Type3vpsmm

Proceedingsof20thInternationalCongressonAcoustics,ICA201023-27August2010,Sydney,AustraliaICA20101AStudyonAcousticTheoreticalFormulaeforCompactAcousticReproductionSystemsMasashiNakamura(1),YoshinobuKajikawa(1),YasuoNomura(1)andTakashiMiyakura(2)(1)FacultyofEngineeringScience,KansaiUniversity,3-3-35,yamatecho,Suita-shi,Osaka,Japan(2)HosidenCorporation,1-4-33Kitakyuhoji,Yao-shi,Osaka,JapanPACS:43.
38.
-pTransduction;acousticaldevicesforthegenerationandreproductionofsoundABSTRACTInthispaper,weproposeamethodforanalyzingcompactacousticreproductionsystems(e.
g.
mobilephones)throughacousticequivalentcircuits.
Measuredresponsesofcompactacousticreproductionsystemscannotberepresentedaccuratelybytheanalysisbasedontheconventionalacoustictheory.
Acousticengineersconsequentlyareobligedtodesigncompactacousticreproductionsystemsbytrialanderror.
Moreover,thesoundqualityofthosesystemsislikelytodeteriorateduetothedifficultyofsuchanacousticdesign.
Wethereforeclarifythecauseofthedifferencebetweenthemeasuredresponseandtheanalysisonecalculatedbythefiniteelementmethod(FEM)analysisandconsiderthepossibilityofobtainingnewacoustictheoricalformulaebasedontheanalysisresultsinordertomakeiteasierforacousticengineerstodesigncompactacousticreproductionsystems.
INTRODUCTIONRecently,thedemandforsmall,thinacousticreproductionsystems(e.
g.
mobilephones)hasbeenincreasing.
Theacousticstructuredesignformobilephonesisbecomingmoreandmoredifficultbecausethemobilephonesaremadesmallerandmorecomplicated.
Asaresult,evenexperiencedengineersdesigncompactacousticreproductionsystemsbythetrialanderror.
Thetrialanderrordesignincreasescost,wastestime,anddeterioratesthesoundquality.
Tosolvethisproblem,weproposedanautomaticdesigntechniqueusinggeneticalgorithm(GA)fortheacousticcomponentsofmobilephones[1].
Thissystemisbasedontheacousticequivalentcircuitanalysisusingtheconventionalacousticformulae.
However,thissystemisimpracticalbecauseitcannotdescribethevariationofacousticparametersrelatedtothespatialrelationshipofacousticholes.
Tosolvethisproblem,wehavealreadyexaminedtheinfluenceofthespatialrelationshipbetweenacousticholesusingtwodimensionalFEManalysis[2],[3].
However,thephysicalmechanismhasnotbeenclarifiedenough.
WethereforeanalyzeanactualacousticphenomenonusingthreedimensionalFEManalysis,andclarifythecausethroughtheanalysisresults.
Moreover,wediscussthepossibilityofnewacoustictheoricalformulaebasedontheanalysisresults.
CF2CF1ZCBPout(s)L1R1L3R3L5R5C5L7R7Ein(s)ReceiverholeFrontcoverholeDiaphragmBackcavityBackholeCoupler2ndFrontcavityInputOutput1stFrontcavityType1Type2Type3ReceiverholeFrontcoverhole(Fixed)(Changed)Figure1.
Structureofamobilephone.
Pin(s)Pout(s)ZL5R5C5R7L7L3R3L1R1CF1CF2CBReceiverFrontcoverDiaphragmBackcavityBackhole1stFrontcavity2ndFrontcavityCouplerholeholeCONVENTIONALACOUSTICFORMULAEFORACOUSTICHOLEANDTHEIRPROBLEMFigure2.
EquivalentcircuitmodelofFig.
1.
Thegeneralacousticformulaeforacousticholearegivendependinguponthefrequencyrangeasfollows[4]:23-27August2010,Sydney,AustraliaProceedingsof20thInternationalCongressonAcoustics,ICA20102ICA2010-10010203040501000Response[dB]Frequency[Hz]5005000Type1Type3Type2(a)MeasuredcharacteristicThe1stresonanceThe2ndresonanceThe3rdresonanceTable1.
