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SoundSystemDesignReferenceManual6-1Chapter6:BehaviorofSoundSystemsIndoorsIntroductionTheprecedingfivechaptershaveprovidedthegroundworkonwhichthischapterisbuilt.The“fineartandscience”ofsoundreinforcementnowbeginstotakeshape,andmanyreaderswhohavepatientlyworkedtheirwaythroughtheearlierchapterswillsoonbegintoappreciatethedisciplineswhichhavebeenstressed.Thedateatwhichsoundreinforcementgrewfrom“publicaddressbyguesswork”toamethodicalprocessinwhichperformancespecificationsareworkedoutinadvancewasmarkedbythepublicationin1969ofapapertitled“TheGainofaSoundSystem,”byC.P.andR.E.Boner(4).Itdescribesamethodofcalculatingpotentialsoundsystemgain,andthatmethodhassincebecomeafundamentalpartofmodernsoundsystemdesign.ThefollowingdiscussionisbasedontheBonerpaper.Certainpointsareexpanded,andexamplesaregiventhatrequirecalculationsmorecomplicatedthanthoseintheoriginalstudy.Alsodiscussedistherelationbetweentheoreticallyachievablesystemgainandpracticaloperatingparametersoftypicalindoorsoundsystems.Figure6-1.AnindoorsoundsystemSoundSystemDesignReferenceManualAcousticalFeedbackandPotentialSystemGainJustasintheoutdoorcasestudiedearlier,ifwehaveamicrophone/amplifier/loudspeakercombinationinthesameroomandgraduallyturnupthegainoftheamplifiertoapointapproachingsustainedfeedback,theelectricalfrequencyresponseofthesystemchangeswiththegainsetting.Theeffectresultsfromanacousticfeedbackpathbetweentheloudspeakerandthemicrophone.Asapersontalksintothemicrophone,themicrophonehearsnotonlythedirectsoundfromthetalker,butthereverberantfieldproducedbytheloudspeakeraswell.Thepurposeofusinghigh-qualityloudspeakersandmicrophoneshavingsmoothresponsecharacteristics,andsoundsystemequalization(apartfromachievingthedesiredtonalresponse)istosmoothoutallofthepotentialfeedbackpointssothattheyareevenlydistributedacrosstheaudiblefrequencyrange.Whenthishasbeendone,thereshouldbeasmanynegativefeedbackpointsaspositivefeedbackpoints,andthepositivefeedbackpointsshouldallreachthelevelofinstabilityataboutthesamesystemgain.Wemightexpectthistoaverageoutinsuchawaythatthelevelproducedbytheloudspeakerreachingthemicrophonecanneverbegreaterthanthatproducedbythetalkerwithoutcausingsustainedoscillation.Inotherwords,weassumethattheextragainsuppliedbyallthepositivefeedbackspikesisjustbalancedoutbythelosscausedbyallthenegativefeedbackdips.IftheBonercriteriaforoptimumsystemgeometryarefollowed,themicrophonewillbeclosetothetalkersothatithearsmostlydirectsoundfromthetalker.Itwillbefarenoughfromtheloudspeakertobewellintothereverberantfieldoftheloudspeaker,sothatdirectsoundfromtheloudspeakerisnotanappreciablefactorintriggeringsystemfeedback.Assumingthatlistenersarealsointhereverberantfieldoftheloudspeaker,itfollowsthatthesoundlevelinthelisteningareawiththesystemturnedoncannotbegreaterthanthatoftheunaidedtalkeratthemicrophonepositionwiththesystemturnedoff.UsingtheBonerconceptofsystemdelta,thesituationatmaximumgaincorrespondstoadeltaofunity.(Deltaisdefinedasthedifferenceindecibelsbetweensoundlevelatthesystemmicrophonewithsystemoffandthelevelintheaudienceareawithsystemon.SeeFigure6-1).Althoughwehavedescribedtheseasconditionsofmaximumpotentialsystemgain,itispossibleinpracticetoachieveadeltagreaterthanunity.Forexample,ifadirectionalmicrophoneisuseditcandiscriminateagainstthereverberantfieldandallowanother3to4dBofsystemgain.Anotherpossibilityistoplacethelistenerinthedirectfieldoftheloudspeaker,allowingafurtherincreaseinsystemgain.Ifthelevelofthereverberantfieldislowerintheperformingareathaninthelisteningarea,additionalsystemgainalsoresults.ThissituationisdescribedbytheBonersasaroomconstantinthemicrophoneareadifferentfromthatintheseatingarea.Similarresultsmaybenotedinroomshavinglargefloorareas,relativelylowceilings,andsubstantialsoundabsorption.Insuchrooms,aswehaveseen,soundfromapointsourcetendstodwindleoffbeyondDCatarateof2or3dBforeachdoublingofdistanceratherthanremainingconstantinlevel.Stillanotherwaytoincreasegainistoelectricallysuppressthepositivefeedbackfrequenciesindividuallywithverynarrowbandwidthfilters.Ifonecouldchannelallenergyintothenegativefeedbackfrequencies,thepotentialsystemgainwouldtheoreticallybecomeinfinite!Unfortunately,theacousticfeedbackpathisnotstableenoughtopermitthisdegreeofnarrow-bandequalization.Inallothersituations,againsettingisreachedatwhichsustainedoscillationoccurs.Bydefinition,maximumsystemgainisreachedjustbelowthispoint.However,thesystemcannotbeoperatedsatisfactorilyatapointjustbelowoscillationbecauseofitsunpleasantcomb-filterresponseandtheprolongedringingcausedbypositivefeedbackpeaks.Togetbacktoreasonablyflatelectricalresponseandfreedomfromaudibleringing,itusuallyisrecommendedthataproperlyequalizedsystembeoperatedabout6dBbelowitsmaximumgainpoint.Evenanelaboratelytunedsystemusingnarrow-bandfilterscanseldombeoperatedatgainsgreaterthan3dBbelowsustainedoscillation.SoundFieldCalculationsforaSmallRoomConsidertheroomshowninFigure6-2.Thisisatypicalsmallmeetingroomorclassroomhavingavolumelessthan80m3.Theaverageabsorptioncoefficientais0.2.Totalsurfaceareais111m2.Theroomcons