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A R C H I T E C T U R A L A C O U S T I C S
by Marshall Longfrom theApplications of Modern Acoustics SeriesEdited bv Moises Levy and Richard Stern
FLSPVTFRACADEMIC Amsterdam • Boston • Heidelberg • London • New York • Oxford
PRESS Paris • San Diego San Francisco • Singapore • Sydney • Tokyo
CONTENTS
Preface xxvAcknowledgement xxvii
1 HISTORICAL INTRODUCTION 11.1 Greek and Roman Period (650 BC - AD 400) 1
Early Cultures 1Greeks 2Romans 4Vitruvius Pollio 5
1.2 Early Christian Period (AD 400-800) 7Rome and the West 7Eastern Roman Empire 8
1.3 Romanesque Period (800-1100) 101.4 Gothic Period (1100-1400) 11
Gothic Cathedrals 11
1.5 Renaissance Period (1400-1600) 14Renaissance Churches 14Renaissance Theaters 15
1.6 Baroque Period (1600-1750) 16Baroque Churches 16Baroque Theaters 17Italian Opera Houses 17Baroque Music 18Protestant Music 19
1.7 Origins of Sound Theory 201.8 Classical Period (1750-1825) 211.9 Romantic Period (1825-1900) 23
Shoebox Halls 261.10 Beginnings of Modern Acoustics 30
1.11 Twentieth Century 33
2 FUNDAMENTALS OF ACOUSTICS 372.1 Frequency and Wavelength 37
Frequency 37Wavelength 37
viii ARCHITECTURAL ACOUSTICS
Frequency Spectrum 40Filters 40
2.2 Simple Harmonic Motion 40Vector Representation 43The Complex Plane 43The Complex Exponential 44Radial Frequency 45Changes in Phase 46
2.3 Superposition of Waves 46Linear Superposition 46Beats 48
2.4 Sound Waves 50Pressure Fluctuations 50Sound Generation 50Wavelength of Sound 51Velocity of Sound 51Waves in Other Materials 55
2.5 Acoustical Properties 55Impedance 55Intensity 57Energy Density 59
2.6 Levels 59Sound Levels — Decibels 59Sound Pressure Level 61Sound Power Level 62
2.7 Source Characterization 65Point Sources and Spherical Spreading 65Sensitivity 67Directionality, Directivity and Directivity Index 67Line Sources 70Planar Sources 71
Human Perception and Reaction to Sound 733.1 Human Hearing Mechanisms 73
Physiology of the Ear 73
3.2 Pitch 77Critical Bands 77Consonance and Dissonance 78Tone Scales 79Pitch 81
3.3 Loudness 81Comparative Loudness 81Loudness Levels 82Relative Loudness 83
CONTENTS ix
Electrical Weighting Networks 84
Noise Criteria Curves (NC and RC) 85
Just Noticeable Difference 88
Environmental Impact 90
3.4 Intelligibility 91
Masking 91
Speech Intelligibility 93
Speech Interference Level 94
Articulation Index 95
ALCONS 9 6
Privacy 97
3.5 Annoyance 98
Noisiness 98
Time Averaging - L e q 100
Twenty - Four Hour Metrics - L ^ and CNEL 101
Annoyance 101
3.6 Health and Safety 105
Hearing Loss 105
3.7 Other Effects 107
Precedence Effect and the Perception of Echoes 107
Perception of Direction 110
Binaural Sound 113
ACOUSTIC MEASUREMENTS AND NOISE METRICS 115
4.1 Microphones 115
Frequency Response 118
Directional Microphones 118
Sound Field Considerations 120
4.2 Sound Level Meters 121
Meter Calibration 122
Meter Ballistics 124
Meter Range 125
Detectors 125
Filters 125
4.3 Field Measurements 125
Background Noise 127
Time-Varying Sources 129
Diurnal (24-Hour) Traffic Measurements 130
4.4 Broadband Noise Metrics 132
Bandwidth Corrections 133
Duration Corrections 135
Variability Corrections 13 5
Sound Exposure Levels 136
Single Event Noise Exposure Level 137
x ARCHITECTURAL ACOUSTICS
4.5 Band Limited Noise Metrics 137Preferred Noise Criterion (PNC) Curves 138Balanced Noise Criterion (NCB) Curves (Beranek, 1989) 139Other Octave-Band Metrics 140Octave-Band Calculations 141Third-Octave Bandwidth Metrics 142Aircraft Noise Rating Systems 142Narrow-Band Analysis 143
