音箱線陣列能否產(chǎn)生柱面波

1、關(guān)于音箱的波束導(dǎo)向以及線陣列的指向性控制對于線陣列，多個品牌都在介紹自己的獨特技術(shù)，但從物理層面來講，不少“技術(shù)”都有吹噓之嫌。我在這里拋磚引玉，歡迎大家討論。揚聲器不象手電筒，聲音的特性也跟光線的特性不同，揚聲器不能象手電筒一樣對各頻段的聲音產(chǎn)生銳利的投射聲束，而且聲音也不象光束，不同的聲音覆蓋在同一塊地方會因相位的關(guān)系相互抵消和出現(xiàn)梳狀濾波（事實上，不同的光源發(fā)出的光線在同一處疊加也會相互抵消和產(chǎn)生梳狀濾波，不過由于光速太快，波長太短，使得人眼不能分辨而已）。雖然怎樣處理揚聲器波束導(dǎo)向的書和論文都很少?？墒?，在軍事上很早就有兩個領(lǐng)域應(yīng)用了波束導(dǎo)向技術(shù)：天線陣（相控雷達）和水下天線陣（聲納）

2、，而且應(yīng)用廣泛。相對于雷達和聲納，揚聲器的波束導(dǎo)向是相當(dāng)困難的，因為人耳的聽域范圍非常寬，從20Hz（低頻）到20KHZ（高頻）。一個20Hz純音的波長是15.25米,而一個20KHZ純音的波長僅0.013米。這11倍頻程的頻率范圍使波束導(dǎo)向的變得非常困難。事實上，雷達和聲納的工作頻率范圍最多是單個倍頻程，往往只是工作在單一頻率。如果只需單個頻率的聲音進行導(dǎo)向，也很容易做到，但是，從20Hz（低頻）到20KHZ（高頻）就很困難了。由于陣列的間隔和幾何尺寸對波束的傳播都有影響，通常，對不同的陣列進行優(yōu)化處理用于不同的頻率范圍，而這對于專業(yè)音頻領(lǐng)域的應(yīng)用是不切實際的，它受揚聲器單元尺寸和工藝的限制

3、，波束導(dǎo)向在專業(yè)音頻的應(yīng)用只限制于某一頻段。為了使波束導(dǎo)向能夠應(yīng)用，陣列中的每一個揚聲器單元的輻射區(qū)域必須和陣列中其它揚聲器的輻射區(qū)域相疊加，如果從兩個（或更多）的揚聲器單元輻射出來的聲音不能交疊，聲音的導(dǎo)向跟本無從談起，相關(guān)的理論可以查閱波動力學(xué)。對于現(xiàn)在市場上的所有線陣列音箱，線陣列看上去象緊密排列的單元看上去就象雷達理論書上所示的圖形，也跟介紹波束導(dǎo)向理論中理想化的全指向單元所組成的圖形相同。但是它們的本質(zhì)是非常不同的，現(xiàn)在的所有線陣列的本質(zhì)都是低頻（有的包括中頻）都是采用直接輻射的方式，而高頻采用波導(dǎo)（Waveguides）方式。而也沒有任何的一款線陣列音箱產(chǎn)生柱面波，詳情請查閱Can

4、lineArraysFormCylindricalWaves一文（線陣列能否產(chǎn)生柱面波）。（原文如下）。只是不同品牌采用了不同的波導(dǎo)方式而已。CanLineArraysformcylindricalWavesWrittenbyMeyerSound線陣列能否產(chǎn)生柱面波WhatIsaLineArray?Alinearrayisagroupofradiatingelementsarrayedinastraightline,closelyspacedandoperatingwithequalamplitudeandinphase.DescribedbyOlsoninhis1957classictext

