Architectural Acoustics

943 Pages·2014·25 MB·English

by  Marshall Long (Auth.)

A R C H I T E C T U R A L A C O U S T I C S
Second Edition
by Marshall Long
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Thepreparationofthisbook,whichspannedmorethantenyears,tookplaceinsnatchesoftime–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 andusefulnature. Duringthattimeourtwooldersonsgrewthrough theirteens and
wentofftocollege.Ouryoungestsoncannotrememberatimewhenhisfatherdidnotgoupstairsto
workeveryevening.SoitistomywifeMarilynandoursonsJamie,Scott,andKevinthatIdedicate
thiswork.Iamgratefulforthetime.Ihopeitwasworthit.Andtomyenvironmentallyconscious
children, I hope it isworth thetrees.
PREFACE
Architectural acoustics has been described as something of a black art or perhaps more
charitably,anarcanescience.Whilenotpurelyanart,atits bestitresultsinstructuresthat
are beautiful as well as functional. To produce art, however, the practitioner must first
masterthescienceofthecraftbeforeusefulcreativityispossible,justasapottermustlearn
clay or a painter his oils.
Prior to Sabine’s work at the beginning of the 20th century there was little to go on.
JeanLouisCharlesGarnier(1825–1898),designeroftheParisOperaHouse,expressedhis
frustration at the time:
Igavemyselfpainstomasterthisbizarrescience[ofacoustics]but...nowhere
didIfindapositiveruletoguideme;onthecontrary,nothingbutcontradictory
statements...ImustexplainthatIhaveadoptednoprinciple,thatmyplanhas
beenbasedonnotheory,andthatIleavesuccessorfailuretochancealone...
like an acrobat who closes his eyes and clings to the ropes of an ascending
balloon.
(Garnier,1880)
Since Sabine’s contributions in the early 1900’s, there has been a century of technical
advances.StudiesfundedbytheEPAandHUDinthe1970’swereparticularlyuseful.Work
in Canada, Europe, and Japan has also contributed greatly to the advancement of the field.
When Dick Stern first suggested this work, like Garnier one-hundred years earlier, I
found, at first, few guides. There were many fine books for architects that graphically
illustrated acoustic principles. There were also excellent books on noise and vibration
control,theoreticalacoustics,andothersthatweremorenarrowlyfocusedonconcerthalls,
roomacoustics,andsoundtransmission.Manyofthesewentdeeperintoaspectsofthefield
than there is room for here, and many have been useful in the preparation of this material.
Severalgoodbooksare,unfortunately,outofprintsowherepossibleIhavetriedtoinclude
examples from them.
Thegoalistopresentatechnicaloverviewofarchitecturalacousticsatalevelsuitable
for an upper division undergraduate or an introductory graduate course. The book is
organizedasastep-by-stepprogressionthroughacousticinteractions.Ihavetriedtoinclude
xxviii PREFACE
practical applications where it seemed appropriate. The algorithms are useful not only for
problemsolving,butalsoforunderstandingthefundamentals.Ihaveincludedtreatmentsof
certainareasofaudioengineeringthatareencounteredinreal-lifedesignproblemsthatare
notnormallyfoundintextsonacoustics.Thereisalsosomematerialoncomputermodeling
of loudspeakers and ray tracing. Too often designers accept the conclusions obtained from
software models without knowing the underlying basis of the computations. Above all I
hope the book will provide an intellectual framework for thinking about the subject in a
logical way and be helpful to those working in the field.
FIRST EDITION ACKNOWLEDGMENTS
Many people have contributed directly and indirectly to the preparation of this book.
Various authors have been generous in granting permission to quote figures from their
publicationsand insupplyinghelpfulcommentsand suggestions.Amongthesewere Mark
Alcalde, Don Allen, Michael Barron, Leo Beranek, John Bradley, Jerry Brigham, Bob
Bronsdon, Howard Castrup, Bob Chanaud, John Eargle, Angelo Farina, Jean Francois
Hamet, George Hessler, Russ Johnson, David Klepper, Zyun-iti Maekawa, Nelson
Meacham, Shawn Murphy, Chris Peck, Jens Rindel, Thomas Rossing, Ben Sharp, Chip
Smith, Dick Stern, Will and Regina Thackara, and Floyd Toole. Jean Claude Lesaca and
RichardLentpreparedseveraloftheoriginaldrawings.MysecretaryPatBehnescannedin
many of the quoted drawings and traced over them in AutoCAD before I did the final
versions. She also reviewed and helped correct the various drafts.
