音箱线阵列能否产生柱面波

关于音箱的波束导向以及线阵列的指向性控制对于线阵列，多个品牌都在介绍自己的独特技术，但从物理层面来讲，不少“技术”都有吹嘘之嫌。我在这里抛砖引玉，欢迎大家讨论。扬声器不象手电筒，声音的特性也跟光线的特性不同，扬声器不能象手电筒一样对各频段的声音产生锐利的投射声束，而且声音也不象光束，不同的声音覆盖在同一块地方会因相位的关系相互抵消和出现梳状滤波（事实上，不同的光源发出的光线在同一处叠加也会相互抵消和产生梳状滤波，不过由于光速太快，波长太短，使得人眼不能分辨而已）。虽然怎样处理扬声器波束导向的书和论文都很少。可是，在军事上很早就有两个领域应用了波束导向技术：天线阵（相控雷达）和水下天线阵（声纳），而且应用广泛。相对于雷达和声纳，扬声器的波束导向是相当困难的，因为人耳的听域范围非常宽，从20Hz（低频）到20KHZ（高频）。一个20Hz纯音的波长是15.25米，而一个20KHZ纯音的波长仅0.013米。这11倍频程的频率范围使波束导向的变得非常困难。事实上，雷达和声纳的工作频率范围最多是单个倍频程，往往只是工作在单一频率。如果只需单个频率的声音进行导向，也很容易做到，但是，从20Hz（低频）到20KHZ（高频）就很困难了。由于阵列的间隔和几何尺寸对波束的传播都有影响，通常，对不同的阵列进行优化处理用于不同的频率范围，而这对于专业音频领域的应用是不切实际的，它受扬声器单元尺寸和工艺的限制，波束导向在专业音频的应用只限制于某一频段。为了使波束导向能够应用，阵列中的每一个扬声器单元的辐射区域必须和阵列中其它扬声器的辐射区域相叠加，如果从两个（或更多）的扬声器单元辐射出来的声音不能交叠，声音的导向跟本无从谈起，相关的理论可以查阅波动力学。对于现在市场上的所有线阵列音箱，线阵列看上去象紧密排列的单元——看上去就象雷达理论书上所示的图形，也跟介绍波束导向理论中理想化的全指向单元所组成的图形相同。——但是它们的本质是非常不同的，现在的所有线阵列的本质都是低频（有的包括中频）都是采用直接辐射的方式，而高频采用波导（Waveguides）方式。而也没有任何的一款线阵列音箱产生柱面波，详情请查阅《CanlineArraysFormCylindricalWaves》一文（线阵列能否产生柱面波）。（原文如下）。只是不同品牌采用了不同的波导方式而已。CanLineArraysformcylindricalWavesWrittenbyMeyerSound线阵列能否产生柱面波WhatIsaLineArray?Alinearrayisagroupofradiatingelementsarrayedinastraightline,closelyspacedandoperatingwithequalamplitudeandinphase.DescribedbyOlsoninhis1957classictext,AcousticalEngineering,linearraysareusefulinapplicationswheresoundmustbeprojectedoverlongdistances.Thisisbecauselinearraysaffordverydirectionalverticalcoverageandthusprojectsoundeffectively.什么是线阵列?

线阵列是指一组排列在一条直线上的辐射元件，它们紧密的靠紧，工作时有着相同的振幅及相位。Olson于1957年在他的经典著作＜＜AcousticalEngineering〉＞中说过：线阵列在需要长距离声音传输的场合中是非常有用的。这是因为线阵列提供非常直接的垂直覆盖范围，因而有效地辐射出声音。Fig.1.Directionalbehaviorofaneightmeterlongarrayofsixteenomni-directionalsourcesTheMAPPplotsofFigure1illustratethedirectionalcharacteristicsofalinearraycomposedofsixteenomni-directionalsourcesuniformlyspaced0.5metersapart.Thearrayishighlydirectionalto500Hz;abovethat,thedirectionalcharacteristicbeginstobreakdown.Notethestrongrearlobeatlowfrequencies;allconventionallinearrayswillexhibitthisbehaviorbecausetheyareomnidirectionalinthisrange.Notealsothestrongverticallobesat500Hz.(Thehorizontalpatternofthissystemisindependentofthevertical,andisomni-directionalatallfrequencies.)