4.6 Specialized Measurement Techniques 145Time-Delay Spectrometry 145Energy-Time Curves 146Sound Intensity Measurements 148Modulation Transfer Function and RASTI 149Speech Transmission Index 151RASTI 154
157157157158159161161162163165166167168175175177181182183184186186188189189194
199199199
5
6
ENVIRONMENTAL NOISE5.1
5.2
5.3
5.4
5.55.6
Noise Characterization
Fixed SourcesMoving Sources
Partial Line Sources
BarriersPoint Source Barriers
Practical Barrier ConstraintsLine Source BarriersBarrier Materials
Roadway Barriers
Environmental EffectsAir AttenuationAttenuation Due to Ground Cover
Grazing AttenuationFocusing and Refraction Effects
Combined Effects
Doppler EffectTraffic Noise ModelingSoft Ground Approximation
Geometrical Mean Distance
Barrier CalculationsRoadway Computer Modeling
Traffic Noise SpectraRailroad Noise
Aircraft Noise
Wave Acoustics6.1 Resonance
Simple Oscillators
CONTENTS xi
Air Spring Oscillators 201Helmholtz Resonators 203Neckless Helmholtz Resonators 203
6.2 Wave Equation 205One-Dimensional Wave Equation 205Three-Dimensional Wave Equation 207
6.3 Simple Sources 208Monopole Sources 208Doublet Sources 208Dipole Sources and Noise Cancellation 210Arrays of Simple Sources 211Continuous Line Arrays 213Curved Arrays 214Phased Arrays 217Source Alignment and Comb Filtering 217Comb Filtering and Critical Bands 218
6.4 Coherent Planar Sources 219Piston in a Baffle 219Coverage Angle and Directivity 222Loudspeaker Arrays and the Product Theorem 222Rectangular Pistons 224Force on a Piston in a Baffle 225
6.5 Loudspeakers 226Cone Loudspeakers 226Horn Loudspeakers 228Constant-Directivity Horns 230Cabinet Arrays 233Baffled Low-Frequency Systems 233
7 SOUND AND SOLID SURFACES 2357.1 Perfectly Reflecting Infinite Surfaces 235
Incoherent Reflections 235Coherent Reflections—Normal Incidence 236Coherent Reflections—Oblique Incidence 238Coherent Reflections—Random Incidence 239Coherent Reflections—Random Incidence, Finite Bandwidth 239
7.2 Reflections from Finite Objects 240Scattering from Finite Planes 240Panel Arrays 244Bragg Imaging 245Scattering from Curved Surfaces 247Combined Effects 248Whispering Galleries 249
7.3 Absorption 249Reflection and Transmission Coefficients 249
xii ARCHITECTURAL ACOUSTICS
Impedance Tube Measurements 250
Oblique Incidence Reflections—Finite Impedance 251Calculated Diffuse Field Absorption Coefficients 254Measurement of Diffuse Field Absorption Coefficients 255
Noise Reduction Coefficient (NRC) 255Absorption Data 255
Layering Absorptive Materials 256
7.4 Absorption Mechanisms 261Porous Absorbers 261Spaced Porous Absorbers—Normal Incidence, Finite Impedance 263Porous Absorbers with Internal Losses—Normal Incidence 265Empirical Formulas for the Impedance of Porous Materials 266Thick Porous Materials with an Air Cavity Backing 267Practical Considerations in Porous Absorbers 268Screened Porous Absorbers 269
7.5 Absorption by Nonporous Absorbers 271Unbacked Panel Absorbers 271Air Backed Panel Absorbers 272Perforated Panel Absorbers 274Perforated Metal Grilles 276Air Backed Perforated Panels 276
7.6 Absorption by Resonant Absorbers 277Helmholtz Resonator Absorbers 277Mass-Air-Mass Resonators 278Quarter-Wave Resonators 279Absorption by Seats 282Quadratic-Residue Diffusers 282
SOUND IN ENCLOSED SPACES 2858.1 Standing Waves in Pipes and Tubes 285
Resonances in Closed Tubes 285Standing Waves in Closed Tubes 286Standing Waves in Open Tubes 287Combined Open and Closed Tubes 288
8.2 Sound Propagation in Ducts 289Rectangular Ducts 289Changes in Duct Area 291Expansion Chambers and Mufflers 292
