# Acoustics: Sound Fields and Transducers

## 1st Edition

**Authors:**Leo L. Beranek Tim Mellow

**eBook ISBN:**9780123914866

**Hardcover ISBN:**9780123914217

**Imprint:**Academic Press

**Published Date:**20th September 2012

**Page Count:**720

## Description

*Acoustics: Sound Fields and Transducers *is a thoroughly updated version of Leo Beranek's classic 1954 book that retains and expands on the original's detailed acoustical fundamentals while adding practical formulas and simulation methods.

Serving both as a text for students in engineering departments and as a reference for practicing engineers, this book focuses on electroacoustics, analyzing the behavior of transducers with the aid of electro-mechano-acoustical circuits. Assuming knowledge of electrical circuit theory, it starts by guiding readers through the basics of sound fields, the laws governing sound generation, radiation, and propagation, and general terminology. It then moves on to examine:

- Microphones (electrostatic and electromagnetic), electrodynamic loudspeakers, earphones, and horns
- Loudspeaker enclosures, baffles, and waveguides
- Miniature applications (e.g., MEMS in I-Pods and cellphones)
- Sound in enclosures of all sizes, such as school rooms, offices, auditoriums, and living rooms

Numerical examples and summary charts are given throughout the text to make the material easily applicable to practical design. It is a valuable resource for experimenters, acoustical consultants, and to those who anticipate being engineering designers of audio equipment.

## Key Features

- An update for the digital age of Leo Beranek's classic 1954 book
*Acoustics* - Provides detailed acoustic fundamentals, enabling better understanding of complex design parameters, measurement methods, and data
- Extensive appendices cover frequency-response shapes for loudspeakers, mathematical formulas, and conversion factors

## Readership

Research scientists and engineers working in acoustics; Mechanical, electrical, audio and architectural engineers; Physicists; Acoustical consultants.

