HandbookofSoundStudioConstruction

RoomsforRecordingandListening

F.AltonEverestKenC.Pohlmann

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DedicatedtothememoryofF.AltonEverest

AbouttheAuthorsF.AltonEverest (deceased)wasa leadingexpertandauthority in thefieldofacoustics.Hewasanemeritusmemberof theAcousticalSocietyofAmerica,a lifememberof theInstituteofElectricalandElectronicsEngineers,andlifefellowoftheSocietyofMotionPictureandTelevisionEngineers.Hewas cofounder and director of the Science FilmProduction division of theMoody Institute ofScience, and was also section chief of the Subsea Sound Research section of the University ofCalifornia.KenC.Pohlmanniswellknownasanaudioeducator,consultant,andauthor.HewasdirectoroftheMusicEngineeringTechnology program, and is professor emeritus at theUniversity ofMiami inCoralGables.HeisafellowoftheAudioEngineeringSociety,consultantformanyaudiocompaniesand carmakers, and consultant in patent-infringement litigation.He is authorof numerous articlesandbooksincludingPrinciplesofDigitalAudio(McGraw-Hill),nowinitssixthedition,andcoauthorofMasterHandbookofAcoustics(McGraw-Hill),nowinitsfifthedition.

CreditsforCoverPhotographsFRONTLEFTStudio:GuilfordSound,Guilford,Vermont.StudioDesign:FrancisManzella,FMDesignLtd.Photographer:GeorgeRoosPhotography.FRONTCENTERStudio:DallasAudio Post,Dallas, Texas. StudioDesign: FrancisManzella, FMDesign Ltd. Photographer:GlennKatzPhotoDesign.FRONTRIGHTStudio:StudioatThePalms,LasVegas,Nevada.StudioDesign:FrancisManzella,FMDesignLtd.Photographer:DaveKingPhotography.BACK LEFT Home Theater: Michael Chow. Acoustic Design: Waterland Designs. Electronic Design: Murray Kunis, Future Home.Photography:RandyCordero.BACKRIGHTDetailfromFrontLeftphoto.

Contents

Preface

1IntroductiontoRoomAcousticsImportanceofRoomAcousticsSoundOutdoorsSoundIndoorsDirectSoundandIndirectSoundSmall-RoomAcousticsRoomIsolationRoomTreatmentHumanPerceptionofSoundAcousticalDesignAcousticalDesignProcedureANoteontheRoomDesignExamples

2Sound-ReflectingMaterialsSoundWavelengthandReflectionsReflectionandRoomGeometryCalculatingReflectionsThePrecedenceEffectReverberation-TimeEquationReverberation-TimeMeasurements

3Sound-AbsorbingMaterialsandStructuresAbsorptionGuidelinesRoomGeometryandTreatmentSoundAbsorptionCoefficientNoiseReductionCoefficientStandardMountingTerminologyPorousAbsorbersGlassFiberMineralWoolDensityofAbsorbentSpacebehindAbsorbentandThicknessofAbsorbentTheAreaEffectCeiling-MountedAbsorptionAcousticalTileGlass-FiberAbsorberPanelsBassTrapsPanelAbsorbersPolycylindricalAbsorbersAbsorptionofDrywallConstruction

HelmholtzResonatorsPerforatedPanelAbsorbersSlatAbsorbersMultipurposeAbsorbersPrefabricatedSoundAbsorbersOpen-CellFoamsSonexAreGlassFibersDangeroustoHealth?

4DiffusingMaterialsandStructuresSoundDiffusionLow-FrequencyDiffusionRoleofDiffusersinRoomDesignDiffusionbyGeometricShapesThePolycylindricalDiffuserReflectionPhaseGratingsSpecularReflectionTheoryReflectionPhaseGratingTheoryTheQuadratic-ResidueDiffuserThePrimitive-RootDiffuserFractalsTheDiffusionCoefficientCommerciallyAvailableReflectionPhaseGratingDiffusersTheQRD-734Quadratic-ResidueDiffuserTheFormedffusorTheFRGOmniffusorTheFlutterFreeDiffuser

5RoomModesandRoomGeometryRoomCutoffFrequencyResonancesinTubesResonancesinRoomsAxial,Tangential,andObliqueModesRoomModeEquationGraphingRoomModesExperimentswithModesModalDistributioninNonrectangularRoomsModalWidthandSpacingOptimalRoomProportionsPracticalLimitations

6SoundIsolationandSiteSelectionSoundIsolationTransmissionLossInsulationversusIsolationSoundTransmissionClass(STC)RoomNoiseReduction

TheMassLawTheCoincidenceEffectLead-LoadedVinylSoundLeaksandFlankingOtherPotentialProblemsChecklistofBuildingMaterialsLocatingaStudioFloorPlanConsiderationsLocatingaSpacewithinaFrameStructureLocatingaSpacewithinaConcreteStructure

7WallConstructionandPerformanceWallsasEffectiveNoiseBarriersTheMassLawandWallDesignWallDesignsforEfficientInsulationImprovinganExistingWallFlankingSoundGypsumBoardWallsasSoundBarriersMasonryWallsasSoundBarriersWeakLinksSummaryofSTCRatings

8Floor/CeilingConstructionandPerformanceDataontheFootfallNoiseProblemFloor/CeilingStructuresandTheirIICPerformanceFrameBuildingsResilientHangersFloatingFloorsAttenuationbyConcreteLayersPlywoodWebversusSolidWoodJoists

9WindowandDoorConstructionandPerformanceTheObservationWindowTheSingle-PaneWindowTheDouble-PaneWindowAcousticalHolesAcousticalHoles:CoincidenceResonanceAcousticalHoles:StandingWavesintheCavityEffectofGlassMassandSpacingEffectofDissimilarPanesEffectofLaminatedGlassEffectofPlasticPanesEffectofSlantingtheGlassEffectofaThirdPaneEffectofCavityAbsorbentThermalGlassWeakWindows(orDoors)inaStrongWall

ExampleofanOptimizedDouble-PaneWindowConstructionofanObservationWindowProprietaryObservationWindowsStudioDoorsSound-LockCorridor

10NoiseControlinHVACSystemsSelectionofNoiseCriteriaFanNoiseHVACMachineryNoisePlumbingNoiseAirVelocityandAerodynamicNoiseHVACNoiseAttenuatorsLinedDuctLinedDuctwithBlockedLine-of-SightLinedDuctandLengthEffectPlenumChambersLinedElbowsDiffusersReactiveExpansionChamberTunedStubSilencersActiveNoiseCancellationNaturalSystemAttenuationDuctworkDesign

11RoomPerformanceandEvaluationSound-LevelMetersSpectrumAnalyzersTheNoiseSurveyEnvironmentalNoiseAssessmentsMeasurementandTestingStandardsRecommendedPracticesNoiseCriteriaContoursRelatingNoiseMeasurementstoConstructionEvaluationofRoomAcoustics:ObjectiveMethodsEvaluationofRoomAcoustics:SubjectiveMethodsArticulationIndexandtheSpokenWordRoomReflectionsandPsychoacousticsRoomModeling

12RecordingStudioforPopMusicDesignCriteriaFloorPlanWallSectionsSectionD-DSectionE-E

SectionsF-FandG-GDrumBoothVocalBoothStudioTreatment:NorthWallStudioTreatment:SouthWallStudioTreatment:EastWallStudioTreatment:WestWallStudioTreatment:FloorandCeilingSound-LockCorridorReverberationTimeBaffles

13RecordingStudioforClassicalMusicDesignCriteriaReverberationTimeDiffusionintheRecordingStudioStudioDesignAcousticalTreatmentWallPanelAbsorbersCeilingTreatmentReverberation-TimeCalculationsAirAbsorptionInitialTime-DelayGapCommentsonDesign

14VoiceStudioDesignCriteria:IsolationDesignCriteria:RoomSizeDesignCriteria:RoomShapeAxial-ModeStudyofSelectedRoomAcousticalTreatmentEarlyReflectionsTheSoftOptionandHardOptionDiffusionModeControlStudioDesign:SoftOptionStudioDesign:HardOptionReverberation-TimeCalculationsReverberationTime:SoftOptionReverberationTime:HardOptionSoundFieldResponseCommentsonDesign

15ControlRoomEarlyReflectionsCombingofEarlyReflectionsExamplesofCombFiltering

Reflection-FreeZoneLoudspeakerMountingTwo-ShellControlRoomsDesignCriteriaDesignExampleA:ControlRoomwithRectangularWallsDesignExampleB:Double-ShellControlRoomwithSplayedWallsDesignExampleC:Single-ShellControlRoomwithSplayedWalls

16AnnounceBoothDesignCriteria:IsolationTheSmall-RoomProblemDesignExampleA:TraditionalAnnounceBoothDesignExampleA:AxialModesDesignExampleA:ReverberationTimeDesignExampleB:AnnounceBoothwithTubeTrapsDesignExampleB:TechronTEFMeasurementsDesignExampleB:ReverberationTimeDesignExampleC:AnnounceBoothwithDiffusersDesignExampleC:ReverberationTimeDesignExampleC:EvaluationComparisonofDesignExamplesA,B,andC

17Audio/Video/FilmWorkroomAudioFidelityandNear-FieldMonitoringAxial-ModeConsiderationsMonitorLoudspeakersandEarlySoundLateSoundReverberationTimeWorkbenchMixingEngineer sWorkstationLightingBackgroundNoiseLevelVideoDisplay

18TeleconferenceRoomDesignCriteriaShapeandSizeoftheRoomFloorPlanCeilingPlanElevationViewsReverberationTime

19HomeStudioHomeAcoustics:ModesHomeAcoustics:ReverberationHomeAcoustics:NoiseControlStudioDesignBudget

StudioTreatmentStudioDesign:InitialTreatmentStudioDesign:IntermediateTreatmentStudioDesign:ComprehensiveTreatmentRecordingintheStudioGarageStudio

20HomeListeningandMediaRoomLow-FrequencyResponseModesinTypicalRoomsModeSpacingLow-FrequencyPeaksandNullsEffectsofRoomSizeLoudspeakerPositioningAcousticalTreatmentfortheListeningRoomIdentificationofEarlyReflectionsPsychoacousticalEffectsofReflectionsExamplesofListeningRoomTreatmentListeningRoomDesign:InitialTreatmentListeningRoomDesign:IntermediateTreatmentListeningRoomDesign:ComprehensiveTreatmentBackgroundNoise

21HomeTheaterLocatingtheHomeTheaterHomeTheaterPlanEarlyReflectionsandTheirEffectsControllingEarlyReflectionsOtherTreatmentDetailsTheListeningEnvironmentReverberationTime

Appendix:SelectedAbsorptionCoefficients

Glossary

ReferencesandResources

Index

Preface

Imagineacoldwintermorning30,000yearsago.Youemerge froma lowhutandbeginwalking.Theairisstillandallissilentexceptforthesoundofthesnowcrunchingunderyourfeet.Youpassthroughavalleywhereyou shout aloud, and thevalleyanswersyou in a seriesof faint calls.Andwhenyoupassacertainrockface,youknowthatittooreturnsthesoundofyourvoicebutonlywithonequickresponse.

Thenyouarriveatacavemouth.Youlighta torchfromtheembersyoucarryinapouchandenterthecave.Immediatelyyoufeeltherelativewarmthasyoudescendintotheearth.Inthedarknesslitonlybyyoursmallflame,foremostisthesensationofbeingenclosed;insteadoftheopensoundsoftheoutdoors,inthisplacesoundisstrangelycontainedandenveloping.Intightpassages,evensoftsoundsseemlouder,whileinthevastopencaverns,soundrepeatsendlessly.Youknowthatyouareinaspecialplace.Youstopbeforeasmoothcavewallandsetdownyourtorch.Youwithdrawpigmentsfromyourpouchand,singingsoftlyintheflickeringlight,youbegintopaint.

