Harry F. Olson - Elements of Acoustical Engineering

737 Pages·2009·19.24 MB·English

by  Harry F. Olson

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ACOUSTICAL

ENGINEERING

HARRY F. OLSON, PH.D.
Director, Acoustical and Electromechanical

Research Laboratory, RCA Labora,tories,

Princeton, New Jersey

UNVERSIDADTECNOLOGICADECHiLE
BISUOTECA
SEDE PEREZ ROSALES
D. VAN NOSTRAND COMPANY, INC.
PRINCETON, NEW JERSEY

TORONTO LONDON

NEW YORK
1
D. VAN NOSTRAND COMPANY, INC.
120 Alexander St., Princeton, New Jersey (Principal office)
24 West 40 Street, New York 18, New York
D. VAN NOSTRAND COMPANY, LTD.

358, Kensington High Street, London, W.14, England

D. VAN NOSTRAND COMPANY (Canada) LTD.

25 Hollinger Road, Toronto 16, Canada

COPYRIGHT ©1957, BY
D. VAN NOSTRAND COMPANY, INC.

Library of Congress Catalogue Card No. 57-8143

Published simultaneously in Canada by

D. VAN NOSTRAND COMPANY (Canada), LTD.
No reproduction in any form of this book, in whole or in
part (crcept for brief quotation in critical articles or reviews).
may be made without written authorization from the publishers.
This book is based on an earlier work entitled Elements
of Acoustical Engineering, by Harry F. Olson, copy­
right 1940, 1947 by D. Van Nostrand Company, Inc.
First Published May 1957

Reprinted August 1960

PRINTED IN THE UNITED STATES OF AMERICA
PREFACE
The first edition of this book, published in 1940, was the subject matter
of thirty lectures prepared for presentation at Columbia University. It was
an exposition of the fundamental principles used in modern acoustics and
a description of existing acoustical instruments and systems.
Many and varied advances were made in acoustical engineering in the
seven years following the issuance of the first edition. The second edition
of the book, published in 1947, covered the advances in acoustics which
were made in the period between the first and second editions. Since the
publication of the second edition, the developments in acoustics have been
on an ever greater scale than in the period between the first and second edi­
tions. Today, the science of acoustics includes the generation, transmission,
reception, absorption, conversion, detection, reproduction and control of
sound. An important division of acoustical engineering is sound repro­
duction as exemplified by the telephone, radio, phonograph, sound motion
picture and television. These sound reproducing systems are universally
employed in all variations of modern living. The impact of the reproduc­
tion of sound by these systems upon the dissemination of information, art
and culture has been tremendous.
The ultimate useful destination of all informative sound, direct or repro­
duced, is the human ear. In this connection, great strides have been made
in obtaining knowledge on the characteristics and action of the human hear­
ing machine. Measurements play an essential part in the advancement of
any scientific field. Instruments have been developed and standards have
been established for the measurement of the fundamental quantities in
acoustics. The applications of acoustics in the field of music have led to a
better understanding of the stuff of which music is made. This knowledge
has been applied to the development of new musical instruments employing
the latest electronic and acoustical principles.
Accelerated by the requirements in W orId War II, tremendous advances
were made in underwater sound. The developments in underwater sound
have resulted in systems for detection and accurate location of underwater
craft and obstacles over great distances, depth sounders and other acoustic
applications in undersea communication. The industrial applications of
ultrasonics have unfolded a new field in acoustics. Some of the important
ultrasonic developments include the cleaning of machine parts, drilling and
flaw detection. The science of architectural acoustics has advanced to the
point where auditoriums, studios and rooms can be designed to obtain ex­
cellent acoustics under severe artistic conditions. With ever increasing in-
iii
11
IV PREFACE
dustrial expansion comes an increase in noise. Work is now under way
actively to control noise by the use of a variety of acoustic countermeasures.
The preceding brief description of the present status of acoustics shows
that it plays a very important part in our modern civilization. Furthermore,
the fundamentals and applications of the science of acoustics are so well
formulated and substantiated that a large area of the field of acoustics has
attained an engineering status. In preparing new material and in revising
existing material in the third edition, the same principles were followed as in
the first and second editions. Particular efforts have been directed towards
the development of analogies between electrical, mechanical and acoustical
systems because engineers have found that the reduction of a vibrating
system to the analogous electrical network is a valuable tool in the analysis
of vibrating systems. Each chapter has been brought up to date and ampli­
fied. Two new chapters on Complete Sound Reproducing Systems and
.Yfeans for the Communication of Information have been added. As in the
first and second editions most of the illustrations contain several parts so
that a complete theme is depicted in a single illustration.
The author wishes to express his appreciation to Miss Patricia Duman
for her work in typing the manuscript and to his wife Lorene E. Olson
for assistance in compiling and correcting the manuscript.
HARRY F. OLSON
March,1957
CONTENTS
CHAPTER PAGE
1. SOUND WAVES
1.1 INTRODUCTION .. . ....................................•. 1

