Preface ...................................................... xiii
Chapter 1 Mathematics for Audio ................................ l
Precision, Accuracy, and Resolution ............................. 3
Simple Numbers .................................................. 3
How to Add Gains and Losses Algebraically ....................... 4
The Factor-Label System ......................................... 4
Basic Physical Terms ............................................ 6
Mathematical Operations ......................................... 7
Complex Number Operations ...................................... 12
Decade Calibration ............................................. 13
Converting Linear Scales to Logarithmic Scales ................. 14
Finding the Renard Series for Fractional Octave Spacing ........ 15
Radians and Steradians ......................................... 16
Calculating Percentages and Ratios ............................. 18
Useful Math Tables ............................................. 21
Angles ......................................................... 22
A Little Trigonometry .......................................... 23
The Origin of the Base of the Natural Logarithm, e ............. 24
The Complex Plane .............................................. 24
Euler 's Theorem ............................................... 25
Examples ....................................................... 25
Phasors ........................................................ 26
Rates of Change ................................................ 28
Chapter 2 Using the Decibel .................................... 31
The Decibel .................................................... 33
The Neper ...................................................... 33
Concepts Underlying the Decibel and Its Use in Sound Systems ... 34
Measuring Electrical Power ..................................... 36
Expressing Power as an Audio Level ............................. 36
Conventional Practice .......................................... 37
The Decibel in Acoustics-LP, LW, and LI ........................ 38
Acoustic Intensity Level (LI), Acoustic Power Level (LW),
and Acoustic Pressure Level (LP) ............................ 39
Inverse Square Law ............................................. 39
Directivity Factor ............................................. 39
Ohm's Law ...................................................... 40
A Decibel Is a Decibel Is a Decibel ............................ 41
Older References ............................................... 42
The Equivalent Level (LEq) in Noise Measurements ............... 43
Combining Decibels ............................................. 43
Combining Voltage .............................................. 45
Using the Log Charts ........................................... 45
Finding the Logarithm of a Number to Any Base .................. 46
Semitone Intervals ............................................. 47
System Gain Changes ............................................ 47
The VU and the VI Instrument ................................... 48
Calculating the Number of Decades in a Frequency Span .......... 50
Deflection of the Eardrum at Various Sound Levels .............. 51
The Phon ....................................................... 51
The Tempered Scale ............................................. 52
Measuring Distortion ........................................... 52
The Acoustical Meaning of Harmonic Distortion .................. 52
Playback Systems in Studios .................................... 54
Decibels and Percentages ....................................... 55
Summary ........................................................ 55
Chapter 3 Interfacing Electrical and Acoustic Systems ......... 57
Alternating Current Circuits ................................... 59
Impedance ...................................................... 61
Electric Power ................................................. 63
Detailed Properties of the LCR Circuit ......................... 66
Filters ........................................................ 67
Impedance Bridge ............................................... 73
Constant Resistance Networks ................................... 74
Impedance Properties of Moving Coil Loudspeakers ............... 75
Network Theorems ............................................... 78
The Technician's Viewpoint ..................................... 81
Impedance Defined .............................................. 81
Handling the Acoustic Input and Output of the System ........... 84
Total Electrical Gain of a System .............................. 88
Interfacing the Electrical Output Power to the Acoustic
Environment ................................................. 89
Gain Structure Revisited ....................................... 90
Conclusion ..................................................... 95
Chapter 4 Loudspeaker Directivity and Coverage ................ 97
Essential Definitions .......................................... 99
Describing Q More Accurately .................................. 104
Relationship Between С/ and Q in an Idealized Case ............ 105
Idealized Loudspeaker Geometry ................................ 106
Summary ....................................................... 111
Chapter 5 The Acoustic Environment ........................... 113
The Acoustic Environment ...................................... 115
Inverse Square Law ............................................ 115
Atmospheric Absorption ........................................ 116
Velocity of Sound ............................................. 116
Temperature-Dependent Velocity ................................ 118
The Effect of Altitude on the Velocity of Sound in Air ........ 118
Typical Wavelengths ........................................... 118
Doppler Effect ................................................ 119
Reflection and Refraction ..................................... 119
Effect of a Space Heater on Flutter Echo ...................... 120
Absorption .................................................... 121
Classifying Sound Fields ...................................... 122
The Acoustic Environment Indoors .............................. 124
Conclusion .................................................... 129
Chapter 6 Audio and Acoustic Measurements ..................... 131
Initial Parameters ............................................ 133
Acoustic Tests of Sound Systems ............................... 133
The ETC Plot .................................................. 135
Site Surveys and Noise Criteria Curves ........................ 142
An Improper Use of Real Time Analysis ......................... 146
Evaluation of Listener Response ............................... 147
Fractional Bandwidth Filter Analyzers ......................... 147
Conclusion .................................................... 151
Chapter 7 Large Room Acoustics ............................... 153
What Is a Large Room? ......................................... 155
Levels Defined: Sound Power Level (LW), Sound Intensity
Level (LI), and Sound Pressure Level (LP) .................. 160
Levels in Enclosed Spaces ..................................... 162
Differentiating Between Reverberant Level and Reverberation
Time ....................................................... 166
Evaluation of Signal-to-Noise Ratio, SNR ...................... 166
Analyzing Reflections and Their Paths ......................... 166
Critical Distance ............................................. 169
Conclusion .................................................... 172
Chapter 8 Small Room Acoustics ............................... 175
Non-Statistical Spaces ........................................ 177
Small Room Acoustical Parameters .............................. 178
Small Room Reverberation Times ................................ 178
Small Room Resonances ......................................... 179
Modes ......................................................... 179