Fromourearliestdays,wehavemarveledattheinvisiblepresenceofthesoundsallaroundus.Whethertheyweresoundsofanimals,soundsofnature,soundsofmusicalinstruments,orourownspeaking and singingvoices,we intuitively understood the importance of creating and listening tosounds.Moreover, long before science quantified the phenomenon, we have known that sound isaffected by its environment. The difference between sound in the open air and sound in a cavernpowerfullydefinestheuniquenatureofthoseplaces.

From these early observations, our curiosity surrounding sound evolved into a science. TheGreek philosphers Pythagoras and Aristotle contemplated acoustics (our English word is derivedfromaGreekword)asbothamusicalandscientificphenomenon.KnowledgeofacousticsallowedtheGreekstobuildopen-airauditoriums,andtheRomanarchitectandengineerVitruviusdescribedtheacousticalpropertiesoftheaters.Galileo,Newton,Helmholtz,Rayleigh,andmanyothersbuiltthefoundationsofourmodernunderstandingofacoustics.Placesofworship,concerthalls,auditoriums,recordingstudios,televisionstudios,movietheaters,hometheaters,hospitals,libraries,museums,artgalleries,airports,andevenhotelsneartheairportmustbedesignedandconstructedwithacousticsinmind.

All of which brings us to this book,Handbook of Sound Studio Construction. The previousedition was authored by F. Alton Everest. He was an acknowledged authority in acoustics and aleadingauthorinthefield.Duringhislongtenure,hismanyarticlesandbooksinformedthedesignand construction of countless building projects and inspired a generation of students to choose acareerinacoustics.Hispassing,atage95,markedtheendofanera.

WhileteachingacousticsattheUniversityofMiamiformanyyears,IoftenusedbooksbyMr.Everest as required or recommended texts. I often contemplatedwriting an acoustics book ofmyown, butwaswell aware that excellent books such as those byMr. Everest already dominated themarket.Iwasthusenthusiastic,andhumbled,whenMcGraw-Hillaskedmetoprepareneweditionsofhisbooks.

Thisbook,aboveall,strivestoprovidepracticalinformationonthedesignandconstructionofsound-sensitive spaces. The emphasis is on practicalmaterial thatwill directly assist the reader inplanningaproject,commercialorpersonal,bigor small, for the recordingorplaybackof sound.The opening chapters provide background descriptions of acoustical phenomena, but even these

theoreticaldiscussions relate topractical applicationsof the theory.Theclosingchapterspresent aseriesofdesignexamplesrangingfromasimpleannounceboothtoarecordingstudio.Itisunlikelythatanypublishedroomdesignwillexactlyfityourneeds,orthatyouwouldevenbuilditpreciselyasdescribed.Rather,eachdesigngivenhereisatemplate,anexample,ateachingtoolthatwillhelpguideyoutosuccessfulcompletionofyourproject.

If youwish to dig deeper into the study of sound, I respectfully suggestMasterHandbook ofAcoustics,anotherofMr.EverestsbooksthatIwasaskedtorevise.Itemphasizesmaterialwithmoretheoreticaldepth,andalsocontainsadditionalexamplesofroomdesigns.Together,thesebookswillprovideagoodunderstandingof theoreticalandpracticalroomacoustics.Withintroductorybooksunderyourbelt,youcanwidenyourscopebyaccessingthemanyotheracousticsbooksandcountlessmagazine and journal articles available.Manufacturers of acousticalmaterials and treatments alsopublish a wealth of technical information. Finally, dont forget to consult acousticians and otherprofessionalswhohavedevotedtheircareerstothestudyofarchitectualacoustics.

Whetheryouarereadingthisbookasanacademicexerciseorastheprefacetoaconstructionproject,Iwelcomeyoutotheworldofroomacoustics.Youarefollowingdirectlyinthefootstepsofourearlyancestors,GreekandRomanarchitectsandengineers,19th-centuryscientists,designersofmodernbuildings,andanyonewhoappreciatestheimportanceoftheacousticsofspaces.

KenC.PohlmannDurango,Colorado

CHAPTER1IntroductiontoRoomAcoustics

Trythissimpleexperiment:Gotoanopenfield,andmakesomenoise.Shout,sing,bangtworockstogether,whatever.Youllnotethatalthoughthesoundmaybeloud,youcanalsofeelitdissipateintothe open air. The opennessmakes sounds seem empty.Now repeat the experiment indoors.Youllhearaclosenessandfullnesstothesoundastheroomsurfacesreturnsomeofthesoundtoyou.Youare enveloped by the sound; it is all around you; it ismore involving. The room embellishes thesound.Asyouexploredifferentrooms,youllobservethateachroomhasadifferentsoundquality.Simplybylistening,youcantellwhetheraroomisdeadorliveandwhether theroomsoundsdull or bright. Furthermore, if you listen carefully, you can hear if you are standing near areflectivewall,orfarfromit.Youcanalsodetectdirectionalityandroomsize;forexample,youcanhearifyourroomhasahighceiling.

Weconcludethatroomsimprinttheirsoniccharacteristicsonsoundswithinthem.Thisislogicalbecausesoundemanatingfromasourcewilltraveloutward,strikeroomsurfacessuchasthefloor,ceiling,andwalls,andbounceback.Thecharacteristicsofeachsurfacethusaffectthesoundthatisreturnedtothelistener.Somesoundcomponentsareuniquelyfreeofroomeffects.Imaginethatyouaresittingnearanoisymachine.Somesoundradiatesfromthemachineandtravelsdirectlytoyourears. Because that direct sound does not strike a room surface, it is not affected by the room.(However,itshigh-frequencyresponsewillbeslightlyreducedasittravelsthroughair.)Ontheotherhand,other sound from themachinestrikesa roomsurfaceand returns toyourears; that sound isaffectedbythesurfacecharacteristics.

In any case, rooms have their own sound because they impose their own characteristics onaudio signals contained within them. Lets think about that for a second. Its actually kind ofremarkable. Sound such as music coming from headphones will sound the same everywhere. Nomatterwhat acoustical environmentwe are in, the headphones sound the same. Thats because theroomisnotpartofthatplaybacksignalpath.Butsoundsuchasmusicfromaloudspeakerwillsounddifferentineveryacousticalenvironment.Everyroomwhereyousetuptheloudspeakerwillcausethesoundyouheartobedifferentsometimesdramaticallydifferent;thatisbecausetheroomisnowpartofthesignalpath.Also,inthesameroom,theloudspeakerwillsounddifferentwhenitisplacedindifferent locations in theroomanditwillsounddifferentasyoumovearoundtheroom.Bythesametoken,whenyouarerecordingamusicalinstrument,thesoundyoureceiveatthemicrophonewillbedifferentineveryroomandtherecordedsoundwillsounddifferentastheinstrumentorthemicrophoneismoved.Clearly,acousticalenvironmentssuchasroomsareabigdeal.

Wearefamiliarwiththeideaofanelectricalsignalpassingthroughablackboxthatchangesthesignalpassingthroughit.Wecanimaginethattheboxhasknobsandbuttonsthatletusmanipulatethechanges.Aroomoperatesthesamewayonanacousticsignal,andwecanjustassurelymanipulatethe changes it imposes. Insteadof knobs andbuttons,weuse room size andgeometry, glass fiber,drywall, carpet, ceiling tile, and other common and specialized constructionmaterials to tune theroomtothedesiredresult.Gettingthedesiredresultiswhatthisbookisallabout.

Itsalsoworthnotingthatwithaboxwithknobsandbuttonsitiseasytoeffectchangesandvarythematwill.A rooms acoustical characteristics, on the other hand, aremore permanent.And,wewont fully know how the room sounds until after it is built. Clearly, its important to be able to

predicttheroomsresponsewithreasonableaccuracywhenitstillonlyexistsasasetofblueprints.Doingthisrequiresknowledge,experience,andsomemathematicaltools.Finally,allthedesignworkin the world wont yield the desired result unless the construction is done right. Relatively smalldifferences in construction technique can spell the difference between good and bad acousticalperformance.

ImportanceofRoomAcousticsWhydowecareaboutroomacoustics?Despitethefactthatwespendmostofourlivesinsiderooms,mostpeoplepay littleattenuation to thesoundof thoserooms.That,ofcourse, isamistake.Thesoundofsomeroomsdirectlydeterminesthesuccessorfailureoftheroom.Forexample,aconcerthallthatisvisuallystunning,butmakesanorchestrasoundlousy,isadisaster.Likewisearecordingstudiocontrolroomthatcausesmixingengineerstoconsistentlyturnoutrecordingswithadeficientbassresponse,orahotelroomthatdeniesagoodnightssleepbecauseofthebusyinterstatenearbywillnotbeinbusinessverylong.Athome,wemightobsessoveraroomsarchitecturalflairanditsdcor,butitssoundisoftenignored.Whileyoumighteasilyhearaconversationwiththepersonnexttoyou,youmightalsobesubjectedtonoisesfromthekitchen,laundryroomandupstairsplumbing.Andimaginealavishhometheaterthatmakesyourexpensivecomponentssoundmediocre.

Admittedly, for many rooms, the acoustical performance is not a top priority. But in otherrooms, acoustical performance is paramount. These acoustically sensitive spaces require carefulplanningandconstruction,aswellasexpertevaluation.Also,clearly,acousticalperformancecarriesa price. The additional design work, special construction materials, and skilled labor that bringpremiumperformanceallalsoaddtothebottom-linecost.

Roomacousticscanmakeaprofoundimpressiononalistenerinwaysthatarehardtoquantify.Forexample,imaginethatyouenteraconcerthallfoyerthatisheavilydamped.Thereisalmostnoreverberation and even if the space is physically fairly large, it seems closed and small.Nowyouwalkintotheconcerthallitselfandthesuddenchangeinacousticsisevident.Youhearthatevensmallsounds are magnified and linger with a luxuriously long reverberation time. The concert hallacousticsimmediatelygivesyouasenseofimmensityandafeelingofanticipation.Inotherwords,insomerooms,theacousticsisveryimportant.

SoundOutdoorsItisnotamistaketobelievethatsoundoutdoorsissimplylostintheopenair.Soundleavesasourceandtravelsoutward,unimpeded,asshowninFig.1-1(A).Thisfree-fieldconditionexistswhensoundisnotreflectedfromasurface.Underthiscondition,soundfromapointsourceradiatessphericallyoutwardanditssound-pressureleveltheoreticallydecreasesby6dBwitheachdoublingofdistancefromthesource.Forexample,ifthesound-pressurelevelofasourcemeasures80dBat10ft,itwilltheoreticallymeasure74dBat20ft.Notethatthisreferstosoundpressure;soundintensitybehavesdifferently.This exact theoretical result is rarelyencountered inpractice,but it is ahandy rule forestimating sound changeswith distance.Also, a point source ismainly a theoretically concept buteasilyapproximatedinpractice;asourcecanbeconsideredasapointifitslargestdimensionissmallcompared to the distance from it. For example, a source that is 1 ft acrosswill act as pointwhenmeasuredfrom5ftorfurther.

FIGURE1-1 Soundenergyradiatedfromasourcewill traveloutwardindifferentdirections.(A)Outdoors,soundenergycontinuesunimpeded.(B)Indoors,somesoundenergyreflectsfromthesurfaces;thisformsthebasisoftheroomsacoustics.