1.2 SOUND WAVES ... . ...................... •.• . • ..... • .... 2

1.3 ACOUSTICAL WAVE EQUATION ........•... . .............. 4

A. Equation of Continuity ............................ 4

B. Equation of Motion ............................... 5

C. Compressibility of a Gas .......................... 5

D. Condensation .................................... 6

E. D'Alembertian Wave Equation ... .... ............. 6

1.4 PLANE SOUND WAVES.................................. 10

A. Particle Velocity in a Plane Sound Wave........... 10

B. Pressure in a Plane Sound Wave . .. ............... 10

C. Particle Amplitude in a Plane Sound Wave ......... 10

1.5 SPHERICAL SOUND WAVES .............................. 11

A. Pressure in a Spherical Sound Wave ............... 12

B. Particle Velocity in a Spherical Sound Wave....... 13

C. Phase Angle Between the Pressure and Particle Veloc­
ity in a Spherical Sound Wave.................... 13

D. Ratio of the Absolute Magnitudes of the Particle Ve­
locity and the Pressure in a Spherical Sound Wave. .. 14

1.6 STATIONARY SOUND WAVES............................. 14

1.7 SOUND ENERGY DENSITY . . .... ...•. .................... 15

1.8 SOUND INTENSITY ........................•.........••. 15

1.9 DECIBELS (BELs) ...................................... 15

1.10 DOPPLER EFFECT .•..•.•............ .• ....•.. . .•.••... •. 17

1.11 REFRACTION AND DIFFRACTION •..............•... . ...... 17

1.12 ACOUSTIEAL RECIPROCITY THEOREM .. . . ... ........... • ... 24

1.13 ACOUSTICAL PRINCIPLE OF SIMILARITY ................... 26

1.14 LONGITUDINAL WAVES IN A ROD..... .. .................. 26

1.15 TORSIONAL WAVES IN A ROD........ ... . . . . . . . . . . • . . . . .. 28

1.16 CYLINDRICAL SOUND WAVES ............................ 28

II. ACOUSTICAL RADIATING SYSTEMS
2.1 INTRODUCTION .......... . .............. .. .. . ........... 30

2.2 SIMPLE POINT SOURCE ... • .. • ............. • ............ 30

A. Point Source Radiating into an Infinite Medium. Solid

Angle of 471' Steradians ............................ 30

B. Point Source Radiating into a Semi-Jnfinite Medium.

Solid Angle of 271' Steradians ...................... 31

v
vi CONTE:'-JTS
CHAPTER PAGE
C. Point Source Radiating into a Solid Angle of Stera­
71"
dians ............................................ 31