What Is an Eigen Mode? ........................................ 179
Small Room Geometry ........................................... 180
The Initial Signal Delay Gap (ISD) ............................ 180
Reflections ................................................... 183
Reflection Free Zone .......................................... 184
Diffusion ..................................................... 185
Conclusion .................................................... 188
Chapter 9 Designing for Acoustic Gain ........................ 191
Maximum Physical Distance ..................................... 193
Establishing an Acceptable Signal-to-Noise Ratio (SNR) ........ 194
Establishing an EAD ........................................... 194
Needed Acoustic Gain (NAG) .................................... 194
The Number of Open Microphones ................................ 195
The Feedback Stability Margin ................................. 195
Calculating Potential Acoustic Gain ........................... 197
Obtaining ADX Values .......................................... 199
Measuring Acoustic Gain ....................................... 199
Achieving Potential Acoustic Gain ............................. 199
Limiting Parameters in Sound Reinforcement System Design ...... 200
How Much Electrical Power Is Required? ........................ 201
Finding the Required Electrical Power (REP) ................... 201
Summary ....................................................... 203
Chapter 10 Designing for Speech Intelligibility ............... 205
Introduction .................................................. 207
Articulation Losses of Consonants in Speech ................... 208
Maxfield's Equation ........................................... 210
Speech Power and Articulation ................................. 210
Signal-to-Noise Ratio (SNR) ................................... 211
Speech Intelligibility Calculations ........................... 211
Non-Acoustic Articulation Problems ............................ 215
Relationship Between Qmin and D2(majq ......................... 215
High Density Overhead Distribution ............................ 217
%ALCONS Variables ............................................. 217
A Little History-Intelligibility Workshop 1986 ................ 218
Summary ....................................................... 219
Chapter 11 Microphones ....................................... 221
The Microphone as the System Input ............................ 223
Microphone Sensitivity ........................................ 223
Thermal Noise ................................................. 225
Microphone Selection .......................................... 232
Nature of Response and Directional Characteristics ............ 233
Boundary Microphones .......................................... 240
Wireless Microphones .......................................... 244
Microphone Connectors, Cables, and Phantom Power .............. 246
Measurement Microphones ....................................... 248
Microphone Calibrator ......................................... 250
Chapter 12 Loudspeakers and Loudspeaker Arrays ............... 253
Loudspeaker Types ............................................. 255
Radiated Power ................................................ 267
Axial Sound Pressure Level .................................... 271
Efficiency .................................................... 271
Loudspeaker Electrical Impedance .............................. 272
Loudspeaker Directivity Factor ................................ 273
Loudspeaker Sensitivity ....................................... 273
Direct Radiator Example Calculations .......................... 274
Horns and Compression Drivers ................................. 276
Practical Considerations Involving Horns ...................... 282
Horn Compression Drivers ...................................... 284
Crossover Networks ............................................ 286
Loudspeaker Arrays ............................................ 300
Bessel Array .................................................. 306
Line Arrays ................................................... 308
Vented Enclosure Bass Loudspeakers ............................ 320
Chapter 13 Signal Delay and Signal Synchronization ........... 329
Signal Delay .................................................. 331
Synchronization and Alignment of Arrays ....................... 335
Finding Acoustic Origins of Unlike Devices .................... 336
Conclusion .................................................... 338
Chapter 14 Signal Processing ................................. 341
Spectra ....................................................... 343
Analog to Digital Conversion .................................. 364
System Theory ................................................. 368
Digital Systems and the Z Transform ........................... 386
Dynamics Processing ........................................... 395
Chapter 15 Sound System Equalization ......................... 399
System Criteria ............................................... 401
Early Research on Equalization ................................ 401
The Transient Nature of Acoustic Feedback ..................... 402
Introduction of Real-Time Analyzers ........................... 405
Band-Rejection, Bandpass, and Band-Boost Filters .............. 407
TEF Analysis in Equalization .................................. 413
How to Approach Equalization .................................. 413
What Can an Equalizer Equalize? ............................... 416
A Real-Time Regenerative - Response Method of Equalizing
a Sound System ............................................. 417
Equalizing for Playback ....................................... 419
An Improper Use of Real Time Analysis in Monitoring Music
and Speech ................................................. 419
Diaphragmatic Absorbers ....................................... 419
Don't Equalize for Hearing Loss ............................... 420
Proximity Modes ............................................... 420
Checking Microphone Polarity .................................. 420
Loudspeaker Polarity .......................................... 421
Summary ....................................................... 421
Chaapter 16 Putting It All Together .......................... 423
Acoustical Analysis ........................................... 425
Alternative Solutions for a Given Space ....................... 425
Device Interconnections ....................................... 428
Analog Interconnection Circuitry Types ........................ 429
Signal Cables - Analog Audio, Digital Audio, and Video ........ 435
AES3 .......................................................... 443
Computer Control and Communication of Digital Audio ........... 448
Appendix I Symbols and Abbreviations .......................... 451
Appendix II Wiring Practices .................................. 455
Recommended Wiring Practices .................................. 455
Soldering Tools and Equipment ................................. 455
Soldering Materials ........................................... 457
Preparation for Soldering ..................................... 457
Soldering ..................................................... 460
General Assembly Methods ...................................... 465
Rigging Hardware .............................................. 466
Special Assembly of Electrical Parts .......................... 466
Solderless Lugs and Crimping .................................. 468
Identification of Wire Ends ................................... 470
Cabling and Wiring ............................................ 471
Coaxial Wire .................................................. 474
Miscellaneous ................................................. 474
Index ......................................................... 479
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