Sound from a continuous line of vehicle traffic behaves somewhat differently than a pointsource.We assume that the sound radiates outward cylindrically (not spherically); thus its sound-pressureleveldecreasesonly3dBforeverydoublingofdistancefromthesource.(Inacontinuousline, the traffic point sources reinforce eachother.)Thismay explainwhy the traffic soundof thehighwaynearyourhomeissoannoying.

We usually, and correctly, visualize free-field conditions in an open space, but a free-fieldcondition can also exist in an anechoic (without echoes) chamber, a specially built room withsufficientabsorptiontoeffectivelyabsorballenergyfromthesource.Inpractice,anechoicchamberscannotquiteaccomplishthisatlowfrequencies.

SoundIndoorsMostoftheacousticalpropertiesofaroomareadirectresultoftheeffectscausedbythesurfacesofthe room. Sound energy radiated from a source will travel outward in different directions. SomesoundenergyreturnsfromthesurfacesinreflectedpatternsasshowninFig.1-1(B).Insomecases,sound is reflected in amore complexway known as diffusion. In either case, the returned energycomes together in a complicated way to form the sound field of the room. From a perceptualstandpoint,thesoundfieldcomprisestheintricate,detailedfluctuationsofsoundpressureattheearsofalistener.Suchfluctuationstestthelimitsofthehumanear ssensitivitytosoundintensity,pitch,andtimbre.Inaddition,somesoundwillbeabsorbedbythesurfacesofaroom.Themoreenergythatisabsorbedbytheroomsurfaces,thelowerthesoundlevelintheroom.

DirectSoundandIndirectSoundAs noted, sound behaves differently depending onwhether you are outdoors or indoors.A closer

lookat sound indoorsshows that it exhibitsbothoutdoorand indoorcharacteristics,dependingonyourdistancefromthesoundsource.Anear-fieldconditionexistsveryclosetothesource;sourcescannotbemodeledaspointsources;sounddecreases12dBforeverydoublingofdistance.Thisnearfieldshouldnotbeconfusedwithnear-fieldorclose-fieldmonitoring.

Slightly farther fromthesource (perhaps5 ftaway inasmall room) thesound-pressure leveldecreasesbyabout6dB ina free-fieldcondition; this isdirect sound.Farther than that, thesound-pressurelevelremainsconstantatanydistanceaway;thisisindirectsound.Thesound-pressurelevelis constant because the reverberant field is constant everywhere in the room.There is a transitionregionbetweenthedirectandreverberantsoundfields.Themoreabsorptivetheroom,thelowerthelevel of the indirect reverberant sound field. Thus, in absorptive rooms, the free-field conditionextendssomewhatfartherfromthesource.Inthelimitingcase,ananechoicchamber,theonlysoundis direct sound so the free-field condition extends throughout the room. The relationship betweendirectandindirectsoundinaroomisshowninFig.1-2.

FIGURE1-2 In a room, fairly close to the source, the sound-pressure level in the free field (direct sound)decreasesby6dB foreverydoublingofdistance.Fartherfromthesource,thesound-pressurelevelbecomesconstant(indirectsound);thetransitionbetweenthesetwozonesandthelevelofthereverberantenergydependsontheamountofabsorptionintheroom.

Small-RoomAcousticsAswewillseeinlaterchapters,inmanyways,smallroomsposegreateracousticalchallengesthanlargerooms.Thisisbecauseinsmallrooms,thewavelengthofsoundcanbesimilar to,or longerthan, the rooms dimensions. This promotes a modal response, standing waves, and a lack ofdiffusion.Theseeffectscreateanomaliesintheroomslow-frequencyresponse(forexample,below300Hz)andotherproblems.Incontrast,largeroomshavemorediffusesoundandthelow-frequencyresponseisnotdominatedbymodes; therefore, thefrequencyresponsecanbeflatter.Smallrooms

alsohaverelativelylessabsorptionandthusashorterreverberationtimethanmaybedesirable.Thisbookdealsprimarilywiththeacousticsofsmallrooms.Thespecialproblemsofsmalldimensionswillappearinmanyofthediscussionsoftheseroomdesigns.

RoomIsolationLetstryanotherexperiment.Whileindoors,forafewquietminutes,justlisten.Canyouheartrafficon the roadoutside,or aircraft passingoverhead?Doyouhear interior conversations, footsteporplumbingnoise,airconditioners,orfans?Clearly,evenifaroomhasgoodacoustics,itisntworthmuch if other noises intrude into the space. In other words, good isolation is an importantconsideration.Further,ifyouintendtoplayyourhometheaterloudly,youllhavetoconsiderotherpeopleinyourhouseoryournext-doorneighbors.Isolationisalsoimportantforthem.Isolationalsodepends on the frequency of the sound.Generally low frequencies are harder to isolate than highfrequencies.Forexample,youmightstronglyhearthebasscontentfromastereoplayingdownthehall,butlessofthesongsmidrangeandtreblecontent.

Adequateisolationiscriticalinanyacousticallysensitivespace.Forexample,recordingstudios,concerthalls, libraries, andhomebedrooms require isolation.Conversely, isolation isusually lesscritical in spaces such as retail stores, restaurants, gymnasiums, and home kitchens. The task ofachieving isolation begins with the buildings blueprints. Good isolation across the full audiofrequency range usually demands heavy walls, decoupled noise sources, and other specialtyarchitecturalfeatures.Otherfeaturesmightincludefloatingfloorsandaspeciallydesignedheating,ventilating,air-conditioning(HVAC)system.Inaddition,goodisolationdemandsattentiontodetail;for example, sound leaks between rooms must be eliminated and any accidental couplings in adecoupled element must be prevented. In short, good isolation is hard to obtain. Furthermore, asnoted below, good isolation should begin in the blueprints; adding considerable isolation to anexistingstructureisverydifficultandsometimesimpossibleandisusuallyquitecostly.

RoomTreatmentTotheaverageperson,iftheynoticeitatall,aroomissimplyanassemblageofbuildingmaterials.They see a tile floor, rough stucco walls, arched ceiling, heavy wooden doors, and large glasswindows.Unless theperson isanarchitect, the roomspaint schemeand furnishingsmightmakeagreaterimpressionthantheroomitself.

Toanacoustician,aroomisamatrixofsoundprocessingdevices.Togreaterorlesserdegrees,asshowninFig.1-3,everypartitionorbarrierinaroomwillreflect,absorb,andtransmitsoundthatstrikes it. Reflected sound will continue to play a role, while absorbed sound will disappear. Inaddition, some elements will diffuse sound that strikes it; instead of a simple bounced reflection,soundisreturnedoverarangeofangles.Thebalancingofthesephenomena(reflection,absorption,anddiffusion)iskeytoaroomsacousticaltreatment.Somesoundthatstrikesabarriersuchasawallmaybetransmittedthroughthatbarriertotheadjoiningroom.Thesoundthatistransmittedalwayshaslessenergythantheoriginalsoundbecauseofattenuationprovidedbythebarrier.Becauseofthisattenuation,abarriercanprovidesoundisolation.

FIGURE1-3 Partitionsinaroomwillreflect,absorb,andtransmitsoundthatstrikesthem.Dependingondegree,apartitionmaybeconsideredasreflectiveorabsorptive,andtoprovidegoodsoundisolationornot.

To an acoustician, the tile floor and stucco walls would be sound reflectors, and the archedceiling might create troublesome sound focusing. The heavy doors (and the stucco walls) mightprovide useful sound isolation, while the large windows might allow noise intrusion. The paintschemeisrelativelyunimportant(althoughpaintcanaffectfactorssuchasabsorption).Becausetheirsurfaceareasarerelativelysmall,furnishingsareusuallylessimportantthanthebuildingmaterialsbut,forexample,astuffedsofaandchairswouldaddabsorptiontoaroom.

An acoustician may also view a room as an opportunity for improvement. Through roomtreatment, its acoustical characteristics can be adjusted to providemore suitable performance. Forexample,a roomwith tile floorandstuccowallswouldhavea longreverberation time. If itwasamediaroomusedforteleconferencing, thelongreverberationtimesmightreducetheintelligibilityof thespeechthat isconveyed.Toimprovethis,absorptionin thespeechfrequencyrangecouldbeadded;forexample,heavytapestriescouldbehungfromthewalls.Similarly,heavyfabricbannerscouldbehungfromthearchedceilingtolessenfocusingeffects.

When treating a room, it is naturally easier to add treatment rather than take it away. Forexample,someacousticiansprefertodesignroomsthatareslightlytoolive,andthenaddabsorptionasneeded.Thiskindof roomtuning isan importantpartof roomtreatment. It isalso important tonotethatroomtreatmentmustcloselyobservethefrequencyresponseofanyparticularproblem,andusethis todesignthemostappropriate treatmentsolution.Forexample, ifaroomhasanunwantedlow-frequencyresonance,apanelabsorbercouldbedesignedwithpeakabsorptioninthatparticularlow-frequencyband.

Finally, another aspect of room treatment is the spatiality of the sound. For example, a roommight be designedwith absorption onone end, anddiffuse reflectors on the opposite end.Or, forexample,alargewoodpanelmightbehungfromtheceilingandangledsothatitreflectssoundtoanotherpartoftheroom.Aswithotheracousticaltreatment,spatialitydependsonthepurposeoftheroom.Forexample, a recordingstudiowould requiregooddiffusion throughout,whereasahome

theatermight requiremuch less. In fact, in the latter, toomuch diffusionmight degrade playbackimaging,thatis,theabilitytolocalizewheresoundsarecomingfrom.

HumanPerceptionofSoundIn the end, the only thing that really matters in acoustics is the human perception of it. Becausemeasurementsandnumbersare sowidelyused todescribe sound, it is important toknowwhat thenumbersmean in human terms. The decibel (dB) is awidely usedmeasure of sound level; it is alogarithmicratiooftwoparameterssuchassoundpowers.Sound-pressurelevel(SPL)comparesameasuredsoundpressuretoareferencepressureandismeasuredindecibels.

Because the decibel is not a linear measure, its numerical values can be misleading to theuninformed.Forexample,adifferenceofadecibelisusuallynotperceptible.AchangeinSPLof3dBisjustnoticeable;achangeof5dBisclearlynoticeable;achangeof10dBisheardasadoubling(orhalving)ofsoundlevel.Combiningtwosignalswithidenticalfrequencyandphasewoulddoublethesoundpressure;thisisa6-dBincrease.Intherealworld,withpracticalsignals,theincreasewouldbeabout3dB.

Thelogarithmicnatureofdecibelsmeansthatsimplemathcannotbeused.Forexample,addingtwo50-dBsoundsdoesnotyielda100-dBsound;rather,thenewsoundlevelis53dB.Anydoublingofpowerresultsinanincreaseof3dB.Infact,althoughitmayseemillogical,0dB+0dB=3dB.

Table1-1showsthatwhentwosoundsourcesareplayedtogether(fromthesamelocation),theresultingsoundlevelcanbenomorethan3dBhigherthanonesourcealone.Whenonesourceis9dBorhigherinlevelthantheother,itdominates,andaddingthesecondsourcewillnotmeasurablyincreaseoverallsoundlevel.Someotherdecibelmathematicstoconsider:50dB+50dB+50dB+50dB=56dB;and50dB+51dB+52dB+53dB=58dB.

TABLE1-1AddingDecibels

Table1-2demonstrateshowdecibellevelscanbesubtracted.Thissubtractionwouldbeneededto determine what the level of one source would be if it were operating independently of othersources. For example, if the sound-pressure level of a source is measured to be 80 dB and thebackgroundnoiselevelwhenthesourceisturnedoffis75dB,thedifferenceis5dB.Thus,asshowninthetable,thelevelofthesourcebyitselfis802=78dB.