D. Point Source Radiating into a Solid Angle of ?T12 Ste­
radians ......................................... . 31

E. Application of the Simple Source ................. . 31

2.3 DOUBLE SOURCE (DOUBLET SOURCE) ...•••••....•..•....• 32

2.4 SERIES OF POINT SOURCES ••.•..•.••••.•.•••••..•.•••••• 35

2.5 STRAIGHT LINE SOURCE ..•.••.••.••••....••..•.••.•.••. 36

2.6 BEAM TILTING BY PHASE SHIFTING ...•••.•.•..•.•••...• 36

2.7 TAPERED STRAIGHT LINE SOURCE •••••••••••••••••••••••• 37

2.8 NONUNIFORM STRAIGHT LINE SOURCE ••.•••••••..••••••. 38

2.9 END FIRED LINE SOURCE •....••••....•.••....•••••..... 38

2.10 SUPER DIRECTIVITY SOURCE .••••••....•.••••..••••••.... 39

2.11 CURVED LINE SOURCE (ARC OF A CIRCLE) ..••.••...••••.• 40

2.12 CIRCULAR RING SOURCE ..•••••...••.•....••••••..•••••• 43

2.13 PLANE CIRCULAR-PISTON SOURCE .•......••....••.•.....• 43

2.14 NONUNIFORM PLANE CIRCULAR SURFACE SOURCE •.......• 44

2.15 PLANE CIRCULAR-PISTON SOURCE SET IN THE END OF AN

INFINITE PIPE •.•••••.•.••••••.••••••.••.••••...••••••. 45

2.16 PLANE CIRCULAR-PISTON SOURCE IN FREE SPACE •.•••.•.• 45

2.17 PLANE SQUARE SURFACE SOURCE ••....••••....•••••.... , 45

2.18 PLANE RECTANGULAR SURFACE SOURCE .....••••...•.•.... 46

2.19 HORN SOURCE •.•.••..•.•••••••..••••.••..•••.•..•.••.. 47

A. Exponential Horns .............................. . 47

B. Conical Horns .................................. . 48

C. Parabolic Horns ................................. . 48

2.20 CURVED SURFACE SOURCE ..•.•.•••....••.••••.••••.••.•. 50

2.21 CONE SURFACE SOURCE .........•.....•••........•....•. 53

III. MECHANICAL VIBRATING SYSTEMS
3.1 INTRODUCTION .•....••.....•.••••....••........•.•...•. 56

3.2 STRINGS ..•••......••.•....•••.•...•••.•.•.••••.....•• 56

3.3 TRANSVERSE VIBRATION OF BARS ..•••...•.••••...••••.•. 57

A. Bar Clamped at One End .......................... 58

B. Bar Free at Both Ends ........................... 59

C. Bar Clamped at Both Ends ........................ 60

D. Bar Supported at Both Ends ....................... 60

E. Bar Clamped at One End and Supported at the Other 60

F. Bar Supported at One End and Free at the Other. . .. 60

G. Tapered Cantilever Bars .......................... 60

3.4 STRETCHED MEMBRANES .•.••.•...••.•....•.••....••.•.. 61

A. Circular Membrane ..~ . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62

B. Square Membrane ................................ 63

C. Rectangular Membrane ............................ 63

3.5 CIRCULAR PLATES ••••..••••....•.••.•....•.••....••.... 63

A. Circular Clamped Plate ........................... 64

B. Circular Free Plate ............................... 66

C. Circular Plate Supported at the Center ............. 66

D. Circular Plate Supported at the Outside ... . . . . . . . . .. 66
CONTENTS vii
CHAPTER PAGE
3.6 LONGITUDINAL VIBRATION OF BARS 66