The staff of Academic Press including Zvi Ruder, Joel Stein, Shoshanna Grossman,
Angela Dooley, and Simon Crump were helpful in shepherding me through the process.
Dick Stern was present at the beginning and his steady hand and wise counsel were most
appreciated.MywifeMarilynMcAmisandourfamilyshowedgreatpatiencewiththelong
hours required, for which I am very grateful.
AlthoughIhavetriedtopurgethedocumentoferrors,thereareundoubtedlysomethat
I have missed. Errors in earlier printings were pointed out by Michael Haberman at the
University of Texas, Austin, Herb Kuntz, and Bob Celmer, at the University of Hartford.
I hope that those that remain are few and do not cause undue confusion.
SECOND EDITION ACKNOWLEDGMENTS
Since the initial publication many people have made suggestions and contributions for the
next edition. Where possible I have tried to accommodate these but due to time and other
constraints not all could be included.
It is with great sadness that I remember Prof. Richard Stern, my friend and mentor,
who introduced me to acoustics and whose patient guidance led me through my post
graduate studies. Unfortunately his recent, untimely death prevented him from seeing this
resultofhisoriginalidea.Icherishourfriendshipandregularconversationsovertheyears,
and will miss his wisdom and unflagging good humor.
My assistant of twenty-four years, Pat Behne, also died last year. She was a steady
hand and a good helper. Candyce Francis has ably assumed her duties and also acted as a
proofreader and editor.
Contributions from Nick Antonio, Leo Beranek, Bob Bravermaan, Howard Castrup,
Bob Celmer, Elzo Gernhart, Mike Haberman, Jean-Francois Hamet, Russ Johnson, David
Klepper, Kevin Long, Neil Miller, Garry Ritchie, Istvan Ver, and others have helped me
with a number of sections.
GentleproddingbytheElseviereditorialstaff:HayleyGray,LisaJones,andCharlotte
(Charlie) Kent, has kept this edition on track.
Again I regret any lingering errors, which are my sole responsibility.
1
HISTORICAL
INTRODUCTION
Theartsofmusic,drama,andpublicdiscoursehavebothinfluencedandbeeninfluencedby
theacousticsandarchitectureoftheirpresentationenvironments.ItistheorizedthatAfrican
musicanddanceevolvedahighlycomplexrhythmiccharacter,ratherthanthemelodiclineof
earlyEuropeanmusicdue,inpart,toitsbeingperformedoutdoors.WallaceClementSabine
(1868–1919),anearlypioneerinarchitecturalacoustics,feltthatthedevelopmentofatonal
scale in Europe rather than in Africa could be ascribed to the differences in living environ-
ment.InEurope,prehistorictribessoughtshelterin cavesandlaterconstructedincreasingly
large and reverberant temples and churches. Gregorian chant grew out of the acoustical
characteristics of the Gothic cathedrals, and subsequently baroque music was written to
accommodatethechurchesofthetime.Inthelatterhalfofthetwentiethcenturyboththeater
designandperformingartsbecametechnology-driven,particularlywiththeinventionofthe
electronicsystemsthatmadetherecording,film,andtelevisionindustriespossible.Withthe
development of computer programs capable of creating the look and sound of any environ-
ment, a work of art can now not only influence, but also define the space it occupies.
1.1 GREEK AND ROMAN PERIOD (650 BC–AD 400)
Early Cultures
The origin of music, beginning with some primeval song around an ancient campfire, is
impossible to date. There is evidence (Sandars, 1968) to suggest that instruments existed as
earlyas13,000BC.Theunderstandingofmusicandconsonancedatesbackatleastto3000BC,
whentheChinesephilosopherFohiwrotetwomonographsonthesubject(Skudrzyk,1954).
The earliest meeting places were probably no more than conveniently situated open
areas. Their form was whatever existed in nature and their suitability to purpose was
haphazard.Astheneedarosetoaddresslargegroupsforentertainment,military,orpolitical
purposes,it became apparent that concentric circles brought the greatest number of people
closetothecentralarea.Sincethehumanvoiceisdirectionalandintelligibilitydecreasesas
thelistenermovesoffaxis,seatingarrangementsweredefinedbythevocalpolarpatternand
developednaturally,as people soughtlocationsyielding the best audibility.This led to the
construction of earthen or stone steps, arranging the audience into a semicircle in front
2 ARCHITECTURAL ACOUSTICS
of the speaker. The need to improve circulation and permanence evolved in time to the
construction of dedicated amphitheaters on hillsides based on the same vocal patterns.