TABLE1-2SubtractingDecibels

AcousticalDesignWhat does it mean to design the acoustics of a room? At first glance, it may seem similar todecorating a room.While putting down carpet and hanging drapeswill affect a rooms acoustics,thereismuchmoreinvolvedinacoustics.Forstarters,thedesignofaroomsacousticsbeginswellbefore the room is built. The acoustics is greatly influenced by the essentials of the roomsarchitectural design. The rooms volume, geometry, and dimensions all play important roles.Moreover,thestructuraldesignofthefloor,ceiling,andwallsisimportant.Forexample,onetypeofwall design (studs andgypsumboard)may absorbbass frequencieswhile another (masonry) doesnot. The rooms designwill also greatly influence how quiet the roomwill be even if it is noisyoutside.

Beyonddesigncriteria,thequalityofthephysicalconstructionitselfisvital.Forexample,evenif it is well designed, a poorly constructed wall could let sound penetrate into the room. Skilledcarpenters and careful interim inspection are just as important as well-conceived blueprints.Following structural construction, acoustics is further affected by the way in which the interiorsurfaceareasaretreated.Differenttypesofabsorbers,reflectors,anddiffusers,andtheirlocationsintheroomwilldeterminethesoundoftheroom.Acousticsisalsoaffectedbythetypeoffurnishingsintheroom,andevenbythenumberofpeopleintheroom.

Clearly, inmany cases, new construction is not possible, so an existing room is used. Roomtreatment and furnishings are thus the only tools available and depending on the initial roomconditions, the ultimate performance of the roommay be compromised. For example, an existingroommayhave inadequate isolation fromoutsidenoise, so even if the treatment is successful, theroommay be plagued by noise from outside. It is alsoworth noting that any acoustical design islimited by the space that is available, and the budget. For example, a bass trap might be the bestremedyforaparticularlow-frequencyresonanceproblem,buttheroommightbetoosmalltopermititsinstallation.Likewise,soundisolationisalwaysdesirableinacousticallysensitivespaces,butitisalsothemostcostlyaspectofmostprojects.

It is also important to remember that different types of rooms will demand very differentacoustical designs. Some rooms (such as recording studios) are used for sound productionwhileothers(suchasconcerthallsandhometheaters)areusedforsoundreproduction.Otherrooms(suchasclassrooms,auditoriums,sportsarenas,placesofworship,hotels,airports,andrestaurants)havetheirownuniqueacousticalrequirements.Addingtothecomplexityisthefactthatinsomespacesthe

intelligibilityofspokenwords is themost important requirement,while inothers theenjoymentofmusicismoreimportant.Someroomsmustaccommodateboth.Inanycase,theacousticaldesignofaroommustbetailoredtofititsspecificuse.

Some acoustics projects focus exclusively on noise control. For example, a rooms acousticperformancemaybecompromisedbyanair-conditioningsysteminthebuildingthatintroduceslow-frequencyvibrations,aswellasnoiseatthesupplyvents.Solutionstotheproblemcouldbeplacedatthe air conditioner, along the ducts, and at the vents. For example, to reduce vibrations, the airconditionercouldbeplacedonresilientmounts,andnoisecouldbereducedbyplacingsilencersintheductsandbyusinglarge-openingvents.Thevibrationproblemisanexampleofstructurebornenoise, and the duct noise is an example of airborne noise. A complete acoustical design studiespotentialproblemssuchastheseandtakesstepstominimizeoreliminatethem.

AcousticalDesignProcedureAlthough each project is different, the general procedure for preparing an acoustical design isusually the same.The acoustician, professional or not, usually beginswith the blueprints or otherdrawings of the room; it might be new construction or an existing room. The acoustician mustdetermineexactlyhowtheroomwillbeused; this isoftendifficultbecausemanydiversedemandsmaybemadeonaroom.Becausenoiseintrusionisusuallyaconcern,anoisesurveyofthesiteisoftenundertaken.Basedontheacousticiansanalysis,thegoalsoftheacousticaldesignaredecided.Then, based on the size and shape of the room, buildingmaterials, and other factors, a design ispreparedandintegratedwiththeoverallarchitecturaldesign.Becauseofbudget,taste,orsomeothernecessity,plansareoftenmodifiedmanytimesbeforeconstructioniscompleted.Clearly,itisbesttofinalizeadesignbeforeconstructionbegins,but this isoftennotpossibleandrunningchangesareusuallyinevitable.

During thedesignphase,blueprints formthebasisof thediscussionandallowthedesigner toliterallyvisualizeandexploreideasandtosharethemwithothers.Asabuildingisconstructed,itisthe blueprints that inform and guide the builders during the construction process.Good blueprintsgivebuilders theessential information theyneedincludingbuildingmaterials, fabricationmethods,anddimensions.Theblueprintssupplementthewrittencontractsignedbetweenclientandbuilderandallowverificationthattheworkwasdoneproperlyoratleastaccordingtothespecificationsstatedinthe blueprints. Moreover, blueprints document the work that has been done and serve as futurereference.Thisrecordisinvaluableduringupgradesandrenovations.

After construction is completed, the rooms acoustical characteristics can be objectively andsubjectively evaluated. Inmany cases, some treatment can be adjusted to optimize results. In somecases,somepartsoftheconstructioncanbeleftunfinishedpendingfinalevaluation.Forexample,aroom can be preliminarily left with deficient absorption, and then absorption can be added asnecessarytoachievethedesiredreverberationtime.Itiseasierandcheapertoaddabsorptionratherthan take it away. Similarly, other modifications can be made to a finished design to furtheroptimizetheacoustics.Asnoted,itshouldberememberedthatfurnishingsandpeoplewillalsoaffectaroomsacoustics.

Acousticians are often asked the questionwhat is good sound? We will explore ways toobjectively and subjectively evaluate room acoustics in later chapters, but its worth nothing thatacousticaldesigniscertainlynotaonesizefitsallsituation.Differentroomsrequireverydifferentkinds of acoustical characteristics, and even rooms used for the same purpose can have differentacoustics, and still have good sound. For example,many concert halls are admired for their fine

acoustics,yettheyallsounddistinctlydifferent.Infact,partofthepleasureofacousticsishearingandappreciating these differences. In addition, listeners have different tastes and come from differentcultures,andthusmayhaveverydifferentopinionsonwhattheoptimalsoundshouldbe.Ontheotherhand,thereisusuallynodisagreementwhenitcomestopooracoustics;itisusuallyapparentwhenspeechisunintelligible,whenmusicdoesnotsoundfullandrich,orwhenintrusiveoutsidenoisesareheard.

Thereisnosimplesolutiontothedesignproblem,butultimatelyitisthedutyofacousticianstoreconcilemanydifferentandsometimescontradictorycriteria,andtomakesuretheirroomdesignsprovideaconsensusgoodsound.Acousticaldesignisanartandascience.Ithastheoreticalrootsin physics, material science, and psycho-acoustics, but many subtle aspects of acoustical designcannotbeeasilyexplainedbytheory.Goodacousticiansacquireafeelforexpertdesignthatcomesfromyearsofpracticalexperience.

ANoteontheRoomDesignExamplesFollowing the introductory chapters in this book, the remaining chapters present a number ofpractical roomdesignsanddesignvariations.Theseexamples range fromrelativelysimple roomssuchasannounceboothstocomplicatedroomssuchascontrolrooms.Eachroomexampleismeanttodemonstratesolutionstoproblemsthatarecommonlyfoundinthosekindsofrooms.Forexample,the small dimensions of an announce boothmean that frequency-response irregularities caused byroommodesmustbeaddressed,andcontrol roomsrequirecarefuldesignso that thesoundatoneparticularlocation,themixingposition,isasneutralandaccurateaspossible.

However, each room-example chapter also contains more general information that may beapplicable to other types of rooms. For example, the chapter describing a home project studiodescribesawaytobuildawoodcovertohelpinsulatewindowsagainstnoiseintrusion.Clearly,thisdesigndetailcouldbeappliedtoanykindofroom.Inotherwords,ifyouareinterestedinaspecifictypeofroom,readthatchapterfirst.Butalsoskimtheotherchaptersforfurtherinformationthatmayimproveyourdesign.

In anumberof roomexamples,proprietary acousticalproducts are cited in thedesign.Theseproductswillcertainlyfulfilltheacousticalrequirements,butotherproprietaryproductsmaybeused.And, in most cases, similar systems can be constructed from scratch using common buildingmaterials.Inotherwords,theproprietaryproductsareexamples,notparticularrecommendationsorrequirements.On the other hand,when substitutions aremade, be sure to check that the acousticalpropertiesofthenewmaterialsmatchthosegivenintheroomexamples.Or,ifthepropertiesofthematerialsaredifferent,accountfortheeffectsandmodifyyourdesignaccordingly.

Thereaderwillnoticealargenumberofillustrationsinthisbook.Intheintroductorychapters,manygraphsareusedtoillustratetheconceptsexplainedinthetext.Manygraphsdeservemorethanaquick glance; there is often a good deal of information contained in the figure, and a greaterunderstanding can be gained by studying it. The later chapters show a number of architecturaldrawings for the various room design examples. These drawings use the style of constructionblueprints,andaswithearlierfigures,canconveyagooddealofinformation.Theplansinthisbookarelessformalthanblueprints,butshouldsimilarlyconveythearchitecturalconceptsbothinbroadscale and in construction details. Also, by studying these drawings, the reader will gain anunderstandingofhowthedesignandconstructionofroomsarecommunicatedthroughplans.

Finally,thereisnobetterwaytounderstandacomplexjobthanbydoingityourself.Thereaderisencouragedtouse the informationpresentedhereandelsewhere,andmakeoriginaldrawingsof

structures such as absorbing panels, as well as complete room designs. By practicing andexperimenting with drawings, over time, it will be possible to envision and complete a finisheddrawingsetthatcanserveasthebasisforconstruction,oratleastbeusedtocommunicateideaswithanarchitectoracoustician.

CHAPTER2Sound-ReflectingMaterials

Thereflectionofsoundisperhapsthemostintuitivelyunderstoodacousticalproperty.Weknowthatwhenwe standoutdoors in anopen field and shout, the sound is immediately lost.Wededuce thatmostof theenergy travelsoutward into theairwhile some isabsorbedby theground.Butwhenasheerrockwallisnearby,wehearadistinctecho.Soundenergyhastraveledoutward,struckthewalland bounced from it, and traveled back to us. This is sound reflection. It takes some time for thereflectedsoundtoreturn tous,andweobserve that thefurtherawaythewall, the longer thereturntime.Withsomeexperimentation,wemightcalculatethespeedofsound:soundtravelsabout1130ftinonesecond.Nowconsiderarockwallwiththickmossgrowingonit.Thereisanecho,but it issofter.Weobservethatsomesurfacesarebettersoundreflectorsthanothers.Itappearsthatagoodreflectorreturnsalmostallthesoundenergytouswhileapoorreflectorabsorbsmuchoftheenergyandreturnslittle.

Next we go indoors and repeat the experiments. The results are similar, but also morecomplicated.Ahardsurfacesuchasaplasterwallefficientlyreflectshigh-frequencysoundwhileasoftsurfacesuchasacarpetedfloorreflectsalmostnone.However,wealsoobserve that theroomenclosingusprovidesnot justone reflection,butmany.Asoundmight reflect fromonewall, thenanotherandanother.Eachtripacrosstheroomtakessometime(thelargertheroom,thelongerthetime),and theresult isamultiplicityof reflectionsspreadover time. Insteadofadiscreteecho,wehear densely spaced reflections, that is, reverberation. Logically, rooms with highly reflectivesurfacesprovide long reverberation timeswhile roomswithweakly reflective surfacesoffer shortreverberationtimes.