5、,AcousticalEngineering,linearraysareusefulinapplicationswheresoundmustbeprojectedoverlongdistances.Thisisbecauselinearraysaffordverydirectionalverticalcoverageandthusprojectsoundeffectively.什么是線陣列?線陣列是指一組排列在一條直線上的輻射元件，它們緊密的靠緊，工作時有著相同的振幅及相位。Olson于1957年在他的經(jīng)典著作AcousticalEngineering中說過：線陣列在需要長距離聲音傳輸?shù)膱龊现?/p>

6、是非常有用的。這是因為線陣列提供非常直接的垂直覆蓋范圍，因而有效地輻射出聲音。Fig.1.Directionalbehaviorofaneightmeterlongarrayofsixteenomni-directionalsourcesTheMAPPplotsofFigure1illustratethedirectionalcharacteristicsofalinearraycomposedofsixteenomni-directionalsourcesuniformlyspaced0.5metersapart.Thearrayishighlydirectionalto500Hz;abov

7、ethat,thedirectionalcharacteristicbeginstobreakdown.Notethestrongrearlobeatlowfrequencies;allconventionallinearrayswillexhibitthisbehaviorbecausetheyareomnidirectionalinthisrange.Notealsothestrongverticallobesat500Hz.(Thehorizontalpatternofthissystemisindependentofthevertical,andisomni-directionalat

8、allfrequencies.)Fig.2.Directionalbehaviorofaneightmeterlongarrayofthirty-twoomni-directionalsourcesFigure2showsalineofthirty-twosourcesspaced0.25metersapart.Noticethatthisarraymaintainsitsdirectionalcharacteristicto1kHz,wherethestrongverticallobeappears.Thisillustratesthefactthatdirectionalityathigh

9、frequenciesrequiresprogressivelymorecloselyspacedelements.HowDoLineArraysWork?Linearraysachievedirectivitythroughconstructiveanddestructiveinterference.Asimplethoughtexperimentillustrateshowthisoccurs.Consideraspeakercomprisingasingletwelve-inchconeradiatorinanenclosure.Weknowfromexperiencethatthiss

10、peakersdirectivityvarieswithfrequency:atlowfrequencies,itisomni-directional;asthesoundwavelengthgrowsshorter,itsdirectivitynarrows;andaboveabout2kHz,itbecomestoobeamyformostapplications.Thisiswhypracticalsystemdesignsemploycrossoversandmultipleelementstoachievemoreorlessconsistentdirectivityacrossth

11、eaudioband.Stackingtwoofthesespeakersoneatoptheotheranddrivingbothwiththesamesignalresultsinadifferentradiationpattern.Atpointson-axisofthetwothereisconstructiveinterference,andthesoundpressureincreasesby6dBrelativetoasingleunit.Atotherpointsoff-axis,pathlengthdifferencesproducecancellation,resultin

12、ginalowersoundpressurelevel.Infact,ifyoudrivebothunitswithasinewave,therewillbepointswherethecancellationiscompleteisoftenreferredtoas(thisisbestdemonstratedinananechoicchamber).Thisisdestructiveinterference,whichcombing.Alinearrayisalineofwooferscarefullyspacedsothatconstructiveinterferenceoccurson

13、-axisofthearrayanddestructiveinterference(combing)isaimedtothesides.Whilecombinghastraditionallybeenconsideredundesirable,linearraysusecombingtowork:withoutcombing,therewouldbenodirectivity.CanaLineArrayFormCylindricalWaves?Inaword,no.Thecommonmisconceptionregardinglinearraysisthattheysomehowmagical

14、lyenablesoundwavestocombine,formingasinglecylindricalwavewithspecialpropagationcharacteristics.Underlinearacoustictheory,however,thisisimpossible:theclaimisnotsciencebutamarketingploy.Unlikeshallowwaterwaves,whicharenon-linearandcancombinetoformnewwaves,soundwavesatthepressurescommoninsoundreinforce

15、mentcannotjointogether:rather,theypassthroughoneanotherlinearly.Evenatthehighlevelspresentinthethroatofcompressiondrivers,soundwavesconformtolineartheoryandpassthroughoneanothertransparently.Evenatpressurelevelsof130dBnonlineardistortionislessthan1%.TheMAPPplotofFigure3,whichshowsacross-firedpairofM