3.7 TORSIONAL VIBRATION OF BARS ••••....••..•.........••. 68

3.8 OPEN AND CLOSED PIPES •••...•.........••...•..•..•.•.• 69

IV. DYNAMICAL ANALOGIES
4.1 INTRODUCTION .•.••........•.••..•••.•.•............••. 71

4.2 DEFINITIONS ..•..•...•....••••••••••....••....•.•..•.. 73

4.3 ELEMENTS .............•••••.•.•.••........•....•..... 77

4.4 RESISTANCE •.....•.•..........•...•.•........••••••••. 78

A. Electrical Resistance .............................. 78

B. Mechanical Rectilineal Resistance .................. 78

C. Mechanical Rotational Resistance .................. 78

D. Acoustical Resistance ............................. 79

4.5 INDUCTANCE, MASS, MOMENT OF INERTIA, INERTANCE .•... 79

A. Inductance ....................................... 79

B. Mass ............................................ 79

C. Moment of Inertia ................................ 80

D. Inertance ........................................ 80

4.6 ELECTRICAL CAPACITANCE, RECTILINEAL COMPLIANCE, ROTA­
TIONAL COMPLIANCE, ACOUSTICAL CAPACITANCE •••.••..•• 81

A. Electrical Capacitance ............................ 81

B. Rectilineal Compliance ............................ 81

C. Rotational Compliance ............................ 82

D. Acoustical Capacitance ............................ 82

4.7 REPRESENTATION OF ELECTRICAL, MECHANICAL RECTILINEAL,

MECHANICAL ROTATIONAL AND ACOUSTICAL ELEMENTS..... 83

V. ACOUSTICAL ELEMENTS
5.1 INTRODUCTION •..••.••.•...•.•••....••.....••••.•..•... 88

5.2 ACOUSTICAL RESISTANCE ....•.•.••••..•.•...••••.•••••• 88

5.3 ACOUSTICAL IMPEDANCE OF A TUBE OF SMALL DIAMETER. .• 88

504 ACOUSTICAL IMPEDANCE OF A NARROW SLIT ...•••.••••... 89

5.5 ACOUSTICAL RESISTANCE OF SILK CLOTH •...•.••.•••.•••• 90

5.6 INERTANCE ...........•••.••••••.••..••.•••••.•••••.... 91

5.7 ACOUSTICAL CAPACITANCE ..•........•......•....•.•.... 91

5.8 MECHANICAL AND ACOUSTICAL IMPEDANCE LOAD UPON A

VIBRATING PISTON ..•..••...........••..•........•...•. 92

5.9 MECHANICAL AND ACOUSTICAL IMPEDANCE LOAD UPON A

PULSATING SPHERE •...•••••..•.•••..............••...• 93

5.10 MECHANICAL AND ACOUSTICAL IMPEDANCE LOAD UPON AN

OSCILLATING SPHERE .••••.•....•..••••..••.•...••••••• 94

5.11 MECHANICAL AND ACOUSTICAL IMPEDANCE LOAD UPON A

PULSATING CYLINDER .....•....••..•.••.•••••.•..••.•.• 95

5.12 MECHANICAL AND ACOUSTICAL IMPEDANCE lOAD UPON A

VIBRATING STRIP ••••••••••••..•.•......•....••••••••.. 96

5.13 MECHANICAL AND ACOUSTICAL IMPEDANCE LOAD UPON A

VIBRATING PISTON IN THE END OF AN INFINITE TUBE •••• 97

5.14 MECHANICAL AND ACOUSTICAL IMPEDANCE LOAD UPON A

VIBRATING PISTON IN FREE SPACE ••..••..••.......••••. 99
.,

VJ11 CONTENTS
CHAPTER PAGE
5.15 ACOUSTICAL IMPEDANCE OF A CIRCULAR ORIFICE IN A WALL

OF INFINITESIMAL THICKNESS ••••..........••••.••..... 99

5.16 ACOUSTICAL IMPEDANCE OF AN OPEN PIPE WITH LARGE

FLANGES ••.••.•..••..••••.•...••.........••••••••..... 99

