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Architectural acoustics


A R C H I T E C T U R A L

A C O U S T I C S


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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 Long
from the
Applications of Modern Acoustics Series
Edited by Moises Levy and Richard Stern

Amsterdam • Boston • Heidelberg • London • New York • Oxford
Paris • San Diego San Francisco • Singapore • Sydney • Tokyo



Elsevier Academic Press
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Cover image: The cover shows Grosser Musikvereinssaal in Vienna, Austria. The photograph
was provided by AKG Acoustics, U.S., and is reproduced with permission.

Library of Congress Cataloging-in-Publication Data
Application submitted
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 13: 978-0-12-455551-8
ISBN 10: 0-12-455551-9
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Web site at www.books.elsevier.com

Printed in the United States of America
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1


The preparation of this book, which spanned more than ten years, took place in snatches of
time – a few hours every evening and several more each weekend. It was time that was taken
from commitments to family, home maintenance projects, teaching, and other activities forgone, of
a pleasurable and useful nature. During that time our two older sons grew through their teens and
went off to college. Our youngest son cannot remember a time when his father did not go upstairs to
work every evening. So it is to my wife Marilyn and our sons Jamie, Scott, and Kevin that I dedicate
this work. I am grateful for the time. I hope it was worth it. And to my environmentally conscious
children, I hope it is worth the trees.


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CONTENTS
PREFACE
ACKNOWLEDGMENTS

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1

HISTORICAL INTRODUCTION
1.1 GREEK AND ROMAN PERIOD (650 bc–ad 400)
Early Cultures
Greeks
Romans
Vitruvius Pollio
1.2 EARLY CHRISTIAN PERIOD (ad 400–800)
Rome and the West
Eastern Roman Empire
1.3 ROMANESQUE PERIOD (800–1100)
1.4 GOTHIC PERIOD (1100–1400)
Gothic Cathedrals
1.5 RENAISSANCE PERIOD (1400–1600)
Renaissance Churches
Renaissance Theaters
1.6 BAROQUE PERIOD (1600–1750)
Baroque Churches
Baroque Theaters
Italian Opera Houses
Baroque Music
Protestant Music
1.7 ORIGINS OF SOUND THEORY
1.8 CLASSICAL PERIOD (1750–1825)
1.9 ROMANTIC PERIOD (1825–1900)
Shoebox Halls
1.10 BEGINNINGS OF MODERN ACOUSTICS
1.11 TWENTIETH CENTURY

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FUNDAMENTALS OF ACOUSTICS
2.1 FREQUENCY AND WAVELENGTH
Frequency
Wavelength

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Architectural Acoustics
Frequency Spectrum
Filters
SIMPLE HARMONIC MOTION
Vector Representation
The Complex Plane
The Complex Exponential
Radial Frequency
Changes in Phase
SUPERPOSITION OF WAVES
Linear Superposition
Beats
SOUND WAVES
Pressure Fluctuations
Sound Generation
Wavelength of Sound
Velocity of Sound
Waves in Other Materials
ACOUSTICAL PROPERTIES
Impedance
Intensity
Energy Density
LEVELS
Sound Levels — Decibels
Sound Pressure Level
Sound Power Level
SOURCE CHARACTERIZATION
Point Sources and Spherical Spreading
Sensitivity
Directionality, Directivity, and Directivity Index
Line Sources
Planar Sources

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HUMAN PERCEPTION AND REACTION TO SOUND
3.1 HUMAN HEARING MECHANISMS
Physiology of the Ear
3.2 PITCH
Critical Bands
Consonance and Dissonance
Tone Scales
Pitch
3.3 LOUDNESS
Comparative Loudness
Loudness Levels
Relative Loudness

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2.2

2.3

2.4

2.5

2.6

2.7

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Contents

3.4

3.5

3.6
3.7

4

Electrical Weighting Networks
Noise Criteria Curves (NC and RC)
Just Noticeable Difference
Environmental Impact
INTELLIGIBILITY
Masking
Speech Intelligibility
Speech Interference Level
Articulation Index
ALCONS
Privacy
ANNOYANCE
Noisiness
Time Averaging – Leq
Twenty-Four Hour Metrics – Ldn and CNEL
Annoyance
HEALTH AND SAFETY
Hearing Loss
OTHER EFFECTS
Precedence Effect and the Perception of Echoes
Perception of Direction
Binaural Sound