16、eyerMSL-4loudspeakers,illustratesthispoint.AtthearealabeledA,inthecrossfireregion,thereissignificantdestructiveinterferenceinthedarkareas.AtthearealabeledB,however,theoutputofthecorrespondingMSL-4iscompletelyunaffectedbythecross-firingunit.ThoughthewavesinterfereatA,theinterferenceislocaltothatareai

17、nspace,andtheystillpassthroughoneanotherunaffected.Infact,youcouldturnoffthecross-firingunitandhearvirtuallynochangewhatsoeveratB.Fig.3.Cross-firedMSL-4loudspeakersThisexperimentisbestdoneinananechoicchamberoroutdoorsinanopenfield,awayfromreflectingsurfaces.Itsalsoadvisabletoapplyalow-cutfiltertorem

18、oveinformationbelowabout500Hz,wheretheMSL-4startstolosedirectionality.Butdontlinearraysproducewavesthatonlydrop3dBwitheverydoublingofthedistancefromthearray?Thissimplisticmarketingclaimappearstobeamisapplicationofclassicallinearraytheorytopracticalsystems.Classicallinearraymathematicsassumesalineofi

19、nfinitelysmall,perfectlyomni-directionalsourcesthatisverylargecomparedwiththewavelengthoftheemittedenergy.Obviously,practicalsystemscannotapproachtheseconditions,andtheirbehaviorisfarmorecomplexthansomeaudiocompanymarketerssuggest.Modelingthebehaviorofafifteen-inchwooferwithBesselfunctions(whichdesc

20、ribeapiston),MeyerSoundhaswrittencustomcomputercodetomodellinearrayswithvariousnumbersofloudspeakersatvariousspacings.Thiscomputationshowsthatitistheoreticallypossibletoconstructanaudiolinearraythatfollowsthetheoryatlowfrequencies,butitrequiresmorethan1,000fifteen-inchdrivers,spacedtwentyinchescente

21、r-to-center,todoit!Atruncatedcontinuouslinearraywillproducewavesthatdrop3dBperdoublingofdistanceinthenearfield,buttheextentofthenearfielddependsonthefrequencyandthelengthofthearray.Somewouldhaveusbelievethat,forahybridcone/waveguidesystem,thenearfieldextendshundredsofmetersathighfrequencies.Itcanbes

22、hownmathematicallythatthisistrueforalineof100smallomni-directionalsourcesspacedaninchapart,butthatishardlyapracticalsystemforsoundreinforcementandisnotamodelforthebehaviorofwaveguides.Nordoesthepurelytheoreticalcomputationreflecttherealityofairabsorptionanditseffectsathighfrequencies.Thetablebelowsh

23、owstheattenuationatvariousdistancesfromanarrayof100one-inchpistonsspacedoneinchapart,asmodeledusingaBesselfunction.At500Hzandabove,italsoshowsthetotalattenuationwhenairabsorptionisincludedusingthecalculationgiveninANSIStandardS1.26-1995(theconditionsforthistableare20Cambienttemperatureand11%relative

24、humidity).Notethat,whileat16kHzthearrayasmodeledbytheBesselfunctionisapproaching3dBattenuationperdoublingofdistance,airabsorptionmakesitsactualbehaviorcloserto6dBperdistancedoubling.2meters4meters3meters.6meters32meters64meters128meters256meters125Hz05.5111723293541250Hz05111723293541500Hz02.37.2131

25、9253137w/airabsorption381kHz01.33.28.214202632w/airabsorption152128352kHz035.2712182430w/airabsorption8132129414kHz02.76.3911162127w/airabsorption3.17.111142335598kHz02.858.611131824w/airabsorption3.56121725427216kHz03.16.68.212141621w/airabsorption4.18.612203349883dBperdoubling0369121518216dBperdou