5.17 HORNS •••••••.••.••••••••••••••••...•.•••••••••••••••• 100

5.18 FUNDAMENTAL HORN EQUATION ..•••••••.•........•••.• 100

5.19 INFINITE CYLINDRICAL HORN (INFINITE PIPE) .......•.. 101

5.20 INFINITE PARABOLIC HORN .......•••••••••.•......••••• 102

5.21 INFINITE CONICAL HORN •••..•••.••••••.•••.••••••••••• 102

5.22 INFINITE EXPONENTIAL HORN •.•••..•....•••••••••••... 103

5.23 INFINITE HYPERBOLIC HORN ••••••...••....••.•••••••... 104

5.24 THROAT ACOUSTICAL IMPEDANCE CHARACTERISTIC OF INFI­
NITE PARABOLIC, CONICAL, EXPONENTIAL, HYPERBOLIC AND

CYLINDRICAL HORNS •••.•.........••••••••........••..• 104

5.25 FINITE CYLINDRICAL HORN .......•..•....•........•.•.• 105

5.26 FINITE CONICAL HORN ••..•......••.••.•.•.....•..•••.. 106

5.27 FINITE EXPONENTIAL HORN .•.••.••.•••••••.••••••••••• 108

5.28 THROAT ACOUSTICAL IMPEDANCE CHARACTERISTICS OF FI­
NITE EXPONENTIAL HORNS •••••.........•.•••••••••.... 110

5.29 EXPONENTIAL CONNECTORS .••••.••........•.•••••••••.• 112

5.30 A HORN CONSISTING OF MANIFOLD EXPONENTIAL SECTIONS 114

5.31 CLOSED PIPE WITH A FLANGE .....••.•.•••..........••.• 115

5.32 SOUND TRANSMISSION IN TUBES •..••...•.•........•..•• 116

5.33 TRANSMISSION FROM ONE PIPE TO ANOTHER PIPE OF DIF­
FERENT CROSS-SECTIONAL AREA ......•..•..........•••.•. 117

5.34 TRANSMISSION THROUGH THREE PIPES .....•••••••••.... 119

5.35 TRANSMISSION FROM ONE MEDIUM TO ANOTHER MEDIUM.. 120

5;36 TRANSMISSION THROUGH THREE MEDIA ....•••••.•••..•. 121

5.37 TUBES LINED WITH ABSORBING MATERIAL •••••••••••...• 121

5.38 RESPONSE OF A VIBRATING SYSTEM OF ONE DEGREE OF FREE­
DOM ..•............•.•..........•....•..•...........•• 122

VI. DIRECT RADIATOR LOUDSPEAKERS
6.1 INTRODUCTION ••........•••••••.•.....•...•••.••..••... 124

6.2 SINGLE-COIL, SINGLE-CONE LOUDSPEAKER ....•.••.••..... 125

6.3 MULTIPLE, SINGLE-CONE, SINGLE-COIL LOUDSPEAKER •••... 137

6.4 SINGLE-COIL, DOUBLE-CONE LOUDSPEAKER •..•••.•••••.... 141

6.5 DOUBLE-COIL. SINGLE-CONE LOUDSPEAKER •.........••.•• 143

6.6 DOUBLE-COIL. DOUBLE-CONE LOUDSPEAKER ••.....•..••••. 143

6.7 MECHANICAL NETWORKS FOR CONTROLLING THE HIGH FRE­
QUENCY RESPONSE OF A LOUDSPEAKER ••••••.•...•••.•••• 147

A. Conventional Single-Coil Loudspeaker .. . . . . . . . . . . . .. 147

B. Loudspeaker with a Compliance Shunting the Cone

Mechanical Impedance ............................ 148

C. Loudspeaker with a Compliance Shunting; a Compli­

ance and Mass in Parallel. Connected in Series with

the Cone Mechanical Impedance ................... 148

D. Loudspeaker with a "T" Type Filter Connecting the

Voice Coil Mass and the Cone Mechanical Impedance 148
CONTENTS
ix
CHAPTER PAGE

6.8 LOUDSPEAKER BAFFLES • • •• • •...•... • .•• ••• ... • . ••• • • • •• 149

A. Irregular Baffle ........................ ... ........ 149

B. Large Baffle, Different Resonant Frequencies .. . ... . . 149

C. Low Resonant Frequency, Different Baffle Sizes ... . . 150