SizesandacousticparametersofFig.
1.
Parameter5R71076.
2*Diaphragm5L31056.
3*(,,)5R5L5C5C121067.
4*Length1.
6ReceiverholeRadius1.
0(,)1R1LNumber12ndfrontcavity()1FCCapacity3.
30Length0.
3FrontcoverholeRadius1.
35(,)3R3LNumber11stfrontcavity()2FCCapacity0.
43Backcavity()BCCapacity0.
56Length1.
0BackholeRadius0.
9(,)7R7LNumber1-10010203040501000Response[dB]Frequency[Hz]5005000(b)SimulatedcharacteristicFigure3.
ComparisonofmeasuredfrequenyresponsesofFig.
1andthecorrespondingsimulatedfrequencyonescalculatedbytheconventionalacoustictheory.
Length[mm],Radius[mm],Capacity[cc]acousticholeinmetersaradiusofholesinmeters,llengthofopen-endcorrectioninmeters,0,ρairdensityinkilogrampercubicmeter,Nnumberofacousticholes,fa/002.
0<μviscositycoefficientofairinpascalsecond,andScrosssectionalareaofacousticholesinsquaremeter.
NShLNShR012134,8ρμπ==(1)faf/10/01.
0<1showstheacousticstructureofamobilephone,whosesizesandacousticalequivalentcircuitareshowninTable1andFig.
2,respectively.
Fig.
3showsmeasuredresponsesandthecorrespondingcalculatedonesobtainedbytheconventionalacousticformulaeincasewherethepositionofthereceiverholechangesasshowninFig.
1.
FromFig.
3(a),wecanseethattheleveloftheresponsebecomeshighasthepositionofthereceiverholemovesoutwardlyfromthecenterofthereceiverplane.
Ontheotherhand,thecalculatedresponseshowninFig.
3(b)cannotexplainthechangeofmeasuredresponsesat2ndand3rdresonantfrequencies.
Hence,theconventionalacousticformulaeareuselesstopracticaldesign.
Inthenextsection,weclarifythecausesthroughsomeanalysesbyFEManalysis.
+=2202ahNSRωμρ(2)[lhNSL202+=ρ](3)faf/01.
0/002.
0<0/002.
0/008.
0/01.
0213+=(4)ACOUSTICALPHENOMENONANALYSISUSINGFINITEELEMENTMETHOD222111,LjRZLjRZωω+=+=(5)Fig.
4showsthestructureofamobilephone,whosesizesandacousticalequivalentcircuitareshowninTable2andFig.
5,respectively.
Weanalyzetheacousticphenomenonofthisstructurebythefiniteelementmothod(FEM),especially,includingacousticimpedanceanalysis.
where,andisacousticimpedanceofacousticholeinpascalsecondpercubicmeter,1Z2Z3ZRacousticresistanceofacousticholeinpascalsecondpercubicmeter,Lacousticmassinpascalsquaresecondpercubicmeter.
lengthofh23-27August2010,Sydney,AustraliaProceedingsof20thInternationalCongressonAcoustics,ICA2010ICA20103Diaphragm1stFrontcavity2ndFrontcavityReceiverholeFrontcoverholeReceiverholeFrontcoverhole(Fixed)(Changed)CenterShiftedby5mm(a)External(b)StractureFigure4.
Prototypeofamobilephone.
1stFrontcavity1C2L1L1R2RFrontcoverholeααZcs1Receiverhole2ndFrontcavity2CβDiaphragmdLdRdCαβ,:Open-endcorrectionCrosssection1cav1Rcav2RZcs2Crosssection2Figure5.
EquivalentcircuitemodelofFig.
4.
Inthissimulation,themodelshowninFig.
6isused.
Theboundaryconditionontheinsidewallissetastheparticlevelocityisequalto0.
Additionally,theboundaryconditionontheoutputedgeissetasthesoundpressureisequalto0.