26、bling06121824303642Table1.Attenuationindecibelsforoctavefrequencybandsatvariousdistancesfromalinearrayof100one-inchpistonsspacedoneinchapartWithapractical,reallinearrayofsixteencabinets(eachusingfifteen-inchlowfrequencycones),aslightcylindricalwaveeffectcanbemeasuredatabout350Hz,wherethereisa3dBdrop

27、betweentwoandfourmetersfromthearray.Morethanfourmetersfromthearray,however,thesoundspreadsspherically,losing6dBperdistancedoubling.ThisbehaviorcanbeconfirmedwithMAPPusingthemeasureddirectionalityofrealloudspeakers.Atfrequenciesbelow100Hz,thedriversinapracticallinearraywillbeomni-directionalbutthearr

28、aylengthwillbesmallcomparedwiththesoundwavelength,sothesystemwillnotconformtolinearraytheory.Aboveabout400Hzthelow-frequencyconesbecomedirectional,againviolatingthetheorysassumptions.Andathighfrequencies,allpracticalsystemsusedirectionalwaveguideswhosebehaviorcannotbedescribedusinglinearraytheory.In

29、short,thegeometryofrealaudiolinearraysisfartoocomplicatedtobemodeledaccuratelybyantennatheory.Theycanonlybeaccuratelymodeledbyacomputationalcodethatusesahigh-resolutionmeasurementofthecomplexdirectionalityofactualloudspeakers,suchasMAPP.Thatsaid,practicallinearraysystemsremainveryusefultools,regardl

30、essofwhetherthecontinuouslinearrayequationapplies.Theystillachieveeffectivedirectionalcontrol,andskilleddesignerscanmakethembehaveverywellinlong-throwapplications.HowDoPracticalLineArraySystemsHandleHighFrequencies?Figures1and2showthatlinearraytheoryworksbestforlowfrequencies.Asthesoundwavelengthdec

31、reases,moreandmoredrivers,smallerinsizeandspacedmoreclosely,arerequiredtomaintaindirectivity.Thisiswhysomelinearraysystemscrossovertoeight-inchdriversforthemidrange.Eventually,however,itbecomesimpracticaltouse,forexample,hundredsofcloselyspacedone-inchcones.Practicallinearraysystemsthereforeactaslin

32、earraysonlyinthelowandmidfrequencies.Forthehighfrequencies,someothermethodmustbeemployedtoattaindirectionalcharacteristicsthatmatchthoseofthelowsandmids.Themostpracticalmethodforreinforcementsystemsistousewaveguides(horns)coupledtocompressiondrivers.Ratherthanusingconstructiveanddestructiveinterfere

33、nce,hornsachievedirectionalitybyreflectingsoundintoaspecifiedcoveragepattern.Inaproperlydesignedlinearraysystem,thatpatternshouldcloselymatchthelow-frequencydirectionalcharacteristicofthearray:verynarrowverticalcoverageandwidehorizontalcoverage.(Narrowverticalcoveragehasthebenefitthatitminimizesmult

34、iplearrivals,whichwouldharmintelligibility.)Ifthisisachieved,thenthewaveguideelementscanbeintegratedintothelinearrayand,withproperequalizationandcrossovers,thebeamfromthehighfrequenciesandtheconstructiveinterferenceofthelowfrequenciescanbemadetoalignsothattheresultingarrayedsystemprovidesconsistentc

35、overage.CanLineArrayLoudspeakersBeUsedSingly?No,theconedriversinalinearrayloudspeakerneedtheotherconesinthearraytocreatedirectionality.Theconesinasinglecabinethavethesamedirectionalcharacteristicsascomparableconedriversinothertypesofloudspeakers.Inotherwords,eachcabinetinalinearrayisnotproducingasli