A rooms reverberation time is largely determined by the choice of surface materials. Thequestionisthuspresented:whatreverberationtimeisbest?Theanswerdependsonhowtheroomwillbe used. Any musician or music lover will tell you that reverberation is welcome. For example,concert halls tend to have luxuriously long reverberation times because it makes it easier formusicians to perform as an ensemble, and audiences like the reverberant sound. But a longreverberation time in a recording studio is undesirable because excess recorded ambience woulddecrease isolationbetweenrecordedtracksandmakeitdifficult foramixingengineer to tailor thesoundofeachinstrument.Therefore,mostrecordingstudioshaveshorterreverberationtimes.

Also,whilemusiciansmightwelcomereverberation,theywillalsobepickyaboutthequalityofthe reverberation. For example, the frequency response of the reverberation is as important as thereverberation time. The room surfacematerials can dramatically affect the frequency response ofreverberation. For example, a room with surfaces that reflect low frequencies and absorb highfrequencieswillhavearelativelylower-frequencyreverberation.Aroomwithreverberationwiththiskindoffrequencyresponsemightbeconsideredboomyandthusundesirable.Itisalsoimportanttonotethatwhilereverberationishighlyprizedinaconcerthall,isolatedanddiscreteechoesarenot.Any audible echo in a concert hall or a recording studio would indicate a serious flaw in theacousticaldesign.

Itisalsoimportanttoconsiderthetiminganddirectionalityofroomreflections.Forexample,inconcerthalldesigns,earlyreflections(thosearrivingatthelistenersoonest)mustbecarefullytimedto provide an adequate sense of spaciousness. Some control rooms are designed so that no early

reflections arrive from the front of the room,whilemany reflections arrive from the back of theroomwithinacertaintimeperiod.Clearly,thereflectionofsoundisoneofthemostacutelyjudgedqualitiesofanyacousticalspace.

SoundWavelengthandReflectionsInmanyways,thephenomenonofreflectionissimpletounderstand.Wearefamiliarwithreflectionsfrommirrors, aswell asechoes fromadistant rockcliff.Lightor soundbounces froma surface,returningtothesourceoranotherposition.Thisisspecularreflection.However,notallreflectionsaresosimple.

First, reflectioniswavelengthdependent.Wavelength,denotedas,measures theliteral lengthofawaveform,thatis,onecompletecycleofasoundwave.Awaveformcanbemeasuredbetweenany twocorrespondingpoints on the cycle such aspeaksorwhere thewaveformcrosses the zeroaxis.Lookedatanotherway,wavelengthisthedistanceawavetravelsinthetimeittakestocompleteone cycle. Frequency, denoted as f, is the number of cycles per second (or hertz). Frequency andwavelengtharerelated:

=c/f(2-1)

where = wavelength,ft

c = speedofsound=1130ft/secf = frequency,Hz

Fromthisrelationship,forexample,weseethata20-Hzwaveformisabout56.5-ftlong,anda

20,000-Hzwaveformisalittlelessthan3/4inlong.Dependingontheproblemathand,itispropertorefertoasoundintermsofeitheritswavelengthoritsfrequency.

Wavelengthofsoundisimportantbecauseitdetermineshowlargeasurfacemustbetoreflectasound. Sound of a certain wavelength (or frequency) will only reflect from a surface that issufficientlylarge.Inparticular,thisisshownintheexpression:

x>4(2-2)

where x = surfacedimension,ft

= wavelength,ft

This shows us that sound reflects from a surface if the surface length orwidth dimension isgreaterthan4timesthewavelengthofthesound.Forexample,a1-kHzsinewaveisabout1.1-ftlong;thusitwillreflectfromasurfacewithdimensionof4.4ft.Also,clearly,signalshigherinfrequencythan1kHzwillreflectfromthissurface.Itisinterestingtonotethatreflectingpanelscanthusactashigh-passfilters,onlyreflectingfrequenciesthatareaboveacertaincutofffrequency.Also,notethatinthiskindofspecularreflection,theangleofreflectionequalstheangleofincidence.AswewillseeinChap.4,whenx=,soundisnotreflected;instead,itisdiffused.

ReflectionandRoomGeometryThe geometry of room surfaces greatly influences the behavior of reflections. Parallel reflectivesurfacesarecommoninmanyrooms,andcanbeacousticallyproblematicifsoundreflectsbackandforthbetweenthesurfaces.Theserepetitivereflections,calledflutterechoes,canbeveryaudibleasaseriesofimpulses.Flutterechocanalsobeperceivedasapitchortimbrecoloration,whichdegradessoundqualityandspeechintelligibility.

A roomcanbe tested for flutterechoesbysimplyclappinghands togetherand listening foraringingorflutteringhigh-frequencysound.(Forexample,flutterechocanbeheardinmoststairwellsbecause of the many parallel walls.) The experiment should be repeated at different places in theroomwheremorefocusedechoesmayoccur.Morerigorously,thereverberationcharacteristicoftheroom can be plotted; an impulse is sounded and the energy decay is plotted over time until itdisappearsrelativetothebackgroundnoiselevel.Anechowillappearasaspikeinthesounddecayslope;flutterechoeswillappearasaseriesofspikesregularlyspacedovertime.AplotofatypicalflutterechoisshowninFig.2-1;theperiodicspikesareclearlyvisible.

FIGURE2-1Aplotshowingaflutterechoasitdecaysovertime.

Absorption is usually the easiest solution for echoes.Once thewalls involved in the echo areidentified, absorption can be placed on those surfaces. For example, in the case of a flutter echo,absorbingpanels canbe placedononeor bothparallelwalls.As another example, a roomwith awood parquet floor and a plaster ceiling could have significant flutter echo; the floor and/or theceilingmustbe treated(forexample,withcarpetandabsorptive tiles, respectively) toeliminate theflutterecho.Itisimportanttorememberthatechoesarecreatedbyspecificsurfaces;ifabsorptionisplaced on a surface that is not creating the echo, the echowill be unaffected. For example, in theexampleabove,placingabsorbersonthewallswouldnotaffectthefloor/ceilingflutterecho.

In some cases, instead of using absorption, diffusers can be used to break up echoes. Forexample, diffuserswould be a good choice if it is important tomaintain sound energy levels in aroom;addingabsorptionwoulddecreaseenergylevels.Innewconstruction,wallscanbesplayedtopreventflutterechoes;a10:1splay(1ftfor10ftofwalllength)issatisfactory.Caremustbetakentoensurethatanother(third)walldoesnotcompletetheflutterecholoop.

Reflective concave surfaces will focus sound, creating an area of higher sound level at theexpense of lower level elsewhere. This is contrary to the usual need for uniform distributionthroughoutaroom.Adomedceilingisanexampleofaconcavesurface,andacommontroublespotfor acousticians. Large convex reflective surfaces, unlike concave surfaces, can providewelcomediffusion. Sound striking the convex surface reflects in many directions, distributing a broadbandwidthofsoundthroughoutaroom.

CalculatingReflectionsFigure2-2showssomeof the reflections ina rectangular room traveling froma loudspeaker toalistener. For clarity, only reflections from one loudspeaker are shown. The reflections areindividually identifiedby letters (AG).Through simple computationsbasedonperfect reflectionsand inverse square propagation, the magnitude and delay of each reflection are estimated. Inparticular,thereflectionlevelanddelaycanbecalculatedfrom:

Reflectionlevel=20log[(Directpath)/(Reflectedpath)](2-3)

Reflectiondelay=[(Reflectedpath)(Directpath)]/1130(2-4)

FIGURE2-2Examplesofsurfacereflectionsinalisteningroomfromasingleloudspeakertoalistener.

Table2-1tabulatesthesevenreflectionsofFig.2-2,andlistsvaluesforthepathlengths,levels,anddelaysofthereflections.Wenotethatthedirectpathlengthis7.1ft.Furthermore,thesevaluesareplotted in Fig. 2-3 using the original identifying numbers. (Referring to Fig. 11-16, the lateralreflectionsinthisroomfallwithinthefavorableregion.Thissuggeststhatthelateralreflectionswillhelp provide a welcome sense of spaciousness to the room and also provide good loudspeakerimaging.)

TABLE2-1ReflectionComputationsofFig.2-2

FIGURE2-3PlotofthelisteningroomreflectionsshowninFig.2-2withvaluestabulatedinTable2-1.

Allofthesereflectionsareadjustableinregardtoamplitude,althoughthedelayvaluesarefixedbytheroomgeometryanddimensions.Agivenreflectioncanbereducedinamplitudebyapplyinganareaofabsorbingordiffusingmaterialatthepointofreflection.Forexample,squaresofabsorbentonthefloor,thesideandfrontwalls,andtheceilingcangreatlyreduceoressentiallyeliminatethereflections. Absorbers of different absorbing efficiency will affect the reflection amplitude. Anacousticianwouldadjusttheamplitudeofthereflectionstoachievethesenseofspaciousnessandthestereo image qualities desired. Also, the frequency response of the reflection will be varieddependingonthetypeofabsorber.

Withrespecttoreflections,wethenhaveachoice.Somereflectionscanbeadjustedtoprovidethe desired front image and degree of spaciousness, or they can be eliminated (such as the earlyreflectionsatthelisteningpositionofsomecontrolroomdesigns).

ThePrecedenceEffectAsnotedattheoutset,anechoisoneofthemostfamiliaracousticalevents.Atafardistancefromthereflector,ittakesarelativelylongtimeforasoundtomaketheroundtripfromyoutothereflectorandbackagain.Forexample,at100ftfromareflectingsurface,anechowillbeheardafter177msec(millisecond).Asyoumoveclosertothereflector,thedelayisshorter.At50ft,theechoreturnsinabout88msec.Thensomethingunexpectedhappens.Atacertaindistance,andthenasyoumoveevencloser,youceasetoheartheecho.

Ifyouhaveameasuringinstrument,itshowsthattheechoispresent,butyoudonothearit.Thedefect occurs in your brain. The brain cannot resolve acoustical events that happen in rapidsuccession;theechoreturnssosoonafteryouhearthedirectsoundthatyoudonotperceivetheecho.Thereisatransitionzonebetweenperceivingandnotperceivingtheechowhenthedelayisbetween50and80msec,andauditoryfusionisverystrongat35msecandless.

Moreover, our brain integrates spatially separated sounds over short intervals, and tends toperceive them as coming from the location of the sound that arrives first. For example, in anauditorium,theearandbrainhavetheabilitytogatherallreflectionsarrivingwithinabout35msecafter the direct sound, and combine them to give the impression that all this sound is from thedirectionof theoriginal (first) source,even though reflections fromotherdirectionsare involved.Thesoundthatarrivesfirstestablishestheperceptualsourcelocationoflatersounds.Thisiscalledtheprecedenceeffect,Haaseffect,orlawofthefirstwavefront.Thesoundenergyintegratedoverthisperiod isusefulbecause it increases theapparent loudnessof thedirect soundwithoutchanging itsperceivedlocation.

Anotherissueistheloudnessoftheecho.Thefusionzoneisextendediftheechoisattenuated.Forexample,iftheechois3dBbelowthedirectsound,auditoryfusionextendstoabout80msec.Roomreflectionsare lower in level thandirectsound,so inpractice fusionusuallyextendsoveralongertime.However,withverylongdelaysof250msecormore,thedelayedsoundisclearlyheardas a discrete event.The fusion effect can alsobe overcome if the delayed sounds are increased inamplitude,butthisdoesnotoccurnaturallyinroomsbecauseallreflectionsarelowerinamplitudethantheoriginaldirectsound.