Greeks
TheGreeks,perhapsduetotheirdemocraticformofgovernment,builtsomeoftheearliest
outdoor amphitheaters. The seating plan was in the shape of a segment of a circle, slightly
(cid:1)
morethan180 ,oftenonthesideofahillfacingthesea.Oneofthebest-preservedexamples
of Greco-Hellenistic theaters is that built at Epidaurus in the northeastern Peloponnese in
330 BC, about the time of Aristotle. A sketch of the plan is shown in Fig. 1.1. The seating
FIGURE 1.1 Ancient Theater, Epidaurus, Greece (Izenour, 1977)
HISTORICAL INTRODUCTION 3
was steeply sloped in these structures, typically 2:1, which afforded good sight lines and
reduced grazing attenuation. Even with these techniques, it is remarkable that this theater,
which seated as many as 17,000 people, actually functioned.
The ancient Greeks were aware of other acoustical principles, at least empirically.
ChariotwheelsinAsiaMinorwereheavy,whereasthoseoftheGreekswerelightsincethey
had to operate on rocky ground. To achieve high speed, the older Asian design was
modified, so that the four-spoke wheels were smaller and the wooden rims were highly
stressed and made to be very flexible. They were so light that if left overnight under
the weight of the chariot they would undergo deformation due to creep. Telemachus, in
Homer’s story of the Odyssey, tipped his vehicle vertically against a wall, while others
removed their wheels in the evening (Gordon, 1978) to prevent warping. The wheels were
mountedonlightcantileveredshaftsandthevehicleitselfwasveryflexible,tohelpisolate
the rider from ground-induced vibrations.
Greekmusicanddancewerehighlydevelopedarts.In250BCatafestivaltoApollo,a
band of several hundred musicians played a five-movement piece celebrating Apollo’s
victory over Python (Rolland et al., 1948). There is strong evidence that the actors wore
masksthatwerefittedoutwithsmallmegaphonestoassistinincreasingthedirectivityofthe
voices.ItisnotsurprisingthattheGreekoratorDemosthenes(c.384–322BC)wasreputed
tohavepracticedhisdictionandvolumealongtheseashorebyplacingpebblesinhismouth.
Intelligibilitywasenhanced,notonlybythesteeplyrakedseating,butalsobythenaturally
low background noise of a preindustrial society.
The chorus in Greek plays served both as a musical ensemble, as we use the term
today,andasagrouptochantthespokenword.Theytoldthestoryandexplainedtheaction,
particularlyintheearlierplaysbyAeschylus(Izenour,1977).Theymayhavehadapractical
as well as a dramatic purpose, which was to increase the loudness of the spoken word
through the use of multiple voices.
Our knowledge of the science of acoustics also dates from the Greeks. Although
therewasageneraluseofgeometryandotherbranchesofmathematicsduringthesecond
andthirdmillenniaBC,therewasnoattempttodeducetheserulesfromfirstprinciplesina
rigorous way (Dimarogonas, 1990). The origination of the scientific method of inquiry
seems to have begun with the Ionian School of natural philosophy, whose leader was
ThalesofMiletus(624–546BC),thefirstofthesevenwisemenofantiquity.Whileheis
betterknownforhisdiscoveryoftheelectricalpropertiesofamber(electroninGreek),he
alsointroducedthelogicalproofforabstractpropositions(Hunt,1978)thatledintimeto
the formal mathematics of geometry, based on the theorem-proof methods of Euclid
(330–270 BC).
Pythagoras of Samos (c. 570–497 BC), a contemporary of Buddha, Confucius, and
Lao-Tse,can beconsidered astudentof theIonianSchool.He traveledtoBabylon,Egypt,
and probably India before establishing his own school at Crotone in southern Italy.
Pythagoras is best known for the theorem that bears his name, although it was discovered
muchearlierinMesopotamia.Heandhisfollowersmadeimportantcontributionstonumber
theory and to the theory of music and harmony. The word theorii appeared in the time of
Pythagoras meaning “the beauty of knowledge” (Herodotus, c. 484–425 BC). Boethius