ThesimulationconditionsareshowninTable3.
InputsignalInthissimulation,thevirtualplanesoundsourceinFig.
6isdrivenbyaninputsignal(particlevelocity)whichisagaussianpulseasfollows[5]:)(tuvps(){229.
0/0)(TTtnvpseAtuΔ=}Fig.
7showsthedynamicsofgaussianpulseusedfortheanalysis,whoseparametersandelectricpowerspectrumareshowninTable4andFig.
8,respectively.
Parameter(6)Table2.
SizesandacousticparametersofFig.
4.
dR61014.
8*Diaphragm(HDR9310)dL31091.
8*(dR,dL,dC)dC11002.
4*2Length1.
0ReirhoeecvelRadi1.
0us(2R,2L)Number11stfrontcavity(C1)Capacity0.
18Length1.
0FrontcoverholeRadius1.
0(3R,3L)Number12ndfrontcavity(2C)Capacity364π10*hLength[mm],Radius[mm]y[cc]imuitions.
TypeoffluidAir(incompressible),CapacitTable3.
SlationcondSpeTempVcificheatratio1.
4erature20℃ityofair18.
2E-6Piscosas(a)Model1(Theentirestructure)2ndcavityHoleReceiverholeCrosssection11stFrontcavity2ndFrontcavityFrontcoverholeh[mm]5[mm](Virtualplanesoundsource)Crosssection2(Virtualplanesoundsource)(b)Model2(Onlythehole)Figure6.
ModelofsimulationwithFEManalysis.
AcousticimpedanceanalysisThesoundpressureinthestructureiscausedbytheparticlevelocityatthevirtualplanesoundsourceinFig.
6.
atthevirtualplanesoAtthattime,thesoundpressurevpsplculaundsourceiscalculatedbytheFEManalysisandtheacousticimpedancevpsZoftheoutputedgesidetothevirtualplanesoundsourcecanbecatedbywhereΔtissamplingperiod,ninteger,t(t=Δtn)time,A0amplitude,andTisdeterminedaccordingtothefrequencyf0atwhichtheelectricpowerspectrumofthegaussianpulsedecreasesby3dBasfollows:0/646.
0fT=(7))()()ωωvpsvpsvpUSPZ=,(8)(ωswhereistheareaofthevirtualplanesoundsource.
S23-27August2010,Sydney,AustraliaProceedingsof20thInternationalCongressonAcoustics,ICA20104ICA2010Table4.
Parametersofgaussianpulse.
A01.
0E-51stFrontcavityZcs12ndFrontcavityCrosssection11M1R2M2R2C1C1cavR2cavRΔt1.
0E-5secf010.
0kHz00.
10.
20.
30.
40.
50.
60.
70.
80.
91.
000.
00050.
0010.
00150.
002Time[sec]Perticlevelocity]m/s10[5*Figure9.
EquivalentcircuitmodelofModel1.
60708090100110120130100100010000Solidlines:CenterDashedlines:Shiftedby5mmFrequency[Hz]Soundpressurelevel[dB]h=3mmh=6mmh=1mmFigure7.
Dynamicsofgaussianpulse.
-180-170-160-150-140-130-120-110-100-90-8005.
010.
015.
020.
025.
030.
035.
040.
045.
050.
0Frequency[kHz]Amplitude[dB]Figure10.
Measuredfrequencycharacteristicsincasewherethepositionofthereceiverholechanges(SPL).
Therefore,canbeestimatefromrealpartandcanbeestimatedfromthegradientofthereactancetotheangularfrequency.
endasfollows:TheparametersshowninFig.
9aredeterminedbrelationshipbetweentheacousticimbasedontheequivalentcircuitanalysisandtheFEManalysis.
Specifically,theseparametersaredeterminedtobecomeFigure8.
Amplitude-Frequencycharacteristicofgaussianpulse.
Procedureforestimatingacousticparametersissimulation,acousticimpedanceanalysesaredoneofstructuresshowninFig.
6.
Toclarifyhowtheacousticparameteroftheriverholechangesaccordingtotheposition,theacousticparametersshowninFig.