Reverberation-TimeEquationThe reverberation time is a measure of the liveness of a room. Early in the development ofacousticalartsandsciences,reverberationtimewasconsideredtobethemostimportantmeasureofacousticalqualityofamusichall.Todayitisonlyoneofmanysuchindicators.Reverberationtimeisusuallyquotedas the time in seconds required for sound intensity ina room todecreaseby60dBfromitsoriginallevel.TheSabineequationisoftenusedtocalculatereverberationtime.Itshowsthatreverberationtimedependsonroomvolumeandabsorption.Themoretheabsorptioninaroom,theshorterthereverberationtime.Likewise,thelargertheroom,thelongerthereverberationtime.Thisisbecausesoundwillstriketheabsorbingroomboundarieslessoften.TheSabineequationisgivenbelow:

RT60=0.049V/A(2-5)

where RT60 = reverberationtime,sec

V = volumeofroom,ft3

A = totalabsorptionofroom,sabins

A rooms total absorptionA is found by summing the absorption contributed by each type ofsurface. This is obtained by multiplying the square-foot area S of each type of material by itsrespectiveabsorptioncoefficient,andsummingtheresulttoobtaintotalabsorption(A=S).Theabsorption coefficient describes the absorptivity of specific materials. It ranges from 0 (noabsorption)toatheoreticalvalueof1.0(totalabsorption)andvarieswithfrequency.

For example, suppose that an area S1 (expressed in ft2) is covered by a material having anabsorption coefficient 1 at a certain frequency. This area contributes (S1)(1) absorption units (insabins)totheroom.AnotherareaS2hasanabsorptioncoefficient2,anditcontributes(S2)(2)sabinsofabsorption.ThetotalabsorptionintheroomisA=S11+S22+S33.AfterAisobtainedfortheentireroom,Eq.2-5canbeusedtocalculatetheroomsreverberationtime.Itisworthnotingthatthetotalabsorption ina room(S)canbe increasedequallywellbyaddinga low-absorptionmaterialoveralargesurfacearea,orahigh-absorptionmaterialoverasmallersurfacearea.Also,wecanseethateverydoublingoftotalabsorptionwillcutthereverberationtimeinhalf.

Theabsorptioncoefficientsofmostmaterialsvarywithfrequency;therefore,itisnecessarytocalculatetotalabsorptionatdifferentfrequencies.Moreover,anyquotedreverberationtimeshouldbeaccompaniedbyan indicationof frequency.Forexample, a reverberation timeat250Hzmightbequoted as RT60/250 = 2.5 sec. When there is no frequency designation, the reference frequency isassumedtobe500Hz.AbsorptioncoefficientsarediscussedinmoredetailinChap.3.

TheSabineequationiswidelyusedtopredictaroomsreverberationtime.Inlargespacessuchasconcerthalls, ergodic (thoroughlydiffused)conditionsareapproached,and theSabineequationcanbequiteaccurate.However,underotherconditions,theequationhaslimitations.Itisvalidwhenreflectedenergythroughoutaroomisuniformlydiffused;thisisnotalwaysthecaseinsmallrooms(notergodic).Italsoassumesthatabsorptionisuniformlydistributed.Italsoassumesthattheroomdimensionsare similar; that is, a roomdoesnothaveonedimension that isgreatlydifferent fromanother.Inpractice,thereverberationtimeatlowfrequenciesmaydifferfromthatpredictedbytheSabineequation;theerroroccursbecauseatlowfrequenciesthesoundisnotuniforminaroom.(Atlow frequencies, the decay of sound in the roomchiefly involves the decay of a fewmodes.)Theaudible band is so wide (ten octaves) that the wavelength of sound at higher frequencies is shortenough that ergodic conditions are more closely approached in small rooms.We can, therefore,dependmoreonthecalculatedhigh-frequencyvaluesofreverberationtime.

Particularly insmall rooms, reverberation timecanvaryconsiderablyatdifferent locations intheroom;aswewillsee, this ispartlydue torelativelypoordiffusion thatoccurs insmall rooms.Also, theSabineequationismoreaccuratefor liveroomswithlongerreverberationtimes.Indeadrooms where reverberation time is short, the Eyring-Norris equation will provide more accurateresults.

Reverberationtimedescribesonlyonepartofaroomsacoustics.But,itisusefultoknowthischaracteristic of a room because it can be predicted andmeasured with reasonable accuracy and,because it is usually consistent throughout larger rooms, a single value can be quoted. The roomdesignexamplespresentedlaterinthisbookcontainanumberofpracticalexamplesofreverberationtimecalculations.

Reverberation-TimeMeasurementsReverberation time can be measured using an omnidirectional source and an omnidirectional

microphone. The source can be sounded as an impulse. For example, electrical spark discharges,pistols firing blanks, balloon bursts, and even small cannons have been used as sources. Thosesignals all contain energy throughout the audible frequency spectrum.Alternatively, a steady-statesource such as broadband, octave, or 1/3-octave bands of random noise can be played; thereverberation timemeasurement is startedwhen the source is turned off. Sine-wave sources yieldirregular decays that are difficult to analyze. The sound source is amplified and played through aloudspeakerfacingintoaroomcorner.Asound-levelmetercanbeusedtomeasurethesounddecay;sound-levelmetersarediscussedinChap.11.

Thereverberationtimeisthetimeittakesthesoundtodecreasebyacertainamount.Asnoted,whenthesounddecreasesby60dB,themeasurementisknownasRT60.The60-dBfigureisarbitrary,butitapproximatelycorrespondstothetimerequiredforaloudsoundtodecaytoinaudibility.Theear ismost sensitive to the first 20 or 30 dB of decay. In practice, because of high ambient noiselevels, it is often impossible to measure a sound decay over a full 60-dB range. Consider, forexample,thattoovercomeambientbackgroundnoise,thesoundsourcemayhavetobesoloudastorequirehearingprotectionforthetesters.Thusitiscommontomeasuredecayover20or30dB,andthenextendthecurvetoobtainafigureforthedecaytimeover60dB.Alternatively,toincreasethesignal-to-noise ratio of the measurement, a band of noise can be used and the measuring devicefilteredtoexcludeallfrequenciesbutthatband.

Asnoted,althoughreverberationtimeisoftenquotedat500Hz,itisimportanttomeasureitatdifferent frequenciesacross theaudible spectrum.Thiscanprovidemuchuseful information thatasingle number cannot. For example, consider the example in Fig. 2-4. The plot shows that in thisroom,thereverberationtimeisgenerallylongeratlowfrequencies;thismayindicatethattheroomhasaboomysound.Also,itisoftenusefultotakemeasurementsatdifferentlocationsinaroom.Insmall rooms, and particularly at low frequencies, theremay be considerable variations inRT60 indifferent locationsbecauseofdifferentdecay ratesof roommodes; thisvariation isalsoshown inFig.2-4.Toobtain a singlevalue forRT60 for example, at 500Hz,measurements at 500Hz fromdifferentroomlocationscanbeaveraged.

FIGURE2-4Measurementsofreverberationtimeshouldbetakenatdifferentfrequencies,andatdifferentlocations;curvesforthreelocationsareplottedinthisfigure.Thisroomgenerallyhaslongerreverberationtimesatlowfrequencies,aswellasgreatervariationsatlowfrequencies,atdifferentlocations.

CHAPTER3Sound-absorbingMaterialsandStructures

Theuseofabsorptiontoreducesoundlevelsinaroom,andtocontrolcertainreflections,isoneofthemostbasictechniquesinroomtreatment.Absorptiondirectlydeterminesaroomsreverberationtime, and strategic placement of absorption on room surfaces can dampen specific unwantedreflections.Theoptimalamountofabsorptioninaroomdependsontheroomsacousticalpurpose.For example, an auditorium requires relatively more absorption because too much reverberantenergywilldegradespeechintelligibility;areverberationtimeofabout1secinthespeechfrequencyrangeisusuallyrecommended.However,ifaroomabsorbstoomuchsound,theoverallsoundlevelin the roommaybe too low.Some reflection is important tomaintaina satisfactory soundenergylevel. Interestingly,when a sound-reinforcement system is used in a large auditorium, a somewhatlongerreverberationtimeisdesirablebecausetheamplifiedspeechsignalmaysoundunnaturalinahighlyabsorptiveroom.Aconcerthall requiresrelatively lessabsorptionbecauseearlyreflectionsfromthestageanda longer reverberation timeare judged tobenefit thesoundqualityofmusic.Aconcert hallwith just the right amount of absorption (and otherwell-designed details) can yield abeautifulreverberationcharacteristicthatisprizedforbothmusicperformanceandrecording.

Soundabsorbers areoftenclassifiedasoneof three types:porousmaterials,panel absorbers,andvolume(Helmholtz)absorbers.Eachoftheseabsorbersusesthesamebasicmechanismtoabsorbsound.Theyconvert theenergyofvibration in soundwaves intoa small amountofheat,which isdissipated. Porous absorbers trap sound waves inside a porous material and dissipate that energythrough friction. Panel and volume absorbers are similar; both dissipate sound energy throughresonance.

Theabsorptivepropertiesofmaterialsareusuallyfrequencydependent.Forexample,aporousabsorbermaybeveryabsorptiveathighfrequencies,andnotabsorptiveatlowfrequencies.Apanelabsorbermaybetunedtoabsorbatamiddlefrequencyregion.Abasstrapmayabsorbonlyverylowfrequencies. Furthermore, the way that materials are constructed and mounted, for example, theirthicknessanddepthofairspacebehindthem,influencesthefrequencyresponseoverwhichtheyareabsorptive. Thus a frequency-balanced room treatment often calls for a combination of differenttypesofabsorbers,usingdifferentmountingtechniques.

AbsorptionGuidelinesThecorrectamountofabsorptiondependsonhow the roomwillbeused,and inparticularhowlong the rooms reverberation time should be.As instructed by the Sabine reverberation equation,absorptionandreverberationtimearedirectlyandinverselyrelated.Forexample,iftotalabsorptionis doubled, reverberation time is halved. A long reverberation time can be problematic if speechintelligibility isparamount;absorptionwilldecrease reverberation timeand improve intelligibility.Excessive reverberationalsomakes itdifficult to localize soundduringplayback. If localization isimportant,thenaddedabsorptionmaybeneeded.

Absorption is also used to control echoes. For example, a flutter echo comprising soundreflectingfromparallelsurfacesisofteneasilyheard,andisasignificantdefectinaroom.Thisecho

can be reduced or eliminated by placing absorption on one or both of the parallel surfaces. Asanother example, a domed ceilingmight focus sound at a point. This can be overcome by addingabsorptiontothedomedsurfaceorhangingabsorptivepanelsunderneathit.

Absorptionisalsousedtocontrolsoundlevels inaroom.If the totalabsorptioninaroomisdoubled,theambientsoundleveldecreasesby3dB.However,thistreatmentisoftennoteffective.Itcanbe seen that if each3-dBdecreasedemands that absorptionbedoubled, apointofdiminishingreturnsisquicklyreached.Still,alevelreductioncanbeusedtodecreasenoiseinaroom.Insomecases,thereductionisadisadvantage;forexample,whileaddedabsorptiondecreasesreverberationtime and improves intelligibility in a room, it also decreases level.Because of this lower level, itmightbedifficultforahumanspeakertobeheard.