ACOUSTIC MEASUREMENTS AND NOISE METRICS
4.1 MICROPHONES
Frequency Response
Directional Microphones
Sound Field Considerations
4.2 SOUND LEVEL METERS
Meter Calibration
Meter Ballistics
Meter Range
Detectors
Filters
4.3 FIELD MEASUREMENTS
Background Noise
Time-Varying Sources
Diurnal (24-Hour) Traffic Measurements
4.4 BROADBAND NOISE METRICS
Bandwidth Corrections
Duration Corrections
Variability Corrections
Sound Exposure Levels
Single Event Noise Exposure Level

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4.5

4.6

BAND LIMITED NOISE METRICS
Preferred Noise Criterion (PNC) Curves
Balanced Noise Criterion (NCB) Curves (Beranek, 1989)
Other Octave-Band Metrics
Octave-Band Calculations
Third-Octave Bandwidth Metrics
Aircraft Noise Rating Systems
Narrow-Band Analysis
SPECIALIZED MEASUREMENT TECHNIQUES
Time-Delay Spectrometry
Energy-Time Curves
Sound Intensity Measurements
Modulation Transfer Function and RASTI
Speech Transmission Index
RASTI

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ENVIRONMENTAL NOISE
5.1 NOISE CHARACTERIZATION
Fixed Sources
Moving Sources
Partial Line Sources
5.2 BARRIERS
Point Source Barriers
Practical Barrier Constraints
Line Source Barriers
Barrier Materials
Roadway Barriers
5.3 ENVIRONMENTAL EFFECTS
Air Attenuation
Attenuation Due to Ground Cover
Grazing Attenuation
Focusing and Refraction Effects
Combined Effects
Doppler Effect
5.4 TRAFFIC NOISE MODELING
Soft Ground Approximation
Geometrical Mean Distance
Barrier Calculations
Roadway Computer Modeling
Traffic Noise Spectra
5.5 RAILROAD NOISE
5.6 AIRCRAFT NOISE

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6

WAVE ACOUSTICS
6.1 RESONANCE
Simple Oscillators

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Contents

6.2

6.3

6.4

6.5

7

Air Spring Oscillators
Helmholtz Resonators
Neckless Helmholtz Resonators
WAVE EQUATION
One-Dimensional Wave Equation
Three-Dimensional Wave Equation
SIMPLE SOURCES
Monopole Sources
Doublet Sources
Dipole Sources and Noise Cancellation
Arrays of Simple Sources
Continuous Line Arrays
Curved Arrays
Phased Arrays
Source Alignment and Comb Filtering
Comb Filtering and Critical Bands
COHERENT PLANAR SOURCES
Piston in a Baffle
Coverage Angle and Directivity
Loudspeaker Arrays and the Product Theorem
Rectangular Pistons
Force on a Piston in a Baffle
LOUDSPEAKERS
Cone Loudspeakers
Horn Loudspeakers
Constant-Directivity Horns
Cabinet Arrays
Baffled Low-Frequency Systems

SOUND AND SOLID SURFACES
7.1 PERFECTLY REFLECTING INFINITE SURFACES
Incoherent Reflections
Coherent Reflections—Normal Incidence
Coherent Reflections—Oblique Incidence
Coherent Reflections—Random Incidence
Coherent Reflections—Random Incidence, Finite Bandwidth
7.2 REFLECTIONS FROM FINITE OBJECTS
Scattering from Finite Planes
Panel Arrays
Bragg Imaging
Scattering from Curved Surfaces
Combined Effects
Whispering Galleries
7.3 ABSORPTION
Reflection and Transmission Coefficients