8.3 Sound in Rooms 293Normal Modes in Rectangular Rooms 294Preferred Room Dimensions 297
8.4 Diffuse-field Model of Rooms 298Schroeder Frequency 298Mean Free Path 299
CONTENTS xiii
Decay Rate of Sound in a Room 299Sabine Reverberation Time 300Norris Eyring Reverberation Time 301Derivation of the Sabine Equation 301Millington Sette Equation 302Highly Absorptive Rooms 302Air Attenuation in Rooms 302Laboratory Measurement of the Absorption Coefficient 303
8.5 Reverberant Field Effects 304Energy Density and Intensity 304Semireverberant Fields 305Room Effect 305Radiation from Large Sources 307Departure from Diffuse Field Behavior 307Reverberant Falloff in Long Narrow Rooms 309Reverberant Energy Balance in Long Narrow Rooms 310
Fine Structure of the Sound Decay 312
SOUND TRANSMISSION LOSS 3159.1 Transmission Loss 315
Sound Transmission between Reverberant Spaces 315Measurement of the Transmission Loss 316Sound Transmission Class (STC) 317Field Sound Transmission Class (FSTC) 318Noise Reduction and Noise Isolation Class (NIC) 318
9.2 Single Panel Transmission Loss Theory 319Free Single Panels 319Mass Law 320Large Panels—Bending and Shear 322Thin Panels—Bending Waves and the Coincidence Effect 323Thick Panels 326Finite Panels—Resonance and Stiffness Considerations 330Design of Single Panels 330Spot Laminating 332
9.3 Double Panel Transmission Loss Theory 333Free Double Panels 333Cavity Insulation 335Double-Panel Design Techniques 338
9.4 Triple-panel Transmission Loss Theory 342Free Triple Panels 342Comparison of Double and Triple-Panel Partitions 343
9.5 Structural Connections 345Point and Line Connections 345Transmission Loss of Apertures 347
xvi ARCHITECTURAL ACOUSTICS
Driving Point Impedance 432Power Transmitted through a Plate 433
Impact Generated Noise 434Improvement Due to Soft Surfaces 437Improvement Due to Locally Reacting Floating Floors 440
Improvement Due to Resonantly Reacting Floating Floors 440
12.4 Structural Deflection 441Floor Deflection 441Low-Frequency Tests 444Structural Isolation of Floors 446
12.5 Floor Squeak 447Shiners 447Uneven Joists 449Hangers 449Nailing 449
13 NOISE IN MECHANICAL SYSTEMS 45113.1 Mechanical Systems 451
Manufacturer Supplied Data 453Airborne Calculations 453
13.2 Noise Generated by HVAC Equipment 453Refrigeration Equipment 454Cooling Towers and Evaporative Condensers 454Air Cooled Condensers 456Pumps 456
13.3 Noise Generation in Fans 457Fans 458Fan Coil Units and Heat Pumps 462VAV Units and Mixing Boxes 464
13.4 Noise Generation in Ducts 466Flow Noise in Straight Ducts 466Noise Generated by Transitions 469Air Generated Noise in Junctions and Turns 469Air Generated Noise in Dampers 472Air Noise Generated by Elbows with Turning Vanes 473Grilles, Diffusers, and Integral Dampers 474
13.5 Noise from other Mechanical Equipment 476Air Compressors 476Transformers 477Reciprocating Engines and Emergency Generators 478
14 SOUND ATTENUATION IN DUCTS 48114.1 Sound Propagation Through Ducts 481
Theory of Propagation in Ducts with Losses 481
CONTENTS xvii
Attenuation in Unlined Rectangular Ducts 486Attenuation in Unlined Circular Ducts 486Attenuation in Lined Rectangular Ducts 487Attenuation of Lined Circular Ducts 487Flexible and Fiberglass Ductwork 488End Effect in Ducts 488Split Losses 490Elbows 490
14.2 Sound Propagation Through Plenums 492Plenum Attenuation—Low-Frequency Case 492Plenum Attenuation—High Frequency Case 493
14.3 Silencers 495Dynamic Insertion Loss 496Self Noise 496Back Pressure 497
14.4 Breakout 497Transmission Theory 498Transmission Loss of Rectangular Ducts 500Transmission Loss of Round Ducts 501Transmission Loss of Flat Oval Ducts 502