Fig.2.Directionalbehaviorofaneightmeterlongarrayofthirty-twoomni-directionalsourcesFigure2showsalineofthirty-twosourcesspaced0.25metersapart.Noticethatthisarraymaintainsitsdirectionalcharacteristicto1kHz,wherethestrongverticallobeappears.Thisillustratesthefactthatdirectionalityathighfrequenciesrequiresprogressivelymorecloselyspacedelements.HowDoLineArraysWork?Linearraysachievedirectivitythroughconstructiveanddestructiveinterference.Asimplethoughtexperimentillustrateshowthisoccurs.Consideraspeakercomprisingasingletwelve-inchconeradiatorinanenclosure.Weknowfromexperiencethatthisspeaker'sdirectivityvarieswithfrequency:atlowfrequencies,itisom-ndiirectional;asthesoundwavelengthgrowsshorter,itsdirectivitynarrows;andaboveabout2kHz,itbecomestoobeamyformostapplications.Thisiswhypracticalsystemdesignsemploycrossoversandmultipleelementstoachievemoreorlessconsistentdirectivityacrosstheaudioband.Stackingtwoofthesespeakersoneatoptheotheranddrivingbothwiththesamesignalresultsinadifferentradiationpattern.Atpointson-axisofthetwothereisconstructiveinterference,andthesoundpressureincreasesby6dBrelativetoasingleunit.Atotherpointsoff-axis,pathlengthdifferencesproducecancellation,resultinginalowersoundpressurelevel.Infact,ifyoudrivebothunitswithasinewave,therewillbepointswherethecancellationiscomplete(thisisbestdemonstratedinananechoicchamber).Thisisdestructiveinterference,whichisoftenreferredtoascombing.Alinearrayisalineofwooferscarefullyspacedsothatconstructiveinterferenceoccurson-axisofthearrayanddestructiveinterference(combing)isaimedtothesides.Whilecombinghastraditionallybeenconsideredundesirable,linearraysusecombingtowork:withoutcombing,therewouldbenodirectivity.CanaLineArrayFormCylindricalWaves?Inaword,no.Thecommonmisconceptionregardinglinearraysisthattheysomehowmagicallyenablesoundwavestocombine,formingasingle"cylindricalwave"withspecialpropagationcharacteristics.Underlinearacoustictheory,however,thisisimpossible:theclaimisnotsciencebutamarketingploy.Unlikeshallowwaterwaves,whicharenon-linearandcancombinetoformnewwaves,soundwavesatthepressurescommoninsoundreinforcementcannotjointogether:rather,theypassthroughoneanotherlinearly.Evenatthehighlevelspresentinthethroatofcompressiondrivers,soundwavesconformtolineartheoryandpassthroughoneanothertransparently.Evenatpressurelevelsof130dBnonlineardistortionislessthan1%.TheMAPPplotofFigure3,whichshowsacross-firedpairofMeyerMSL-4loudspeakers,illustratesthispoint.AtthearealabeledA,inthecrossfireregion,thereissignificantdestructiveinterferenceinthedarkareas.AtthearealabeledB,however,theoutputofthecorrespondingMSL-4iscompletelyunaffectedbythecross-firingunit.ThoughthewavesinterfereatA,theinterferenceislocaltothatareainspace,andtheystillpassthroughoneanotherunaffected.Infact,youcouldturnoffthecross-firingunitandhearvirtuallynochangewhatsoeveratB.Fig.3.Cross-firedMSL-4loudspeakersThisexperimentisbestdoneinananechoicchamberoroutdoorsinanopenfield,awayfromreflectingsurfaces.It'salsoadvisabletoapplyalow-cutfiltertoremoveinformationbelowabout500Hz,wheretheMSL-4startstolosedirectionality.Butdon'tlinearraysproducewavesthatonlydrop3dBwitheverydoublingofthedistancefromthearray?Thissimplisticmarketingclaimappearstobeamisapplicationofclassicallinearraytheorytopracticalsystems.Classicallinearraymathematicsassumesalineofinfinitelysmall,perfectlyomni-directionalsourcesthatisverylargecomparedwiththewavelengthoftheemittedenergy.Obviously,practicalsystemscannotapproachtheseconditions,andtheirbehaviorisfarmorecomplexthansomeaudiocompanymarketerssuggest.Modelingthebehaviorofafifteen-inchwooferwithBesselfunctions(whichdescribeapiston),MeyerSoundhaswrittencustomcomputercodetomodellinearrayswithvariousnumbersofloudspeakersatvariousspacings.Thiscomputationshowsthatitistheoreticallypossibletoconstructanaudiolinearraythatfollowsthetheoryatlowfrequencies,butitrequiresmorethan1,000fifteen-inchdrivers,spacedtwentyinchescenter-to-center,todoit!Atruncatedcontinuouslinearraywillproducewavesthatdrop3dBperdoublingofdistanceinthenearfield,buttheextentofthenearfielddependsonthefrequencyandthelengthofthearray.Somewouldhaveusbelievethat,forahybridcone/waveguidesystem,thenearfieldextendshundredsofmetersathighfrequencies.Itcanbeshownmathematicallythatthisistrueforalineof100smallomni-directionalsourcesspacedaninchapart,butthatishardlyapracticalsystemforsoundreinforcementandisnotamodelforthebehaviorofwaveguides.Nordoesthepurelytheoreticalcomputationreflecttherealityofairabsorptionanditseffectsathighfrequencies.Thetablebelowshowstheattenuationatvariousdistancesfromanarrayof100one-inchpistonsspacedoneinchapart,asmodeledusingaBesselfunction.At500Hzandabove,italsoshowsthetotalattenuationwhenairabsorptionisincludedusingthecalculationgiveninANSIStandardS1.26-1995(theconditionsforthistableare20°Cambienttemperatureand11%relativehumidity).Notethat,whileat16kHzthearrayasmodeledbytheBesselfunctionisapproaching3dBattenuationperdoublingofdistance,airabsorptionmakesitsactualbehaviorcloserto6dBperdistancedoubling.2meters4meters8meters16meters32meters64meters128meters256meters125Hz05.5111723293541250Hz05111723293541500Hz02.37.21319253137w/airabsorption381kHz01.33.28.214202632w/airabsorption152128352kHz035.2]712182430w/airabsorption8132129414kHz02.76.3911162127w/airabsorption3.17.111142335598kHz02.858.611131824w/airabsorption3.56121725427216kHz03.16.68.212141621w/airabsorption4.18.612203349883dBperdoubling036]9121518216dBperdoubling06121824303642Table1.Attenuationindecibelsforoctavefrequencybandsatvariousdistancesfromalinearrayof100one-inchpistonsspacedoneinchapartWithapractical,reallinearrayofsixteencabinets(eachusingfifteen-inchlowfrequencycones),aslight"cylindricalwave"effectcanbemeasuredatabout350Hz,wherethereisa3dBdropbetweentwoandfourmetersfromthearray.Morethanfourmetersfromthearray,however,thesoundspreadsspherically,losing6dBperdistancedoubling.ThisbehaviorcanbeconfirmedwithMAPPusingthemeasureddirectionalityofrealloudspeakers.Atfrequenciesbelow100Hz,thedriversinapracticallinearraywillbeomni-directionalbutthearraylengthwillbesmallcomparedwiththesoundwavelength,sothesystemwillnotconformtolinearraytheory.Aboveabout400Hzthelow-frequencyconesbecomedirectional,againviolatingthetheory'sassumptions.Andtahighfrequencies,allpracticalsystemsusedirectionalwaveguideswhosebehaviorcannotbedescribedusinglinearraytheory.Inshort,thegeometryofrealaudiolinearraysisfartoocomplicatedtobemodeledaccuratelybyantennatheory.Theycanonlybeaccuratelymodeledbyacomputationalcodethatusesahigh-resolutionmeasurementofthecomplexdirectionalityofactualloudspeakers,suchasMAPP.Thatsaid,practicallinearraysystemsremainveryusefultools,regardlessofwhetherthecontinuouslinearrayequationapplies.Theystillachieveeffectivedirectionalcontrol,andskilleddesignerscanmakethembehaveverywellinlong-throwapplications.HowDoPracticalLineArraySystemsHandleHighFrequencies?Figures1and2showthatlinearraytheoryworksbestforlowfrequencies.Asthesoundwavelengthdecreases,moreandmoredrivers,smallerinsizeandspacedmoreclosely,arerequiredtomaintaindirectivity.Thisiswhysomelinearraysystemscrossovertoeight-inchdriversforthemidrange.Eventually,however,itbecomesimpracticaltouse,forexample,hundredsofcloselyspacedone-inchcones.Practicallinearraysystemsthereforeactaslinearraysonlyinthelowandmidfrequencies.Forthehighfrequencies,someothermethodmustbeemployedtoattaindirectionalcharacteristicsthatmatchthoseofthelowsandmids.Themostpracticalmethodforreinforcementsystemsistousewaveguides(horns)coupledtocompressiondrivers.Ratherthanusingconstructiveanddestructiveinterference,hornsachievedirectionalitybyreflectingsoundintoaspecifiedcoveragepattern.Inaproperlydesignedlinearraysystem,thatpatternshouldcloselymatchthelow-frequencydirectionalcharacteristicofthearray:verynarrowverticalcoverageandwidehorizontalcoverage.