5arecimpedanceatlowfrequenciescanbeapproximatedasfollows:thereactancetotheangularfrequencyshowsthesumtotaloftheacousticmass.
Hence,thesumtotaloes(11)2Rd2LTofinallystimateotherparameters,theequivaletcircuitshowninFig.
9toModel1isemployed.
1Mand2MinFig.
9aredefineInthonthetwokindseceestimated.
)212MM+=(211MLMLMt+=++=αβα(10)Firstofall,Model1showninFig.
6isconsidered.
FromFig.
5,wecanseethattheacousticcomplianceofthecavityisconsideredtobeopenatlowfrequenciesbecausetheacousticimpedanceofthecavitygrowsverymuch.
Therefore,theacoustiythepedancecharacteristicssmallmostthesumtotalofsquareerrorofcharacteristicsbasedontheequivalentcircuitanalysisandtheFEManalysisbyMaximumLikelihoodEstimation(MLE).
Inaddition,sincethereceiverholeandthefrontcoverholearethesamesizes,21RR=and21LL=.
Therefore,allparametersofModel1aredetermined.
However,itisdifficulttoestimatethoseparametersaccuratelybecausetherearealotofthecombinationsoftheparameterstomatchbothcharacteristics.
ANALYSISRESULTSFig.
10showsthemeasuredfrequencycharacteristicsofamobilephoneshowninFig.
4.
FromFig.
10,wecanseethat)2()(21211βαω+++++≈LLjRRZcs(9)(Lowfrequencyband)Inaword,thegradientoftMfthe)2(21βα+++=LLMtacousticmasstMcanbetimated.
Next,theanalysisofModel2isdescribed.
Theacousticimpedance2csZinModel2isshownasfollows:222csLjRZω+=thefrequencycharacteristicsthereceiverhole.
Inthissvaryaccordingtothepositionofection,suchaphenomenonisclarifiedbasedonsomeanalysisresults.
23-27August2010,Sydney,AustraliaProceedingsof20thInternationalCongressonAcoustics,ICA2010ICA201050200040006000800010000810710610510410Acousticimpedance2csZFrequency[Hz]}Re{2csZ}Im{2csZ2csZ02000400060008000100001010910810710610510Frequency[Hz]Acousticimpedance1csZ]s/mPa[3Solidlines:CenterDashedlines:Shiftedby5mmh=3mmh=6mmh=1mmFigure13.
Acousticimpedancecharasteristics(Model2).
Figure11.
Acousticimpedancecharasteristicsincasewherethepositionofthereceiverholechanges(Model1).
00.
51.
01.
52.
02.
51002003004005006007008009001000)10(7*Frequency[Hz]Reactanceof1csZSolidlines:CenterDashedlines:Shiftedby5mmh=3mmh=6mmh=1mm02000400060008000100001010910810710610510Frequency[Hz]Acousticimpedance1csZ]s/mPa[3Solidlines:CenterDashedlines:Shiftedby5mmh=3mmh=6mmh=1mmFigure12.
Reactancecharacteristicsincasewherethepositionofthereceiverholechanges(Model1).
AcousticimpedanceanalysisModel1Fig.
11showstheacousticimpedancecharacteristicsofel1bytheFEManalysis.
FromFig.
11,itcanbefrontFig.
13showstheacousticimpedancecharacteristicsofel3bytheFEManalysis.
FromFig.
13,wecanFig.
14showsacousticimpedancecharacteristicsthatusetheestimatedparameters.
FromFig.
14,wecanseethatthesecharacteristicsareconsistentwiththecharacteristicsobtainedFigure14.
Acousticimpedancecharacteristicthatusesestimatedparameters.
fromtheFEManalysis.
Hence,itcanbeseenthattheparameterscanbeestimatedaccurately.
Next,Figs.
15-17showparametersestimatedbyMLE.
romFig.
15,itcanbeseenthatthesumtotaloftheacousticmassincreasesasthepositionoftheacousticholeshiftscauseavirtualtubeisastheeofttothepositionoftheacoustichole.