14.5 Break-in 503Theoretical Approach 503
14.6 Control Of Duct Borne Noise 504Duct Borne Calculations 504
15 DESIGN AND CONSTRUCTION OF MULTIFAMILY DWELLINGS 50915.1 Codes and Standards 510
Sound Transmission Class—STC 510Reasonable Expectation of the Buyer 512Impact Insulation Class—IIC 513Property Line Ordinances 514Exterior to Interior Noise Standards 515
15.2 Party Wall Construction 515General Principles 515Party Walls 516Structural Floor Connections 518Flanking Paths 519Electrical Boxes 519Wall Penetrations 520Holes 521
15.3 Party Floor-Ceiling Separations 522Airborne Noise Isolation 522Structural Stiffness 523Structural Decoupling 524
xviii ARCHITECTURAL ACOUSTICS
Floor Squeak 527Floor Coverings 528
15.4 Plumbing and Piping Noise 529Supply Pipe 529Water Hammer 534Waste Stacks 535Tubs, Toilets, and Showers 535Pump and Piping Vibrations 536Fluid Pulsations 537
15.5 Mechanical Equipment 537Split Systems 537Packaged Units 538
15.6 Appliances and other Sources of Noise 540Stairways 540Appliances 540Jacuzzis 540Trash Chutes 541Elevator Shafts and Equipment Rooms 541Garage Doors 541
16 DESIGN AND CONSTRUCTION OF OFFICE BUILDINGS 54316.1 Speech Privacy in Open Offices 543
Privacy 543Privacy Calculations 544Articulation Weighted Ratings 548Speech Reduction Rating and Privacy 550Source Control 551Partial Height Panels 553Absorptive and Reflective Surfaces 556Open-Plan Ceilings 558Masking Sound 560Degrees of Privacy 562
16.2 Speech Privacy in Closed Offices 563Private Offices 563Full-Height Walls 563Plenum Flanking 564Duct Flanking 567Exterior Curtain Walls 567Divisible Rooms 569Masking in Closed Offices 569
16.3 Mechanical Equipment 571System Layout 571Mechanical Equipment Rooms 572Roof-Mounted Air Handlers 574
CONTENTS xix
Fan Coil and Heat Pump Units 576Emergency Generators 577
17 DESIGN OF ROOMS FOR SPEECH 57917.1 General Acoustical Requirements 579
General Considerations 579Adequate Loudness 579Floor Slope 580Sound Distribution 583Reverberation 585Signal-to-Noise Ratio 587Acoustical Defects 587
17.2 Speech Intelligibility 588Speech-Intelligibility Tests 588Energy Buildup in a Room 589Room Impulse Response 590Speech-Intelligibility Metrics—Articulation Index (AI) 592Articulation Loss of Consonants (ALcons) 593Speech Transmission Index (STI) 596Signal-to-Noise Ratios (Ct and Ut) 599Weighted Signal-to-Noise Ratios (C? and U?) 600A-Weighted Signal-to-Noise Ratio 602Comparison of Speech-Intelligibility Metrics 602
17.3 Design of Rooms for Speech Intelligibility 603The Cocktail Party Effect 603Restaurant Design 604Conference Rooms 606Classrooms 606Small Lecture Halls 607Large Lecture Halls 607
17.4 Motion Picture Theaters 609Reverberation Times 610
18 Sound Reinforcement Systems 61118.1 LOUDSPEAKER SYSTEMS 611
Loudspeaker Types 611Loudness 612Bandwidth 614Low-Frequency Loudspeakers 615Loudspeaker Systems 615Distributed Loudspeaker Systems 615
Single Clusters 617Multiple Clusters 617Other Configurations 618
xx ARCHITECTURAL ACOUSTICS
18.2 Sound System Design 618Coverage 619Intelligibility 619Amplifier Power Handling 621Electrical Power Requirements 622Heat Load 623Time Coincidence 624Imaging 625Feedback 627Multiple Open Microphones 631Equalization 631Architectural Sensitivity 634
18.3 Characterization of Transducers 635Microphone Characterization 635Loudspeaker Characterization 638The Calculation of the On-axis Directivity 642
18.4 Computer Modeling of Sound Systems 644Coordinate Systems and Transformation Matrices 644Determination of the Loudspeaker Coordinate System 646Directivity Angles in Loudspeaker Coordinates 649Multiple Loudspeaker Contributions 650