(Narrowverticalcoveragehasthebenefitthatitminimizesmultiplearrivals,whichwouldharmintelligibility.)Ifthisisachieved,thenthewaveguideelementscanbeintegratedintothelinearrayand,withproperequalizationandcrossovers,thebeamfromthehighfrequenciesandtheconstructiveinterferenceofthelowfrequenciescanbemadetoalignsothattheresultingarrayedsystemprovidesconsistentcoverage.CanLineArrayLoudspeakersBeUsedSingly?No,theconedriversinalinearrayloudspeakerneedtheotherconesinthearraytocreatedirectionality.Theconesinasinglecabinethavethesamedirectionalcharacteristicsascomparableconedriversinothertypesofloudspeakers.Inotherwords,eachcabinetinalinearrayisnotproducinga"sliceofacylindricalwave."Thatisamarketingconcept,notascientificone.CanYouCurveaLineArraytoGetWiderCoverage?Inpractice,gentlycurvingalinearray(nomorethanfivedegreesofsplayamongcabinets)canaidincoveringabroaderarea.Radicallycurvinglinearrays,however,introducesproblems.First,ifthehigh-frequencysectionhasthenarrowverticalpatternthat'srequiredtomakeastraightarraywork,curvingthearraycanproducehotspotsandareasofpoorhigh-frequencycoverage.Second,whilethecurvaturecanspreadhighfrequenciesoveralargerarea,itdoesnothingtothelowfrequencies,whichremaindirectionalbecausethecurvatureistrivialatlongwavelengths.Figure4illustratesthesepoints.OntheleftisaseriesofMAPPplotsforacurvedarray,andontherightareplotsofastraightarray.Botharraysareconstructedofidenticalloudspeakershavinga12-inchconelow-frequencydriverandahigh-frequencyhornwitha45-degreeverticalpattern.Notableintheleft-handplotsisthat,whilethewiderhornaidsinspreadingthehighfrequencies,italsointroducespronouncedlobingduetointerference.At1kHzandbelow,thearrayremainshighlydirectional,followinglinearraytheory.Inpractice,thisbehaviorwouldproduceveryunevencoverage,withthefrequencyresponsevaryingsubstantiallyacrossthecoverageareaandalargeproportionofthatareareceivingalmostnolow-frequencyenergy.Theright-handseriesofplotsrevealsthataloudspeakerwithamoderatelywide-coveragehorndesignedforcurvedarraysbehavespoorlyinastraightarray.Whilethearrayishighlydirectional,pronouncedverticallobingoccursat1kHzandabove.Thesestrongsidelobesdivertenergyfromtheintendedcoverageareaandwouldexcitethereverberantfieldexcessively,reducingintelligibility.

Fig.4.Directionalcharacteristicsofacurved(left)andstraight(right)linearrayusingahigh-frequencyhornwitha45-degreeverticalpatternCanYouCombineLineArraysWithOtherTypesofSpeakers?Yes,sincelinearwavespassthroughoneanotherregardlessofwhethertheyarecreatedbyadirectradiatororawaveguide,itispossibletocombinelinearraysystemswithothertypesofloudspeakersaslongastheirphaseresponsematchesthatofthelinearrayspeakers.Thereisnothingspecialaboutthesoundwavesthatlinearrayscreate.Theyaremerelytheoutputoflow-frequencycones,spacedusinglinearraytheory,andhigh-frequencywaveguides.Therefore,skilleddesignerswiththepropertoolscanflexiblyintegrateothercompatibletypesofloudspeakerstocovershort-throwareas.Fig.5.ACQ-1riggedunderanM3DlinearrayprovidesdownfillcoverageHowDoLineArraysBehaveintheNearandFarField?Aswehaveseen,practical"linearray"systemsasusedinhigh-powerapplicationsareactuallyacombinationof"classical"linearraysforthelowfrequenciesandhighlydirectivewaveguidesforthehighfrequencies.Becauseofthishybridnature,itisdifficulttoapplypredictionsfromclassicallinearraytheoryacrossthewholeaudiospectrum.Nonetheless,linearraysystemscanbemadetoworkreasonablywellinboththefarfieldandmoderatelyclosetothearray.Seenfromthefarfield,theoutputsoftheindividualsourcesinalinearraycombineconstructively,andappeartooperateasonesource.Figure6illustratesthisconcept.Thefigureshowsthe-ffiealrdfrequencyresponseforlinearraysoftwo,fourandeightomni-directionalradiators(asingle-omniresponseisincludedforreference)spaced0.4metersapart.Noticethateachdoublingofthenumberofelementsresultsinauniform6dBlevelincreaseacrossthefullfrequencyrangeofoperation.Thehighfrequencyresponseissmooth,butreflectsanaturalrolloffduetoa