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7.4

7.5

7.6

8

Impedance Tube Measurements
Oblique Incidence Reflections—Finite Impedance
Calculated Diffuse Field Absorption Coefficients
Measurement of Diffuse Field Absorption Coefficients
Noise Reduction Coefficient (NRC)
Absorption Data
Layering Absorptive Materials
ABSORPTION MECHANISMS
Porous Absorbers
Spaced Porous Absorbers—Normal Incidence, Finite Impedance
Porous Absorbers with Internal Losses—Normal Incidence
Empirical Formulas for the Impedance of Porous Materials
Thick Porous Materials with an Air Cavity Backing
Practical Considerations in Porous Absorbers
Screened Porous Absorbers
ABSORPTION BY NONPOROUS ABSORBERS
Unbacked Panel Absorbers
Air Backed Panel Absorbers
Perforated Panel Absorbers
Perforated Metal Grilles
Air Backed Perforated Panels
ABSORPTION BY RESONANT ABSORBERS
Helmholtz Resonator Absorbers
Mass-Air-Mass Resonators
Quarter-Wave Resonators
Absorption by Seats
Quadratic-Residue Diffusers

SOUND IN ENCLOSED SPACES
8.1 STANDING WAVES IN PIPES AND TUBES
Resonances in Closed Tubes
Standing Waves in Closed Tubes
Standing Waves in Open Tubes
Combined Open and Closed Tubes
8.2 SOUND PROPAGATION IN DUCTS
Rectangular Ducts
Changes in Duct Area
Expansion Chambers and Mufflers
8.3 SOUND IN ROOMS
Normal Modes in Rectangular Rooms
Preferred Room Dimensions
8.4 DIFFUSE-FIELD MODEL OF ROOMS
Schroeder Frequency
Mean Free Path

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Contents

8.5

9

Decay Rate of Sound in a Room
Sabine Reverberation Time
Norris Eyring Reverberation Time
Derivation of the Sabine Equation
Millington Sette Equation
Highly Absorptive Rooms
Air Attenuation in Rooms
Laboratory Measurement of the Absorption Coefficient
REVERBERANT FIELD EFFECTS
Energy Density and Intensity
Semireverberant Fields
Room Effect
Radiation from Large Sources
Departure from Diffuse Field Behavior
Reverberant Falloff in Long Narrow Rooms
Reverberant Energy Balance in Long Narrow Rooms
Fine Structure of the Sound Decay

SOUND TRANSMISSION LOSS
9.1 TRANSMISSION LOSS
Sound Transmission Between Reverberant Spaces
Measurement of the Transmission Loss
Sound Transmission Class (STC)
Field Sound Transmission Class (FSTC)
Noise Reduction and Noise Isolation Class (NIC)
9.2 SINGLE PANEL TRANSMISSION LOSS THEORY
Free Single Panels
Mass Law
Large Panels—Bending and Shear
Thin Panels—Bending Waves and the Coincidence Effect
Thick Panels
Finite Panels—Resonance and Stiffness Considerations
Design of Single Panels
Spot Laminating
9.3 DOUBLE PANEL TRANSMISSION LOSS THEORY
Free Double Panels
Cavity Insulation
Double-Panel Design Techniques
9.4 TRIPLE-PANEL TRANSMISSION LOSS THEORY
Free Triple Panels
Comparison of Double and Triple-Panel Partitions
9.5 STRUCTURAL CONNECTIONS
Point and Line Connections
Transmission Loss of Apertures

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10

SOUND TRANSMISSION IN BUILDINGS
10.1 DIFFUSE FIELD SOUND TRANSMISSION
Reverberant Source Room
Sound Propagation through Multiple Partitions
Composite Transmission Loss with Leaks
Transmission into Absorptive Spaces
Transmission through Large Openings
Noise Transmission Calculations
10.2 STC RATINGS OF VARIOUS WALL TYPES
Laboratory vs Field Measurements
Single Wood Stud Partitions
Single Metal Stud Partitions
Resilient Channel
Staggered-Stud Construction
Double-Stud Construction
High-Mass Constructions
High Transmission Loss Constructions
10.3 DIRECT FIELD SOUND TRANSMISSION
Direct Field Sources
Direct Field Transmission Loss
Free Field—Normal Incidence
Free Field—Non-normal Incidence
Line Source—Exposed Surface Parallel to It
Self Shielding and G Factor Corrections
10.4 EXTERIOR TO INTERIOR NOISE TRANSMISSION
Exterior Walls
Windows
Doors
Electrical Boxes
Aircraft Noise Isolation
Traffic Noise Isolation