## Table of Contents

Preface

Acknowledgements

Chapter 1. Introduction and terminology

Part I Introduction

1.2 What is sound?

1.3 Propagation of sound through gas

1.4 Measurable aspects of sound

Part II: Terminology

1.5 General

1.6 Standard International (SI) units

1.7 Pressure and density

1.8 Speed and velocity

1.9 Impedance

1.10 Intensity, energy density, and levels

Notes

Chapter 2. The wave equation and solutions

Part III The Wave Equation

2.2 Derivation of the wave equation

Part IV Solutions of the Wave Equation in One Dimension

2.4 Solution of wave equation for air in a tube terminated by an impedance

2.5 Solution of wave equation for air in a tube filled with absorbent material

2.6 Freely traveling plane wave

2.7 Freely traveling cylindrical wave

2.8 Freely traveling spherical wave

Part V Solutions of the Helmholtz Wave Equation in three Dimensions

2.10 Cylindrical coordinates

2.11 Spherical coordinates

Notes

Chapter 3. Electro-mechano-acoustical circuits

Part VI Mechanical circuits

3.2 Physical and mathematical meanings of circuit elements

3.3 Mechanical elements

Part VII Acoustical circuits

Part VIII Transducers

3.5 Electromechanical transducers

3.6 Mechano-acoustic transducer

3.7 Examples of transducer calculations

Part IX Circuit theorems, energy, and power

3.8 Conversion from admittance-type analogies to impedance-type analogies

3.9 Thévenin’s theorem

3.10 Transducer impedances

Notes

Chapter 4. Acoustic components

4.1 Introduction

Part X Acoustic elements

4.3 Acoustic compliances

4.4 Acoustic resistances

4.5 Cavity with holes on opposite sides—mixed mass-compliance element

4.6 Intermediate-sized tube—mixed mass-resistance element [a (in meters)>0.01/ and a<10/f] [2]

4.7 Perforated sheet—mixed mass-resistance element[a (in meters)>0.01/ and a<10/f] [2]

4.8 Acoustic transformers

Part XI Elementary reflection and radiation of sound

4.9 Reflection of a plane wave from a plane

4.10 Radiation from a pulsating sphere

4.11 Radiation from a monopole point source (simple source)

4.12 Combination of point sources in phase

4.13 Steered beam-forming array of point sources

4.14 Dipole point source (doublet)

4.15 Radiation from an oscillating sphere

Part XII Directivity index

Part XIII Radiation impedances

4.18 Oscillating sphere

4.19 Plane circular piston in infinite baffle

4.20 Plane circular free disk

4.21 Plane circular piston radiating from one side only in free space

Part XIV Viscous and thermal losses

4.23 Wave equation for an infinite lossy tube

Notes

Chapter 5. Microphones

Part XV General characteristics of microphones

5.1 Pressure microphones

5.2 Pressure-gradient microphones

5.3 Combination pressure and pressure-gradient microphones

Part XVI Pressure microphones

5.4 Electromagnetic moving-coil microphone (dynamic microphone)

5.5 Electrostatic microphone (capacitor microphone)

Part XVII Pressure-Gradient microphones

Part XVIII Combination microphones

5.8. Acoustical combination of pressure and pressure-gradient microphones

5.9. Dual-diaphragm combination of pressure and pressure-gradient microphones

Notes

Chapter 6. Electrodynamic loudspeakers

Part XIX Basic theory of electrodynamic loudspeakers

6.2 Construction [2]

6.3 Electro-mechano-acoustical circuit

6.4 Power output

6.5 Thiele–Small parameters [5]

6.6 Sound pressure produced at distance r

6.7 Frequency-response curves

6.8 Electrical input impedance

6.9 Efficiency

6.10 Measurement of Thiele–Small parameters

6.11 Examples of loudspeaker calculations

Part XX Design factors affecting direct-radiator loudspeaker performance

6.12 Magnet size

6.13 Voice-coil design

6.14 Diaphragm behavior

6.15 Directivity characteristics

6.16 Transfer functions and the Laplace transform

6.17 Transient response

6.18 Nonlinearity [14]

References

Chapter 7. Loudspeaker systems

Part XXI Simple enclosures

7.1 Brief summary of common loudspeaker systems

7.2 Unbaffled direct-radiator loudspeaker

7.3 Infinite baffle

7.4 Finite-sized flat baffle

7.5 Open-back cabinets

7.6 Closed-box baffle [1,2]

7.7 Measurement of baffle constants

Part XXII Bass-reflex enclosures

7.9 Acoustical circuit

7.10 Electro-mechano-acoustical circuit

7.11 Radiated sound

7.12 Alignments for predetermined frequency-response shapes

7.13 Port dimensions

7.14 Diaphragm displacement

7.15 Electrical input impedance and evaluation of QL

7.16 Performance

7.17 Construction and adjustment notes

Part XXIII 2-port network for small enclosures

7.18 2-port network for a bass-reflex enclosure

Part XXIV Transmission-line enclosures

Part XXV Multiple drive units

7.21 Dual concentric drive units

References

Chapter 8. Cellphone acoustics

Part XXVI Acoustical transducers for cellphones

8.1 Loudspeaker and microphone

8.2 Circuit diagram for a cellphone loudspeaker

8.3 Design considerations

8.4 Head and torso simulator

8.5 Microphones

Part XXVII Type approval testing of cellphones

8.6 Measurements for type approval

References

Chapter 9. Horn loudspeakers

Part XXVIII Horn drive units

9.2 Electro-mechano-acoustical circuit [1]

9.3 Reference efficiency

9.4 Frequency response

9.5 Examples of horn calculations

Part XXIX Horns

9.7 Possible profiles [2]

9.8 Mouth size

9.9 Infinite parabolic horn [11]

9.10 Infinite conical horn

9.11 Infinite exponential horn

9.12 Infinite hyperbolic horn (hypex) [12]

9.13 Finite horns

9.14 Bends in horns

9.15 Cross-sectional shapes

9.16 Materials

References

Chapter 10. Sound in enclosures

Part XXX Sound Fields in Small, Regularly Shaped Enclosures

10.2 Stationary and standing waves

10.3 Normal modes and normal frequencies

10.4 Steady-state and transient sound pressures

10.5 Examples of rectangular enclosures

Part XXXI Sound in Large Enclosures

10.7 The reverberation equations

10.8 Air absorption

10.9 Total steady sound-pressure level

10.10 Optimum reverberation time

10.11 Sound Strength G

10.12 Early and reverberant sound in concert halls

10.13 Distance for equality of direct and reverberant sound fields

10.14 Sound levels for speech and music

References

Chapter 11. Room design for loudspeaker listening

Part XXXII Home room design

11.2 Listening room acoustics

References

Chapter 12. Radiation and scattering of sound by the boundary value method

Part XXXIII Radiation in cylindrical coordinates

12.2 Radiation from an infinite line source

Part XXXIV Radiation and scattering in spherical coordinates

12.4 Scattering from a rigid sphere by a point source

12.5 Radiation from a point source on a sphere

12.6 Radiation from a spherical cap in a sphere

12.7 Radiation from a rectangular cap in a sphere

12.8 Radiation from a piston in a sphere

12.9 Radiation from an oscillating convex dome in an infinite baffle

12.10 Radiation from an oscillating concave dome in an infinite baffle

References

Chapter 13. Radiation and scattering of sound by the boundary integral method

Part XXXV Boundary integrals and the Green’s function

13.2 The Rayleigh integrals and Green’s function

13.3 The Kirchhoff–Helmholtz boundary integral

13.4 The Green’s function in different coordinate systems

13.5 Boundary integral method case study: Radially pulsating cap in a rigid sphere

13.6 Reflection of a point source from a plane

Part XXXVI Radiation and scattering in cylindrical-spherical coordinates

13.8 Radiation from a resilient circular disk without a baffle [16]

13.9 Radiation from a resilient disk in an infinite baffle [19]

13.10 Radiation from a rigid circular piston in a finite circular open baffle [23, 24]

13.11 Radiation from a rigid circular piston in a finite circular closed baffle [30] (one-sided radiator)

13.12 The Babinet–Bouwkamp principle

Part XXXVII Radiation theorems, radiation in rectangular-spherical coordinates, mutual impedance