36、ceofacylindricalwave.Thatisamarketingconcept,notascientificone.CanYouCurveaLineArraytoGetWiderCoverage?Inpractice,gentlycurvingalinearray(nomorethanfivedegreesofsplayamongcabinets)canaidincoveringabroaderarea.Radicallycurvinglinearrays,however,introducesproblems.First,ifthehigh-frequencysectionhasth

37、enarrowverticalpatternthatsrequiredtomakeastraightarraywork,curvingthearraycanproducehotspotsandareasofpoorhigh-frequencycoverage.Second,whilethecurvaturecanspreadhighfrequenciesoveralargerarea,itdoesnothingtothelowfrequencies,whichremaindirectionalbecausethecurvatureistrivialatlongwavelengths.Figur

38、e4illustratesthesepoints.OntheleftisaseriesofMAPPplotsforacurvedarray,andontherightareplotsofastraightarray.Botharraysareconstructedofidenticalloudspeakershavinga12-inchconelow-frequencydriverandahigh-frequencyhornwitha45-degreeverticalpattern.Notableintheleft-handplotsisthat,whilethewiderhornaidsin

39、spreadingthehighfrequencies,italsointroducespronouncedlobingduetointerference.At1kHzandbelow,thearrayremainshighlydirectional,followinglinearraytheory.Inpractice,thisbehaviorwouldproduceveryunevencoverage,withthefrequencyresponsevaryingsubstantiallyacrossthecoverageareaandalargeproportionofthatarear

40、eceivingalmostnolow-frequencyenergy.Theright-handseriesofplotsrevealsthataloudspeakerwithamoderatelywide-coveragehorndesignedforcurvedarraysbehavespoorlyinastraightarray.Whilethearrayishighlydirectional,pronouncedverticallobingoccursat1kHzandabove.Thesestrongsidelobesdivertenergyfromtheintendedcover

41、ageareaandwouldexcitethereverberantfieldexcessively,reducingintelligibility.Fig.4.Directionalcharacteristicsofacurved(left)andstraight(right)linearrayusingahigh-frequencyhornwitha45-degreeverticalpatternCanYouCombineLineArraysWithOtherTypesofSpeakers?Yes,sincelinearwavespassthroughoneanotherregardle

42、ssofwhethertheyarecreatedbyadirectradiatororawaveguide,itispossibletocombinelinearraysystemswithothertypesofloudspeakersaslongastheirphaseresponsematchesthatofthelinearrayspeakers.Thereisnothingspecialaboutthesoundwavesthatlinearrayscreate.Theyaremerelytheoutputoflow-frequencycones,spacedusinglinear

43、raytheory,andhigh-frequencywaveguides.Therefore,skilleddesignerswiththepropertoolscanflexiblyintegrateothercompatibletypesofloudspeakerstocovershort-throwareas.Fig.5.ACQ-1riggedunderanM3DlinearrayprovidesdownfillcoverageHowDoLineArraysBehaveintheNearandFarField?Aswehaveseen,practicallinearraysystems

44、asusedinhigh-powerapplicationsareactuallyacombinationofclassicallinearraysforthelowfrequenciesandhighlydirectivewaveguidesforthehighfrequencies.Becauseofthishybridnature,itisdifficulttoapplypredictionsfromclassicallinearraytheoryacrossthewholeaudiospectrum.Nonetheless,linearraysystemscanbemadetowork

45、reasonablywellinboththefarfieldandmoderatelyclosetothearray.Seenfromthefarfield,theoutputsoftheindividualsourcesinalinearraycombineconstructively,andappeartooperateasonesource.Figure6illustratesthisconcept.Thefigureshowsthefar-fieldfrequencyresponseforlinearraysoftwo,fourandeightomni-directionalradiators(asingle-omniresponseisincludedforreference)spaced0.4metersapart.Noticethateachdoublingofthenumberofelementsresultsinauniform6dBlevelincreaseacrossthefullfrequencyrangeofoperation.Thehighfrequencyresponseissmooth,butreflectsanaturalrolloffdueto