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11

VIBRATION AND VIBRATION ISOLATION
11.1 SIMPLE HARMONIC MOTION
Units of Vibration
11.2 SINGLE DEGREE OF FREEDOM SYSTEMS
Free Oscillators
Damped Oscillators
Damping Properties of Materials
Driven Oscillators and Resonance
Vibration Isolation
Isolation of Sensitive Equipment
Summary of the Principles of Isolation

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Contents

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11.3 VIBRATION ISOLATORS
Isolation Pads (Type W, WSW)
Neoprene Mounts (Type N, ND)
Steel Springs (Type V, O, OR)
Hanger Isolators (Type HN, HS, HSN)
Air Mounts (AS)
Support Frames (Type IS, CI, R)
Isolator Selection
11.4 SUPPORT OF VIBRATING EQUIPMENT
Structural Support
Inertial Bases
Earthquake Restraints
Pipe Isolation
Electrical Connections
Duct Isolation
11.5 TWO DEGREE OF FREEDOM SYSTEMS
Two Undamped Oscillators
Two Damped Oscillators
11.6 FLOOR VIBRATIONS
Sensitivity to Steady Floor Vibrations
Sensitivity to Transient Floor Vibrations
Vibrational Response to an Impulsive Force
Response to an Arbitrary Force
Response to a Step Function
Vibrational Response of a Floor to Footfall
Control of Floor Vibrations

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NOISE TRANSMISSION IN FLOOR SYSTEMS
12.1 TYPES OF NOISE TRANSMISSION
Airborne Noise Isolation
Footfall
Structural Deflection
Squeak
12.2 AIRBORNE NOISE TRANSMISSION
Concrete Floor Slabs
Concrete on Metal Pans
Wood Floor Construction
Resiliently Supported Ceilings
Floating Floors
12.3 FOOTFALL NOISE
Impact Insulation Class—IIC
Impact Insulation Class Ratings
Vibrationally Induced Noise
Mechanical Impedance of a Spring Mass System

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Architectural Acoustics
Driving Point Impedance
Power Transmitted through a Plate
Impact Generated Noise
Improvement Due to Soft Surfaces
Improvement Due to Locally Reacting Floating Floors
Improvement Due to Resonantly Reacting Floating Floors
12.4 STRUCTURAL DEFLECTION
Floor Deflection
Low-Frequency Tests
Structural Isolation of Floors
12.5 FLOOR SQUEAK
Shiners
Uneven Joists
Hangers
Nailing

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NOISE IN MECHANICAL SYSTEMS
13.1 MECHANICAL SYSTEMS
Manufacturer Supplied Data
Airborne Calculations
13.2 NOISE GENERATED BY HVAC EQUIPMENT
Refrigeration Equipment
Cooling Towers and Evaporative Condensers
Air Cooled Condensers
Pumps
13.3 NOISE GENERATION IN FANS
Fans
Fan Coil Units and Heat Pumps
VAV Units and Mixing Boxes
13.4 NOISE GENERATION IN DUCTS
Flow Noise in Straight Ducts
Noise Generated by Transitions
Air Generated Noise in Junctions and Turns
Air Generated Noise in Dampers
Air Noise Generated by Elbows with Turning Vanes
Grilles, Diffusers, and Integral Dampers
13.5 NOISE FROM OTHER MECHANICAL EQUIPMENT
Air Compressors
Transformers
Reciprocating Engines and Emergency Generators

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14

SOUND ATTENUATION IN DUCTS
14.1 SOUND PROPAGATION THROUGH DUCTS
Theory of Propagation in Ducts with Losses

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Contents

14.2

14.3

14.4

14.5
14.6

15

Attenuation in Unlined Rectangular Ducts
Attenuation in Unlined Circular Ducts
Attenuation in Lined Rectangular Ducts
Attenuation of Lined Circular Ducts
Flexible and Fiberglass Ductwork
End Effect in Ducts
Split Losses
Elbows
SOUND PROPAGATION THROUGH PLENUMS
Plenum Attenuation—Low-Frequency Case
Plenum Attenuation—High Frequency Case
SILENCERS
Dynamic Insertion Loss
Self Noise
Back Pressure
BREAKOUT
Transmission Theory
Transmission Loss of Rectangular Ducts
Transmission Loss of Round Ducts
Transmission Loss of Flat Oval Ducts
BREAK-IN
Theoretical Approach
CONTROL OF DUCT BORNE NOISE
Duct Borne Calculations