13.14 Radiation from an infinitely long oscillating strip in an infinite baffle [36,37]

13.15 The far-field pressure distribution as a spatial frequency spectrum of the source velocity distribution

13.16 The bridge product theorem

13.17 Radiation from a rigid rectangular piston in an infinite baffle [38,39]

13.18 Mutual radiation impedance between rigid circular pistons in an infinite baffle [40]

13.19 Near-field acoustical holography [41]

13.20 Time-reversal

References

Chapter 14. State variable analysis of circuits

14.1 A brief history

14.2 What is state variable analysis?

14.3 Why use state variable analysis?

14.4 What are the restrictions?

14.5 Some basic circuit theory

14.6 Graph theory

14.7 Worked example No. 1: Loudspeaker in an enclosure with a bass-reflex port

14.8 Solution of the worked example using the Faddeev–Leverrier algorithm [10]

14.9 Far-field on-axis pressure

14.10 Worked example No. 2: Loudspeaker in an enclosure with a bass-reflex port using the Norton equivalent source

14.11 Worked example No. 3: Loudspeaker in an enclosure with a bass-reflex port using a transformer and gyrator

14.12 Worked example No. 4: Loudspeaker in an enclosure with a bass-reflex port using controlled sources

14.13 Gyrator comprising two current-controlled voltage sources

References

Appendix I. Frequency-response shapes for loudspeakers [1]

Appendix II. Mathematical formulas [1,2]

Appendix III. Conversion factors

Index

## Details

- No. of pages:
- 720

- Language:
- English

- Copyright:
- © Academic Press 2012

- Published:
- 20th September 2012

- Imprint:
- Academic Press

- eBook ISBN:
- 9780123914866

- Hardcover ISBN:
- 9780123914217

## About the Author

### Leo L. Beranek

Educated at Harvard and Cornell, Dr. Leo Beranek is an acoustical design consultant. Recent work includes several concert halls in Japan. In 1948 he co-founded Bolt, Beranek and Newman (now BBN Technologies) to provide consultation for major auditoriums. BBN also reduced jet noise, developed the ARPANET (internet forerunner), and founded Channel 5 among other achievements. Leo has won numerous awards and fellowships including AES, ASA and ASME gold medals, Presidential National Medal of Science, and ICA Lifetime Achievement in Science Award. He has published 13 books.

### Affiliations and Expertise

Multi award-winning and world-renowned acoustical consultant, author and former professor at Massachusetts Institute of Technology, Cambridge, USA

### Tim Mellow

Tim Mellow was educated at Boundary Oak School and Lancing College before obtaining a B.Sc. in Electrical Engineering and Electronics from the University of Dundee, Scotland, in 1985. A career as a Design engineer at BICC, Marconi, Thorn EMI, Racal, VTech, and Nokia followed. Recently, he co-founded Mellow Acoustics Ltd with Philip Trevelyan to develop high fidelity loudspeakers and amplifiers. Tim takes a keen interest in music and plays the piano. He appreciates technology that brings musical performances to life, especially those which can no longer be heard live.

### Affiliations and Expertise

Director, Mellow Acoustics Ltd., Farnham, UK, www.mellowacoustics.com

## Reviews

*"It contains more recent and additional material, including material that is difficult to find elsewhere.…this highly recommended book is a treasure of information and problem-solving technique for both the novice and expert in the areas of acoustical transducers and fields."**--Journal of the Acoustical Society of America,* September 2013*"Even to those that already own a copy of the 1954 edition, I would recommend acquiring a copy of the revision. It has sufficient new material and it is a pleasure to read to justify that cost. To those starting out in the fields of room acoustics or electro-acoustics or those wishing to extend their existing knowledge, it would be invaluable…very well worth the current list price."***--Acoustics Bulletin, January/February 2013, Vol. 38, No 1, page 51**"…a modern expansion and re-working of Acoustics, the 1954 classic reference…updated throughout and focused on electroacoustics with the needs of a broad range of acoustics engineers and scientists in mind, this new book retains and expands on the detailed acoustical fundamentals included in the original while added practical formulas and simulation methods for practicing professionals."--

**Acoustics Today, October 2012, page 48 Review Magazine.com,**January 9, 2013

"…this reference work could be regarded as the counterpart to the advanced, computational acoustic engineering software such as Comsol now becoming popular, providing much of the grounding for these multi discipline, coupled modelling programs…It is a welcome surprise to see Leo Beranek’s Acoustics so exhaustively revised."--

**Audio Review Magazine.com,**January 9, 2013

"Beranek and Mellow…offer engineering students a textbook on acoustics that can also serve as a reference for experimenters and consultants. They assume knowledge of electric circuit theory."--

**Reference and Research Book News,**December 2012