D. Different Resonant Frequencies and Different Baffle

Sizes ........................... .... .... . ... . ... . 152

6.9 CABINET LOUDSPEAKERS ..•..•••.•••••.•• • • • • •• ••.•.• .• • 152

A. Low Resonant Frequency, Different Cabinet Sizes .... 153

B. Different Resonant Frequencies and Different Cabinet

Sizes ....................... . .... . . . ..... . ....... 154

C. Effect of the Depth of the Cabinet .. .. ...... . .. . ... 155

6.10 BACK ENCLOSED CABINET LOUDSPEAKER . • • • • ••••• . • ••..•• 155

6.11 COMPOUND DIRECT RADIATOR LOUDSPEAKER •..••• • ..•.•.• 157

6.12 ACOUSTICAL PHASE INVERTER LOUDSPEAKER . •• .•••..•.••. 159

6.13 DRONE CONE PHASE INVERTER .•..•••••••.• ••• •...•••••• 161

6.14 ACOUSTICAL LABYRINTH LOUDSPEAKER .••..•.••••.•.•.... 162

6.15 COMBINATION HORN AND DIRECT RADIATOR LOUDSPEAKER .. 163

6.16 LOUDSPEAKER MECHANISMS FOR SMALL SPACE REQUIRE­
MENTS •...• . ••. • •.. . .... •• •.•..•.• •• .• • •••••••••••••.• 167

6.17 FEEDBACK ApPLIED TO A LOUDSPEAKER • ... • •... • ••••••.• 168

6.18 CABINET CONFIGURATION ... . .. • . • • . •• .•.•. • • • ...••..•.• 169

6.19 LOUDSPEAKER MOUNTING ARRANGEMENT IN THE CABINET

WALL . • .........•• • . • . • . . .. •...• • • • . •...• •• •••..••••• 169

6.20 LOUDSPEAKER LOCATIONS IN TELEVISION RECEIVERS • • .••.. 171

6.21 LOUDSPEAKER LOCATIONS IN PHONOGRAPHS . • ......•.... • 173

6.22 LOUDSPEAKER LOCATIONS IN RADIO RECEIVERS • .. •• • • •. . •• 176

6.23 LOUDSPEAKER LOCATIONS IN COMBINATION INSTRUMENTS .. 177

6.24 CONCENTRATED SOURCE LOUDSPEAKER .•.. • • • .•. • ..•.•.. • . 178

6.25 TRANSIENT RESPONSE ......... •. ... . . . . .. . . .. . . • . . .•.•. 178

6.26 DISTORTION .............•......... . . .•.• ...•.........• . 183

A. Distortion Due to Nonlinear Cone System .......... 183

B. Nonlinear Suspension System .. ... . ................ 184

C. Distortion Characteristics of a Nonlinear Suspension

System ......... . ... ... .. .. . . ................... 186

D. Response Frequency Characteristics of a Direct Radi­
ator Loudspeaker with a Nonlinear Suspension System 188

E. Distortion Due to Inhomogeneity of the Air Gap Flux 188

F. Frequency Modulation Distortion ................... 190

G. Air Nonlinear Distortion . . ....... . ................ 190

6.27 DIAPHRAGMS, SUSPENSIONS, AND VOICE COILS ••.••.••...• 192

6.28 HIGH FREQUENCY SOUND DISTRIBUTOR •• • •• ..•.•....••.. 197

r 6.29 FIELD STRUCTURES . .. .. .•• .••.•. • ••••• • .•.. • .•.••...•• 198

6.30 ELECTROSTATIC LOUDSPEAKER . . •. .•..•. •••. .. •. .. • •..... 205

6.31 SOUND POWER EMITTED BY A LOUDSPEAKER • ...•.. . . . •••. 210

6.32 LOUDSPEAKER DIRECTIVITY INDEX ..•.• •• .••.. • .•.••.•• •• 211

VII. HORN LOUDSPEAKERS
7.1 INTRODUCTION •••.•. ••• ••• • • • • • . • • . . . . . • . . • • • • • . . . • • •• 212

7.2 EFFICIENCY . • ... • . • ... •• ••••.••. . •. . .. •• •.•• ••••• •.••• 212