
5 |
1.5 |
Some Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . |
6 |
1.6Logarithmic Level Ratios and Logarithmic Frequency
|
|
Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
7 |
|
1.7 |
Double-Logarithmic Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . |
10 |
|
1.8 |
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
11 |
2 |
Mechanic and Acoustic Oscillations . . . . . . . . . . . . . . . . . . . . . . . . |
15 |
|
|
2.1 |
Basic Elements of Linear, Oscillating, Mechanic Systems . . . . |
16 |
|
2.2 |
Parallel Mechanic Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . |
18 |
|
2.3 |
Free Oscillations of Parallel Mechanic Oscillators . . . . . . . . . . |
19 |
|
2.4 |
Forced Oscillation of Parallel Mechanic Oscillators . . . . . . . . . |
21 |
|
2.5 |
Energies and Dissipation Losses . . . . . . . . . . . . . . . . . . . . . . |
24 |
|
2.6 |
Basic Elements of Linear, Oscillating, Acoustic Systems . . . . . |
25 |
|
2.7 |
The Helmholtz Resonator . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
26 |
|
2.8 |
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
27 |
3 |
Electromechanic and Electroacoustic Analogies . . . . . . . . . . . . . . . |
31 |
|
|
3.1 |
The Electromechanic Analogies . . . . . . . . . . . . . . . . . . . . . . . |
32 |
|
3.2 |
The Electroacoustic Analogy . . . . . . . . . . . . . . . . . . . . . . . . . |
33 |
|
3.3 |
Levers and Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
33 |
|
3.4 |
Rules for Deriving Analog Electric Circuits . . . . . . . . . . . . . . |
35 |
|
3.5 |
Synopsis of Electric Analogies of Simple Oscillators. . . . . . . . |
36 |
|
3.6 |
Circuit Fidelity, Impedance Fidelity and Duality . . . . . . . . . . . |
36 |
|
3.7 |
Examples of Mechanic and Acoustic Oscillators . . . . . . . . . . . |
38 |
|
3.8 |
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
39 |
xi
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Contents |
4 |
Electromechanic and Electroacoustic Transduction . . . . . . . . . . |
. . 43 |
|
|
4.1 |
Electromechanic Couplers as Twoor Three-Port Elements . . |
. 44 |
|
4.2 |
The Carbon Microphone—A Controlled Coupler . . . . . . . . . |
. 45 |
|
4.3 |
Fundamental Equations of Electroacoustic Transducers . . . . . |
. 46 |
|
4.4 |
Reversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
. 49 |
4.5Coupling of Electroacoustic Transducers to the Sound
|
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Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
50 |
|
4.6 |
Pressure and Pressure-Gradient Receivers . . . . . . . . . . . . . . . . |
52 |
|
4.7 |
Further Directional Characteristics . . . . . . . . . . . . . . . . . . . . . |
56 |
|
4.8 |
Absolute Calibration of Transducers . . . . . . . . . . . . . . . . . . . . |
58 |
|
4.9 |
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
59 |
5 |
Magnetic-Field Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
63 |
|
|
5.1 |
The Magnetodynamic Transduction Principle . . . . . . . . . . . . . |
65 |
|
5.2 |
Magnetodynamic Sound Emitters and Receivers . . . . . . . . . . . |
66 |
|
5.3 |
The Electromagnetic Transduction Principle . . . . . . . . . . . . . . |
73 |
|
5.4 |
Electromagnetic Sound Emitters and Receivers . . . . . . . . . . . . |
75 |
|
5.5 |
The Magnetostrictive Transduction Principle . . . . . . . . . . . . . . |
76 |
|
5.6 |
Magnetostrictive Sound Transmitters and Receivers . . . . . . . . |
77 |
|
5.7 |
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
77 |
6 |
Electric-Field Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
79 |
|
|
6.1 |
The Piezoelectric Transduction Principle. . . . . . . . . . . . . . . . . |
79 |
|
6.2 |
Piezoelectric Sound Emitters and Receivers . . . . . . . . . . . . . . |
82 |
|
6.3 |
The Electrostrictive Transduction Principle . . . . . . . . . . . . . . . |
86 |
|
6.4 |
Electrostrictive Sound Emitters and Receivers . . . . . . . . . . . . . |
87 |
|
6.5 |
The Dielectric Transduction Principle . . . . . . . . . . . . . . . . . . . |
87 |
|
6.6 |
Dielectric Sound Emitters and Receivers . . . . . . . . . . . . . . . . |
90 |
|
6.7 |
Further Transducer and Coupler Principles . . . . . . . . . . . . . . . |
93 |
|
6.8 |
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
94 |
7 The Wave Equation in Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 7.1 Derivation of the One-Dimensional Wave Equation . . . . . . . . 99
7.2Three-Dimensional Wave Equation in Cartesian
Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7.3 Solutions of the Wave Equation . . . . . . . . . . . . . . . . . . . . . . 106 7.4 Field Impedance and Power Transport in Plane Waves . . . . . . 108 7.5 Transmission-Line Equations and Reflectance . . . . . . . . . . . . . 108 7.6 The Acoustic Measuring Tube . . . . . . . . . . . . . . . . . . . . . . . . 111 7.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8 Horns and Stepped Ducts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
117 |
|
8.1 |
Webster’s Differential Equation—The Horn Equation . . . . . . . |
118 |
8.2 |
Conical Horns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
120 |
8.3 |
Exponential Horns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
122 |
Contents |
