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

741741741

742744

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781781782

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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