19 DESIGN OF ROOMS FOR MUSIC 65319.1 General Considerations 653
The Language of Music 653The Influence of Recording 653Concert Halls 655
Opera Houses 65619.2 General Design Parameters 657
The Listening Environment 657Hall Size 658Hall Shape 658Hall Volume 658Surface Materials 659Balconies and Overhangs 660Seating 661Platforms 663
Orchestra Shells 664
Pits 66519.3 Quantifiable Acoustical Attributes 666
Studies of Subjective Preference 667Modeling Subjective Preferences 670Early Reflections, Intimacy, and Clarity 671Liveness, Reverberation Time, and Early Decay Time 674
CONTENTS xxi
Envelopment, Lateral Reflections, and Interaural Cross-correlation 675Loudness, Gmid, Volume, and Volume per Seat 678Warmth and Bass Response 678Diffusion, SDI 681Ensemble, Blend, and Platform Acoustics 681
19.4 Concert Halls 682Grosser Musikvereinssaal, Vienna, Austria 682Boston Symphony Hall, Boston, MA, USA 684Concertgebouw, Amsterdam, Netherlands 685Philharmonie Hall, Berlin, Germany 687Eugene McDermott Concert Hall in the Morton H. Meyerson SymphonyCenter, Dallas, TX, USA 688
19.5 Opera Halls 691Theatro Colon, Buenos Aires, Argentina 691Theatro Alia Scala, Milan, Italy 692
20 Design of Multipurpose Auditoria and Sanctuaries 69720.1 General Design Considerations 697
Program 698Room Shape 698Seating 700Room Volume 701Reverberation Time 701Absorption 701Balconies 702Ceiling Design 703Audio Visual Considerations 705
20.2 Design of Specific Room Types 706Small Auditoria 706Mid-Sized Theaters 710Large Auditoria 711Traditional Churches 712Large Churches 715Synagogues 719
20.3 Specialized Design Problems 720Wall and Ceiling Design 720Shell Design 720Platform Risers 724Pit Design 725Diffusion 725Variable Absorption 728Variable Volume 729Coupled Chambers 730Sound System Integration 734Electronic Augmentation 736
xxii ARCHITECTURAL ACOUSTICS
21 DESIGN OF STUDIOS AND LISTENING ROOMS21.1 Sound Recording
Early Sound Recording
Recording ProcessRecording Formats
21.2 Principles of Room DesignStanding Waves
Bass ControlAudible Reflections
Flutter EchoReverberationDiffusion
Imaging
Noise ControlNoise IsolationFlanking
HVAC Noise21.3 Rooms for Listening
Music Practice RoomsListening Rooms
Screening Rooms
Video Post Production21.4 Rooms for Recording
Home Studios
Sound StagesScoring Stages
Recording StudiosFoley and ADR
21.5 Rooms for MixingDubbing Stages
Control Rooms21.6 Design Details in Studios
Noise Isolation
Symmetry
Loudspeaker PlacementBass Control
Studio Window DesignDiffusion
22 ACOUSTIC MODELING, RAY TRACING, AND AURALIZATION22.1 Acoustic Modeling
Testing Scale ModelsSpark Testing
Ray Casting
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CONTENTS xxiii
Image Source Method 786Hybrid Models 786
22.2 Ray Tracing 787Rays 787Surfaces and Intersections 788Planar Surfaces 789Ray Plane Intersection 789Ray-Polygon Intersections 790Ray-Sphere Intersection 791Ray-Cylinder Intersection 792Ray-Quadric Intersections 793Ray-Cone Intersection 794Ray-Paraboloid Intersection 794
22.3 Specular Reflection of Rays from Surfaces 795Specular Reflections 795Specular Reflections with Absorption 796Specular Absorption by Seats 797
22.4 Diffuse Reflection of Rays from Surfaces 798Measurement of the Scattering Coefficient 799Diffuse Reflections 799Multiple Reflections 801Edge Effects 802Hybrid Models and the Reverberant Tail 803
22.5 Auralization 804Convolution 804Directional Sound Perception 807Directional Reproduction 808
REFERENCES 813
INDEX 829