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8.4 Radiation Impedances and Sound Radiation . . . . . . . . . . . . . . 124 8.5 Steps in the Area Function . . . . . . . . . . . . . . . . . . . . . . . . . . 126 8.6 Stepped Ducts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 8.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
9 Spherical Waves, Harmonics, and Line Arrays. . . . . . . . . . . . . . . . 133 9.1 The Spherical Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . 134 9.2 Spherical Sound Sources of the First Order . . . . . . . . . . . . . . 138 9.3 Spherical Harmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 9.4 Higher-Order Spherical Sound Sources . . . . . . . . . . . . . . . . . . 143 9.5 Line Arrays of Monopoles . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 9.6 Analogies to Fourier Transform in Signal Theory . . . . . . . . . . 146 9.7 Directional Equivalence of Sources and Receivers. . . . . . . . . . 149 9.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
10 Piston Membranes, Diffraction and Scattering . . . . . . . . . . . . . . . . 153 10.1 The Rayleigh Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 10.2 Fraunhofer’s Approximation . . . . . . . . . . . . . . . . . . . . . . . . . 155 10.3 The Far-Field of Piston Membranes . . . . . . . . . . . . . . . . . . . . 156 10.4 The Near-Field of Piston Membranes . . . . . . . . . . . . . . . . . . 158 10.5 General Remarks on Diffraction and Scattering . . . . . . . . . . . . 164 10.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
11 Dissipation, Reflection, Refraction, and Absorption . . . . . . . . . . . . 167 11.1 Dissipation During Sound Propagation in Air . . . . . . . . . . . . . 169 11.2 Sound Propagation in Porous Media. . . . . . . . . . . . . . . . . . . . 170 11.3 Reflection and Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 11.4 Wall (Surface) Impedance and Degree of Absorption . . . . . . . 174 11.5 Porous Absorbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 11.6 Resonance Absorbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 11.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
12 Geometric Acoustics and Diffuse Sound Fields . . . . . . . . . . . . . . . . 185 12.1 Mirror Sound Sources and Ray Tracing . . . . . . . . . . . . . . . . . 186 12.2 Flutter Echoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 12.3 Impulse Responses of Rectangular Rooms . . . . . . . . . . . . . . . 191 12.4 Diffuse Sound Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 12.5 Reverberation-Time Formulas . . . . . . . . . . . . . . . . . . . . . . . . 196 12.6 Application of Diffuse Sound Fields . . . . . . . . . . . . . . . . . . . . 199 12.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
13 Insulation of Airand Structure-Borne Sound . . . . . . . . . . . . . . . . 205 13.1 Sound in Solids—Structure-Borne Sound . . . . . . . . . . . . . . . . 205 13.2 Radiation of Airborne Sound by Bending Waves . . . . . . . . . . 207 13.3 Sound-Transmission Loss of Single-Leaf Walls . . . . . . . . . . . 209 13.4 Sound-Transmission Loss of Double-Leaf Walls . . . . . . . . . . . 213
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Contents |
13.5 The Weighted Sound-Reduction Index . . . . . . . . . . . . . . . . . . 215 13.6 Insulation of Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 13.7 Insulation of Floors with Regard to Impact Sounds . . . . . . . . . 220 13.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
14 Noise Control—A Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 14.1 Origins of Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 14.2 Radiation of Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 14.3 Noise Reduction as a System Problem . . . . . . . . . . . . . . . . . . 229 14.4 Noise Reduction at the Source . . . . . . . . . . . . . . . . . . . . . . . . 230 14.5 Noise Reduction Along the Propagation Paths . . . . . . . . . . . . 231 14.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
15 Solutions to the Exercise Problems . . . . . . . . . . . . . . . . . . . . . . . . . 241 15.1 Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 15.2 Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 15.3 Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 15.4 Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 15.5 Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 15.6 Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 15.7 Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 15.8 Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 15.9 Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 15.10 Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 15.11 Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 15.12 Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 15.13 Chapter 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 15.14 Chapter 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
16 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 16.1 Complex Notation of Sinusoidal Signals . . . . . . . . . . . . . . . . . 399 16.2 Complex Notation of Power and Intensity . . . . . . . . . . . . . . . 400 16.3 Supplementary Textbooks for Self Study . . . . . . . . . . . . . . . . 402 16.4 Letter Symbols, Notations, and Units . . . . . . . . . . . . . . . . . . . 403
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
407 |