DESIGN AND CONSTRUCTION OF MULTIFAMILY DWELLINGS
15.1 CODES AND STANDARDS
Sound Transmission Class—STC
Reasonable Expectation of the Buyer
Impact Insulation Class—IIC
Property Line Ordinances
Exterior to Interior Noise Standards
15.2 PARTY WALL CONSTRUCTION
General Principles
Party Walls
Structural Floor Connections
Flanking Paths
Electrical Boxes
Wall Penetrations
Holes
15.3 PARTY FLOOR-CEILING SEPARATIONS
Airborne Noise Isolation
Structural Stiffness
Structural Decoupling

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16

Architectural Acoustics
Floor Squeak
Floor Coverings
15.4 PLUMBING AND PIPING NOISE
Supply Pipe
Water Hammer
Waste Stacks
Tubs, Toilets, and Showers
Pump and Piping Vibrations
Fluid Pulsations
15.5 MECHANICAL EQUIPMENT
Split Systems
Packaged Units
15.6 APPLIANCES AND OTHER SOURCES OF NOISE
Stairways
Appliances
Jacuzzis
Trash Chutes
Elevator Shafts and Equipment Rooms
Garage Doors

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DESIGN AND CONSTRUCTION OF OFFICE BUILDINGS
16.1 SPEECH PRIVACY IN OPEN OFFICES
Privacy
Privacy Calculations
Articulation Weighted Ratings
Speech Reduction Rating and Privacy
Source Control
Partial Height Panels
Absorptive and Reflective Surfaces
Open-Plan Ceilings
Masking Sound
Degrees of Privacy
16.2 SPEECH PRIVACY IN CLOSED OFFICES
Private Offices
Full-Height Walls
Plenum Flanking
Duct Flanking
Exterior Curtain Walls
Divisible Rooms
Masking in Closed Offices
16.3 MECHANICAL EQUIPMENT
System Layout
Mechanical Equipment Rooms
Roof-Mounted Air Handlers

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Contents
Fan Coil and Heat Pump Units
Emergency Generators

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DESIGN OF ROOMS FOR SPEECH
17.1 GENERAL ACOUSTICAL REQUIREMENTS
General Considerations
Adequate Loudness
Floor Slope
Sound Distribution
Reverberation
Signal-to-Noise Ratio
Acoustical Defects
17.2 SPEECH INTELLIGIBILITY
Speech-Intelligibility Tests
Energy Buildup in a Room
Room Impulse Response
Speech-Intelligibility Metrics—Articulation Index (AI)
Articulation Loss of Consonants (ALcons )
Speech Transmission Index (STI)
Signal-to-Noise Ratios (Ct and Ut )
Weighted Signal-to-Noise Ratios (Cαt and Utα )
A-Weighted Signal-to-Noise Ratio
Comparison of Speech-Intelligibility Metrics
17.3 DESIGN OF ROOMS FOR SPEECH INTELLIGIBILITY
The Cocktail Party Effect
Restaurant Design
Conference Rooms
Classrooms
Small Lecture Halls
Large Lecture Halls
17.4 MOTION PICTURE THEATERS
Reverberation Times

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18

SOUND REINFORCEMENT SYSTEMS
18.1 LOUDSPEAKER SYSTEMS
Loudspeaker Types
Loudness
Bandwidth
Low-Frequency Loudspeakers
Loudspeaker Systems
Distributed Loudspeaker Systems
Single Clusters
Multiple Clusters
Other Configurations

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Architectural Acoustics
18.2 SOUND SYSTEM DESIGN
Coverage
Intelligibility
Amplifier Power Handling
Electrical Power Requirements
Heat Load
Time Coincidence
Imaging
Feedback
Multiple Open Microphones
Equalization
Architectural Sensitivity
18.3 CHARACTERIZATION OF TRANSDUCERS
Microphone Characterization
Loudspeaker Characterization
The Calculation of the On-axis Directivity
18.4 COMPUTER MODELING OF SOUND SYSTEMS
Coordinate Systems and Transformation Matrices
Determination of the Loudspeaker Coordinate System
Directivity Angles in Loudspeaker Coordinates
Multiple Loudspeaker Contributions