Sometimes absorption can be unintentionally created, and have a negative effect on soundquality.Forexample,thinwoodenpanelsonfurringstripsmightbeusedforwall-coveringpurposes.Thesecanactasmanysquarefeetofpanelabsorbers,absorbingmid-orlow-frequencysound.Theresultmight be a reverberation that is relatively too bright andharsh sounding.The solution is toeliminatethefurringstripsandmountthewoodenpanelsdirectlyonthestructuralsurface.Likewise,too much porous absorption such as carpeting and draperies can overly reduce high-frequencysound,leavingaboomy,low-frequencyreverberation.

RoomGeometryandTreatmentWheneverspecifyinganyabsorptioninaroom,considerationmustbegiventotheroomgeometryandthelocationofabsorptionintheroomrelativetothesoundsourceandthelistener.Forexample,ceilingtilesprovidecost-effectiveabsorption.Butaceilingplacementisnotalwaysthebestsolution.Inmanyrooms,theceilingisrelativelyfarfromthelistener.Thusalistenernearasoundsourcewillhearmainlydirectsoundfromthesource,andthatsoundwillnotbereducedbyceilingtileoverhead.On the other hand, if the sound source is farther away, and the listener is hearing both direct andreflectedsound,ceilingtilewillhelpabsorbsoundthatwouldotherwisebereflectedfromtheceiling.Itcanbeseenthatceilingabsorptionisrelativelymosteffectiveinaroomthatislongandwidewithalowceiling,andrelativelylesseffectiveinaroomwithasmallfloorandtallceiling.Inotherwords,theroomgeometrymustbeconsideredwhenapplyingabsorption.

Inasmallroomwithreflectivesurfacesandaceilingofabout500ft2,ceilingtilemightdecreaseindirectreverberantsoundlevelsbyabout3dBclosetothesoundsource,andbyabout10dBfartherfromthesource.Ifabsorptionisalsoplacedonthefourwalls,thesoundlevelnearthesourceisnotfurtherreducedbutfartherfromthesourcethelevelmightdecreasebyanother6dB.Thisisperhapsthegreatestlevelreductionthatcanbeachievedinthisroom(Egan,1988).

Inmany cases, when a high ceiling is available, themost efficient absorption is achieved byhangingporousabsorptivepanelsfromtheceiling.Thisismoreeffectivethanattachingpanelstotheceiling because a greater absorptive area is exposed.Moreover, in a hanging labyrinth of panels,soundcanstrikemultiplepanels,increasingabsorption.

SoundAbsorptionCoefficientThesoundabsorptioncoefficientisameasureofamaterialsefficiencyinabsorbingsoundenergy.Itis the fraction of the incident sound energy from all directions that is absorbed. The absorptioncoefficient,expressedas,varies from0 (noabsorption) toa theoreticalvalueof1.0 (total soundabsorption).Forexample,if88%ofthesoundenergyisabsorbedbyagivenmaterialorstructureat

agivenfrequency,itsabsorptioncoefficientwouldbe0.88atthatfrequency.Onesquarefootofthematerialwouldgive0.88absorptionunitsA,expressedinsabins.Ifitwereaperfectabsorber,suchastheproverbialopenwindowthatletsallsoundescapeandreflectsnone,eachsquarefootwouldgive1.0absorptionunits.Whenusingstructuresthatallowformorethan1ft2ofmaterialtobeplacedina1-ft2footprint,suchasceilinglouvers,canbegreaterthan1.0.Notethatametricsabinisdefinedasperfectabsorptionover1m2.Absorptioncoefficientsaredimensionlessquantities; that is,unitsarenotused.

Generally,materialswith less than0.2 are considered tobe reflecting, andmaterialswithgreater than0.5areconsidered tobeabsorbing.Abrickwallmighthaveof0.1at500Hz,whileglassfibermighthaveof0.8. Ifmaterialswith less than0.1areaddedtoaroom, therewillbelittlechangeinabsorption,0.3wouldbenoticeable,and0.6wouldbesignificant.Ofcourse,makingasignificantchangeinaroomstotalabsorptionwouldrequireaconsiderablylargeareaofabsorber,notjustahigh.

Iftheabsorptioncoefficientofamaterialweredetermined,asitusuallyis,bylayingthesampleon the floorof a reverberationchamber, the test soundarrives fromeveryangleand the resultingcoefficient would be an average one. This is called the Sabine absorption coefficient. The Sabinecoefficient,asopposedtoanenergycoefficient,isusedinthisbook.

Theabsorptioncoefficientofmostmaterialsvarieswithfrequency.Becauseofthis,absorptioncoefficients are listed in tables that show the coefficients at a series of octave frequencies; forexample, at 125, 250, 500, 1k, 2k, and 4k Hz. This range is far short of the audible band, but isgenerally sufficient for many practical applications. However, for music applications, where bassplaysanimportantrole,absorptionat31Hzand62.5Hzshouldbeconsideredaswell.

The absorption coefficient is a technical measure of a materials absorptivity at a givenfrequency; as noted, it is standardized over a 1-ft2surface. To use in room design, we mustdeterminehowmanysquarefeetofeachkindofmaterialisintheroom.

The surface area of eachmaterial ismultiplied by and summed.This yields the total roomabsorptionA:

A=S(3-1)

where A = totalabsorptionofroom,sabins

S = surfaceareas,ft2

= soundabsorptioncoefficientatagivenfrequency,decimalequivalent

For example, a cubic roomwith10-ft dimensionshas surface areaof600 ft2. Suppose all sixinteriorsurfacesarehardplasterwithof0.1.Thetotalroomabsorptionisthus:

A=(600)(0.1)=60sabins

Fromthisbaseline,wecanseehowtreatmentcanchangetheroomsabsorption.Forexample,suppose carpetwith of 0.3 is placed on the 100-ft2 floor.Also, acoustical tileswith of 0.8 areplacedonthe100-ft2ceiling.Theplasterwallswithof0.1encompassing400ft2remainuntreated.Allvaluesaremeasuredat500Hz.Thusthenewtotalroomabsorptionis:

A=(100)(0.3)+(100)(0.8)+(400)(0.1)=150sabins

Clearly,absorptioncanbeaddedandsubtractedthroughroomtreatment.Furniturechoicescanalsoinfluenceabsorptivity.Forexample,aheavilypaddedsofawilladdseveralsabinsofabsorption,butmetalchairswillnot.Itiseasytodecreasearoomsreverberationtimebyaddingabsorptiontoahighlyreflectiveroom.However,itisrelativelymoredifficulttofurtherdecreasereverberationtimein an already absorptive room. The Sabine equation for calculating reverberation time wasintroducedinChap.2.

Whenadjustingabsorption,itisimportanttoconsidervaluesofatdifferentfrequencies.Ifthewrongmaterialsareadded,thefrequencyresponseoftheroomsabsorption,andthusthefrequencyresponseof its reverberation, canbecomeunbalanced.For example, addingmaterialwith that ishighathigh frequenciesand lowat low frequenciescan result ina roomwith relatively toomuchabsorption at high frequencies. The resulting reverberation will contain too much low-frequencycontent and may sound boomy. Adding and subtracting absorption is easy. Tuning its frequencyresponseismoredifficult.

The absorption coefficients formany common buildingmaterials are listed in theAppendix.Thesevaluesaretakenfromseveralreferencesandareintendedonlyasguidelines.Infact,tablesofgenericabsorptioncoefficientsshouldalwaysbeviewedwithskepticism;thereareoftensignificantdifferenceswhenmeasuringabsorption,andspecificmaterialsof thesame typeoftenprovideverydifferentabsorptionvalues.Whenavailable,product-specificabsorptioncoefficientsprovidedbythemanufacturer should be used. Absorption data should be provided for several octave-bandfrequencies.Insomecases,manufacturersprovideabsorptiondata in termsofsabins; this isusefulwhen it is difficult to calculate surface area and thus potentially imprecise to use absorptioncoefficients. If needed, the absorption coefficient can be calculated from the sabin value. In eithercase,theusermustbecarefultonotehowabsorptionisbeingspecified.

Clearly,becausequotedabsorptioncoefficientsarenotalwaysaccurateforagivenapplication,calculationssuchasreverberationtimewhichrelyonthecoefficientswillsimilarlyalsonotalwaysbeaccurate.Thesecalculationsare thusonlyguidelines tobeused in thedesignphase.Duringandafter construction, it is important tomeasure criteria such as reverberation time and compare themeasuredvaluestothecalculatedprediction.Absorptionvaluesthatarecalculatedfromameasuredreverberationtimewillbemoreaccuratethanpredictedvalues.Goodacousticiansincludevariabilityoptions in their designs so that final adjustments in absorption can be made; this allows fordiscrepanciesbetweenthepredictedandactualabsorptioninaroom.

NoiseReductionCoefficientThenoise reductioncoefficient (NRC) is a single-number ratingoftenused to specify amaterialsabsorbency.NRCistheaverageofamaterialsfourabsorptioncoefficientsat250,500,1000,and2000Hz:

NRC=(250+500+1000+2000)/4(3-2)

where NRC = noisereductioncoefficient,decimalpercent

= absorptioncoefficient,decimalpercent

NRC is more informative than a single value because it covers a number of differentfrequencies. However, those frequencies are only mid frequencies, so NRC is not useful for

consideringabsorptionatlowerandhigherfrequencies.Inparticular,becausemusiccoversamuchwiderfrequencyrange,NRCshouldnotbereliedonfortheseapplications.Ontheotherhand,NRCisconvenient for lesscriticalapplicationssuchasspeech. It isalso important tonote thataswithanysingle-numberspecification,NRCcansometimesbemisleading.Forexample,twomaterialscanhavethe sameor similarNRCratings,butverydifferent absorption responsesover the same frequencyrange.

Very generally, materials with an NRC value greater than 0.4 are considered to be veryabsorptive.MaterialswithanNRCvalueinthe0.4to0.6rangecanbesuccessfullyusedtoprovideabsorption.MaterialswithNRCvaluesgreaterthan0.8areusedwhenadditionalabsorptionisneededin acoustically sensitive room designs. NRC is defined in the American Society for Testing andMaterials (ATSM) Standard C423-90a Standard Test Method for Sound Absorption and SoundAbsorption Coefficients by Reverberation RoomMethod. NRC values are dimensionless quantities;thatis,unitsarenotused.

StandardMountingTerminologyAmaterialsabsorptivityandthefrequencyresponseofitsabsorptivitycanvarywidelydependingonhow thematerial ismounted to a room surface. There are severalmethodswidely used tomountabsorptivematerialsinbuildings.Toaccountforthese,manufacturersoftenmeasureabsorptionandpublish the data using different testing standards that represent practical mounting methods. Forexample,layingthesampleformeasurementonthefloorofareverberationchamberisintendedtomimic thecommonpracticeofcementingabsorptiondirectly toawall.Therearemanydeviationsfromthisandstandardwaysofreferringtodifferentmountings.TheAmericanSocietyforTestingandMaterials(ASTM)hasstandardizedseveralmethodsincludingtheASTMdesignationE795-83.Some literature may list absorption data adhering to the older Acoustical and Board ProductsManufacturersAssociation(ABPMA).Table3-1listsseveralmountingstandarddesignations.

TABLE3-1CommonMountingStandardsforSound-AbsorbingMaterials

PorousAbsorbersWhensoundfallsonaporoussurface,someofitisabsorbedandsomeisreflected.Inparticular,asthesoundpenetrateswithinaporousmaterial,thevibratingairmolecules(undergoingcompressionandrarefaction)impartmovementtothetinyfibersinside.Suchmovementencountersresistanceas

fiberrubsonfiber,andthisresistancegeneratesasmallamountofheat.Thusabsorbedsoundenergyis changed to heat energy and it appears to vanish; the amount of heat produced is so small it isunnoticeable.