1csZinModseacthehenthatthepositionofthereceiverholeinfluencestheousticalcharacteristics.
Moreover,theinfluencegrowsaseightofthe2ndfrontcavitybecomesshort.
ThemeasuredcharacteristicsshowninFig.
10alsohavethesametendency.
Next,Fig.
12showsthereactancecharacteristicsof1csZ.
Fig.
12showsthattheresonantfrequencychangesaccordingtothesumtotaloftheacousticmass,andinfluencestheacousticcharacteristics.
Thegapbetweenthecoverholeandthereceiverholerelatestotheincreaseoftheacousticmassinthetightspace.
Thecauseisexaminedindetailinthenextsection.
Model2Ftfromcentertoedge.
Furthermore,theincreaseisremarkableasthe2ndfrontcavitynarrows.
ThisisbeMformedbytheopen-endcorrectioninthe2ndfrontcavityandtheinterferencebecomesintenseasthethe2ndfrontcavitynarrows.
FromFig.
16,wecanseethatthereislittleinfluenceofthepositionoftheacousticholeandtheseparametersarealmostthesamevalueasthetheoryones.
Hence,wecanseethatthevariationoftheacousticcharacteristicsaccordingtothepositionofthereceiverholeisrelatedtothechangeintheacousticmass.
Next,1cavRand2cavRshowninTheparametersshowninFig.
17cannotbecalculatedbytheconventionalacoustictheory.
Thisisbecausetheviscosityofairbecomeslargeasthespaceofthecavitynarrows.
Therefore,theresistanceofthe1stcavitywhosecapacitydoesnotchangeisaconstantandtheresistanceofthe2ndcavitywhosecapacitychangesgrowsspachecavitynarrows.
Fromtheanalysisresults,theformulaethataccuratelycalculatetheopen-endcorrectionandtherelatedresistanceshouldbeestablishedforthecompactacousticreproductionsystemssuchasmobilephonesbecausetheacousticcharacteristicschangeaccording3csZinModseethHoreactattheresistanceisafunctionofthefrequency.
wever,thechangeissmallcomparedwiththatoftheance,sothattheresistanceistreatedasaparameterthatdoesnotdependonthefrequency.
Therefore,theacousticresistance1Risregardedasameanvalue.
Estimatedresultofacousticparameters23-27August2010,Sydney,AustraliaProceedingsof20thInternationalCongressonAcoustics,ICA20106ICA2010Certhechangeintheopen-endcorrectionandthatintheacousticresistanceofthenarrowcavitydependingtheacousticholeincasewherecompactacousticreproductionsystemsaredesigned.
1Y.
Nomura,T.
Nakatani,Y.
Kajikawa,"AnAutomaticAcoustics,Rome,Italy,Sep.
Y.
Kajikawa,Y.
Nomura,"AMethodforAnalyzingCompactAcousticReproduction3theRelativePositionofAcousticHolesin45shimoto,T.
Abe,Finite-differencetime-domainONCLUSIONSInthispaper,wehaveexaminedtheinfluenceofthepositionoftheacousticholetotheacousticcharacteristicsbasedonthreedimensionalFEManalysis.
Asaresult,weneedtoconsid18002000220024002600280030003200123456Theory)(tMCenterShiftedby5mmLengthof2ndcavityh[mm]Acousticmass]m/sPa[32onthepositionofInthefuture,wewillobtaintheacoustictheoricalformulaethatcanexplainthemeasurementcharacteristicaccuratelyfromvariousanalysisresults.
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EstimatedparametertM.
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LeoL.
Beranek,Acoustics,McGraw-HillBookCompany,1954.
O.
HaFigure16.
Estimatedparametersand.
1C2C123456710610510CenterShiftedby5mm{{1cavR1cavR2cavR2cavRLengthof2ndcavityh[mm]Acousticresistance]m/sPa[3method,MorikitaPublishingCo.
,Ltd.
,Japan,2006.
,InJapanese.
Figure17.
Estimatedparametersand1cavR2cavR.