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DESIGN OF ROOMS FOR MUSIC
19.1 GENERAL CONSIDERATIONS
The Language of Music
The Influence of Recording
Concert Halls
Opera Houses
19.2 GENERAL DESIGN PARAMETERS
The Listening Environment
Hall Size
Hall Shape
Hall Volume
Surface Materials
Balconies and Overhangs
Seating
Platforms
Orchestra Shells
Pits
19.3 QUANTIFIABLE ACOUSTICAL ATTRIBUTES
Studies of Subjective Preference
Modeling Subjective Preferences
Early Reflections, Intimacy, and Clarity
Liveness, Reverberation Time, and Early Decay Time

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Contents

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Envelopment, Lateral Reflections, and Interaural Cross-correlation
Loudness, Gmid , Volume, and Volume per Seat
Warmth and Bass Response
Diffusion, SDI
Ensemble, Blend, and Platform Acoustics
19.4 CONCERT HALLS
Grosser Musikvereinssaal, Vienna, Austria
Boston Symphony Hall, Boston, MA, USA
Concertgebouw, Amsterdam, Netherlands
Philharmonie Hall, Berlin, Germany
Eugene McDermott Concert Hall in the Morton H. Meyerson Symphony
Center, Dallas, TX, USA
19.5 OPERA HALLS
Theatro Colon, Buenos Aires, Argentina
Theatro Alla Scala, Milan, Italy

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DESIGN OF MULTIPURPOSE AUDITORIA AND SANCTUARIES
20.1 GENERAL DESIGN CONSIDERATIONS
Program
Room Shape
Seating
Room Volume
Reverberation Time
Absorption
Balconies
Ceiling Design
Audio Visual Considerations
20.2 DESIGN OF SPECIFIC ROOM TYPES
Small Auditoria
Mid-Sized Theaters
Large Auditoria
Traditional Churches
Large Churches
Synagogues
20.3 SPECIALIZED DESIGN PROBLEMS
Wall and Ceiling Design
Shell Design
Platform Risers
Pit Design
Diffusion
Variable Absorption
Variable Volume
Coupled Chambers
Sound System Integration
Electronic Augmentation

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xxii

Architectural Acoustics

21

DESIGN OF STUDIOS AND LISTENING ROOMS
21.1 SOUND RECORDING
Early Sound Recording
Recording Process
Recording Formats
21.2 PRINCIPLES OF ROOM DESIGN
Standing Waves
Bass Control
Audible Reflections
Flutter Echo
Reverberation
Diffusion
Imaging
Noise Control
Noise Isolation
Flanking
HVAC Noise
21.3 ROOMS FOR LISTENING
Music Practice Rooms
Listening Rooms
Screening Rooms
Video Post Production
21.4 ROOMS FOR RECORDING
Home Studios
Sound Stages
Scoring Stages
Recording Studios
Foley and ADR
21.5 ROOMS FOR MIXING
Dubbing Stages
Control Rooms
21.6 DESIGN DETAILS IN STUDIOS
Noise Isolation
Symmetry
Loudspeaker Placement
Bass Control
Studio Window Design
Diffusion

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22

ACOUSTIC MODELING, RAY TRACING, AND AURALIZATION
22.1 ACOUSTIC MODELING
Testing Scale Models
Spark Testing
Ray Casting

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Contents

22.2

22.3

22.4

22.5

Image Source Method
Hybrid Models
RAY TRACING
Rays
Surfaces and Intersections
Planar Surfaces
Ray-Plane Intersection
Ray-Polygon Intersections
Ray-Sphere Intersection
Ray-Cylinder Intersection
Ray-Quadric Intersections
Ray-Cone Intersection
Ray-Paraboloid Intersection
SPECULAR REFLECTION OF RAYS FROM SURFACES
Specular Reflections
Specular Reflections with Absorption
Specular Absorption by Seats
DIFFUSE REFLECTION OF RAYS FROM SURFACES
Measurement of the Scattering Coefficient
Diffuse Reflections
Multiple Reflections
Edge Effects
Hybrid Models and the Reverberant Tail
AURALIZATION
Convolution
Directional Sound Perception
Directional Reproduction

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REFERENCES

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INDEX

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