Therearemany typesofporoussound-absorbingmaterials.The fact that theaudioband issowide (ten octaves) results in a basic sound-absorption problem:All practical sound absorbers arefrequency dependent. The determining factor in absorption is the wavelength of the sound beingconsidered.Tobeagoodabsorber,aporousabsorbermusthavea thickness thatcorresponds toasignificant fraction of a wavelength. For example, at 100 Hz, the wavelength of sound is 11.3 ft(1130/100=11.3).Itisnotpracticaltobuildaporousabsorbertoverylargedimensions;thusporousabsorbersarenotusedatlowfrequencies.Ontheotherhand,porousabsorbersaremosteffectiveathigher frequencies. As noted below, the thicker the porous material, the lower the extent of thefrequencyresponseofitsabsorption.Alternatively,thematerialcanbeplacedawayfromthesurfacebehindit,ideallyatone-quarterwavelength,withanairspacebetweenthematerialandthesurface.

GlassFiberIn addition to its widespread use as a thermal insulator, glass fiber is widely used as a porousabsorber. Glass fiber is a composite of materials such as sand, limestone, soda ash, and othercomponents.Theseare thesamecomponentsused tomakeplateglassbut thematerial is spun intofibers. A wide variety of glass-fiber materials is available in various forms, for example, ascompressedboards, semirigidboards,and looseblankets.Table3-2 lists the700-seriesglass fiberproductsfromOwens-Corning.Type701(1.5lb/ft3)isafluffybatt(sometimescalledfuzz)usefulforwallinnerspacesandwhereverrigidityisnotrequired.Type703(3.0lb/ft3)isasemirigidboardthatcutsreadilywithaknifeandholdsitsshapewithoutsupport.Type705(6.0lb/ft3)isadenserandmorerigidboardthanthe703.Glassfiberof3-lb/ft3density,whetherfromOwens-Corningorfromothersuppliers, is widely used in acoustical treatment in diverse places and structures, and can beconsideredsomethingofastandardinthefield.

TABLE3-2Owens-Corning700SeriesInsulationTechnicalData

MineralWoolMineralwoolisanotherwidelyusedporousabsorber.Mineralwoolisacompositeofmaterialssuchassand,basalticrock,glass,andothercomponentsthataremeltedandspunorpulledintofilaments.Binderisaddedtoformthefinalproduct.Itisavailableascompressedboards,semirigidboards,andlooseblankets.Mineralwooliswidelyusedinceilingtiles.Itsacousticalpropertiesaresimilartothatofglassfiber.

DensityofAbsorbentOnewouldexpectdensitytohaveanappreciableeffectonamaterialsabsorptioncoefficient.Afterall, a harder surface would be expected to reflect sound more readily than a softer surface. It issurprising to learn thatdifferencesaresmalloveranormalrangeofdensity,asshowninFig.3-1.Thereisasmalleffectatfrequenciesabove500Hz.Generally,glassfiberwithadensityof3lbs/ft3isoftenused.Asnoted,anacousticallytransparentclothcoverwillnotaffectabsorption.

FIGURE3-1Theeffectofdensityonglass-fiberabsorption.(Owens-Corning)

Independentofthequestionofdensity,Fig.3-1alsoshowsthecharacteristicfrequencyresponseofaporousabsorberonarigidbacking.Theabsorberexhibits theshapeofahigh-passfilterwithrelatively little absorption at low frequencies and much greater absorption at higher frequencies.AlthoughFig.3-1istypicalofaporousabsorber,specificabsorberswillexhibitdifferentcurveswithgreaterorlesserabsorptionaswellasfrequencyshiftsinthecurve.Insomecases,particularlyformaterials such as concrete with little absorption, the curves will be much flatter with respect tofrequency.

SpacebehindAbsorbentandThicknessofAbsorbentThe depth of the airspace behind a porousmaterial, and the thickness of thematerial, has a greateffectonthesoundabsorptioncharacteristicsofthematerial.Foroptimalabsorptioninaparticularfrequency region, a porous material should be placed at a distance of a quarter wavelength(maximumcompression) from the reflecting surface behind the absorber or have a thickness of aquarterwavelength.

Theabsorptioncharacteristicofaglass-fibertestboardof1-inthicknessisshowninFig.3-2;thedensityoftheboardhaslittleeffect,asnotedintheprevioussection.Theboardwithnoairspace(cemented directly on thewall)will be a standard of comparison. Furring a glass-fiber board outfromareflectingsurfacegreatlyincreasestheabsorbingeffect.Infact,the1-inboardfurredouthasthe absorbing efficiency of a much thicker flush-mounted board. The achievement of greaterabsorption can be reduced to the question of whether the furring out is cheaper than a board ofgreaterthickness.

FIGURE3-2Theeffectofairspaceonglass-fiberabsorption.(Owens-Corning)

Generally, absorption at low frequencies increases as the thickness of a porous absorberincreases. Inparticular,absorption ishighwhen theair-particlevelocity ishigh; thusabsorption isincreasedwhenthethicknessoftheabsorberisatleastatenthofthewavelengthtobeabsorbed,andideally should be a quarterwavelength. Particle velocity is low close to a rigid boundary so littleabsorptionoccurs there; thisexplainswhy thinporousabsorbersare ineffective.Velocity ishigherfarther out from the boundary so the outer surfaces of thicker absorbers can absorb longerwavelengths;thisexplainswhythickabsorbers,orabsorbersspacedawayfromthemountingsurface,aremore effective.A practical limit is reachedwhen the thickness required (determining the low-frequency limit of absorption) becomes too great. This is why porous absorbers are not usuallyeffectiveforlow-frequencyabsorption.

Figure3-3shows theeffectof the thicknessofaglass-fiberboard in termsofwave-lengthofsound.Thewavelengthofsoundat250Hzisabout4.5ft.Thequarterwavelengthisabout13in.Thethicknessof the4-inglass-fiberboardapproachesthequarterwavelengthof250-Hzsound,andthegreatsuperiorityoftheabsorptionofthe4-inboardoverthe1-inboardisduestrictlytothisfact.Theconclusionissimple:tobeeffectiveoverarangeoffrequencies,aporousabsorbermustbethick,orelsespacedawayfromtheboundarysurface.

FIGURE3-3Theeffectofthicknessofglassfiberonabsorption.(Owens-Corning)

Handling4-inglass-fiberboards(andeventhicker)canbeaproblemintheacousticaltreatmentofa studio.Some framingstructurewillbeneeded tohold the4-inor6-inboardand toprotect itfrom damage. For low-frequency absorption, porous absorbers inefficiently must occupy a largevolume.Thuswhenabsorptionbelow125Hzis required,attention isusuallydirected towardothermethodsofachievingit,suchasresonators.

TheAreaEffectAs noted, the total absorption is a function of a materials sound absorption coefficient, and theamountofsurfaceareaof thematerial.However, totalabsorption isalsoaffectedby thematerialsdistributionintheroom.Anumberofporouspanelswillhavegreatertotalabsorptionwhenspacedapart fromeach other (for example, in a checkerboard pattern), thanwhenplaced together; this isknownastheareaeffect(Bartel,1981).Theeffectoccursbecauseofsounddiffractionattheedgesofthepanels,andbytheadditionalabsorptionsurfaceareaprovidedbytheexposededgesofthepanels.Thisperimeterareaisefficientlyutilizedbecauseoffurtherreflectionsfromthehardsurfacenearthepaneledges.Theareaeffectcanalsoadddesirablediffusiontoawallsurface.Ontheotherhand,asurfaceofspacedapartpanelswillprovideslightlylesstotalabsorptionthaniftheentiresurfacewascoveredwithabsorption.Obviously,theareaeffectprovidesanefficientwaytominimizeabsorptioncosts.

Ceiling-MountedAbsorptionAbsorption can be efficiently achieved by taking advantage of certain ways of designing ceiling-

mountedabsorbers.Absorbingpanelscanbehungfromtheceilingindividuallyoraspreassembledmodules.Thiscangreatlyincreasetheexposedabsorptionsurfacearea.Forexample,hanginga1-ft2panelcanexposea2-ft2areaofabsorption.Becausetheamountofabsorptionpersquarefootismuchhigher than the materials absorption coefficient measured over 1 ft2, the effective absorptioncoefficientcanbegreater than the theoretical limitof1.0.However,panelsmustbespacedapart topreventonepanelfromblockingsoundentrytoanother;insomecases,theratioofexposedsurfaceareatotheceilingareashouldnotexceed0.5.

AcousticalTileAcousticaltileplacedonwallareasandceilingsisacost-effectivewaytoaddabsorptiontoaroom.Inaddition,tileisnotpronetowearandtearwhenplacedontheceiling.Itiscommontoselect1212-inacoustictilewithanaveragethicknessof1/2in.ThesearecementedtothesurfaceorplacedinT-bar ceiling suspension systems. Figure 3-4 shows the spread of the data among eight differentbrandsof3/4-inacoustictile.Goodabsorptionabove500Hzisthegeneralrule,droppingoffquicklybelowthatfrequency.

FIGURE3-4Thegeneralabsorptioncharacteristicofacousticaltiles.

Glass-FiberAbsorberPanelsAglass-fiberblanket is anefficient absorber. It canbeused toconstruct absorbingpanels thatwillprovide excellent wideband absorption above 125Hz; an example is shown in Fig. 3-5. A frame,measuringperhaps22 ft or larger, canbe constructedof 16-in lumber, reinforcedby cross-bracing.Abackingboardof1/4-inplywoodorMasoniteaddssturdiness.Theframeispackedwitha4-in thickglass-fiberblanketof3-lb/ft3 density. Instead of a 4-in blanket, two2-in blankets can beused.Ifdesired,zig-zagwirescanbestretchedacrossthefrontofthepaneltohelpholdtheblanketinplaceatthefrontofthepanel.Anairspaceofabout2-inbehindtheglassfiberhelpsextendabsorption

to lower frequencies.An expandedmetal lathe can be used across the front.An open-weave clothcover conceals and contains the glass fiber. Alternatively, manufactured cloth-covered glass-fiberpanels are available. In either case, it must be verified that the cloth material is acousticallytransparent;manytypesofclothdonotmeetthisimportantcriteria.

FIGURE3-5Anexampleofabroadbandabsorberpanelusingglassfiberwithinawoodframe.

For a given thickness, in the 125-Hz to 4-kHz range, the absorption properties of glass-fiberblanketsandrigidpanelsaresimilar.High-densityglass-fiberpanelsmaybecomemorereflectiveathigh frequencies. For all types of glass fiber, low-frequency absorption improves with greaterthickness.Insomecases,porousabsorbersarecoveredbyathinplasticorpapermembranetoprotecttheunderlyingmaterial;themembranedecreaseshigh-frequencyabsorptionbutdoesnotaffectotherabsorptioncharacteristics.Whenpossible,thissideshouldbeplacedagainstthewall,andnotfacingtheincidentsound.

Thesemodulescanbeplacedonwallsurfaces.Thepanelsarereversible;hookscanbeplacedonthefrontandbacksurfacessothatboththeabsorptiveandreflectivesidescanbeusedasneeded.Alternatively, the panels can be mounted on hinges so that both sides can be exposed to incidentsound.Asanotheroption,agridcanbeconstructedandpermanentlymountedonthewall;absorberpanels can be inserted into open spaces in the gridwith either the absorptive or refl