INTER-NOISE DECEMBER 2006 HONOLULU, HAWAII, USA

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1 INER-NOISE 6-6 DECEMBER 6 ONOLULU AWAII USA Murmn of rnmiion lo of mril uing ning wv u Oliviro Oliviri Brül & Kær Soun n irion Murmn A/S Skoorgv 7 DK-85 Nærum Dnmrk J. Sur Bolon wook Yoo c Ry W. rrick Lorori School of Mchnicl Enginring uru Univriy S. Inrmurl Driv W Lfy IN 797- USA ABSRAC In hi ppr murmn procur for vluing h norml incinc rnmiion lo of noi conrol mril uing four-microphon ning wv u n n FF nlyzr i cri. h mhmicl formulion i on h rnfr mri rprnion which h n wily u in h p oh o nlyz n o mur h couicl propri of flow ym lmn. h mho cri hr iffr from om rlir pproch h u imilr primnl up in h knowlg of h u rminion coniion i no rquir o nur h ccurcy of h rul. Alhough h oun powr rnmi hrough mpl in h u pn in gnrl oh on i propri n on h u rminion coniion h rnfr mri lmn which r u o clcul h rnmiion lo r propri only of h mpl. INRODUCION In hi ppr murmn procur for vluing h norml incinc rnmiion lo of plug of noi conrol mril plc in four-microphon ning wv u i cri. A rnfr mri rprnion which h n wily u in h p oh o nlyz n o mur h couicl propri of flow ym lmn.g. uomoiv mufflr [-] i u hr o rl h oun prur n h norml couic pricl vlocii on h wo fc of h mpl. Afr rif cion on h hory unrlying h rnfr mri formulion procur for rmining h rnfr mri lmn i cri. h procur i imilr o ho cri in Rf. [-] howvr i iffr from h of Rf. [] in h knowlg of h u rminion coniion i no rquir. Finlly i i hown how h norml incinc rnmiion lo my rl in clo form o h rnfr mri lmn n h vng of uing uch n prion for h rnmiion lo i plin. EXERIMENAL SEU W conir on-imnionl couicl ym coniing of fini-lngh rigi-wll u wih rirrily-hp uniform innr cro-cion. A on n h u fur loupkr proviing ron ionry rnom ciion o h ym. A h ohr n h u cn fi wih rirry rminion coniion incluing for mpl n opn Emil r: ooliviri@kv.com Emil r: olon@puru.u c Emil r: yoo@puru.u

2 n rminion. h inrnl volum of h u i ivi ino wo cion y plug priion of h mril unr invigion ning cro h u cro-cion hown in Figur. h wo fc of h plug r plnr n prpniculr o h u wll. An mpl of uil primnl ppru i hown in Figur. Figur. Iliz rprnion of h primnl up. Figur. h Brül n Kær rnmiion Lo Ki yp 6 i uil for oh low frquncy 5 z o 6 z n high frquncy 5 z o 6 z murmn inc i inclu oh cm hown hr n.9 cm innr imr u cion. EORY. Bckgroun A frqunci low h cuoff frquncy for h fir ipriv mo only pln wv cn propg in h u. In h frquncy rng h oun fil in h wo cion of h u cn wll pproim y uprpoiion of poiiv- n ngiv- going pln wv. By oping compl ponnil rprnion n coorin ym wih i origin h urfc of h mpl rmining h uprm cion of h u Figur h oun prur n pricl vlociy in h up- n ownrm u cion cn wrin : l c D C c B A v l D C B A p k k k k k k k k R R } R{ } R{ } R{ } R{ ρ ρ ighr mo nu ponnilly wih inc o hy r no imporn pprcil inc from h loupkr or mpl [6-7]. An ign convnion h n op.

3 whr R{} mn h rl pr i h compl prur i h compl pricl vlociy A o D r h compl mpliu of h pln wv componn ρ i h min flui niy c i h min oun p i h ngulr frquncy k/c-α i h wv numr which i compl o ccoun for h ffc of vicou n hrml iipion in h ocillory hrmo-vicou ounry lyr h form on h innr urfc of h uc f n l i h hickn of h mpl. From Eq. h cofficin A o D my ily pr in rm of compl prur o poiion o rpcivly hown in Figur. A B k k k k C in k in k k k k k D. in k in k Whn ionry rgoic rnom noi ignl i u o ci h ym w cn u h following quivln formul: A B G G R in k R k k in k R R k k C D G G R in k R k k in k whr h qunii A o D r now h im pln wv mpliu who ph r fin rliv o rfrnc ignl R. Furhr i fin i R R R k k R f GR f / G f : i i i.. h frquncy rpon funcion wn h compl oun prur i n h compl rfrnc ignl R. Finlly G i h vrg on-i uo-pcrl niy funcion of h rfrnc ignl n G i h vrg on-i cro-pcrl niy funcion of h R i rfrnc ignl n ignl i. In uqun clculion of h rnfr mri lmn h qunii A o D lwy ppr in rio wih h rul h G cn nglc. RANSFER MARIX FORMULAION W um h h priion of mril unr invigion cn cri four-pol wo-por piv linr couic u-ym. hn rnfr mri g cn u o rl h rior compl prur n h rior compl norml couic pricl vlocii on h wo fc of h mpl follow:. 5 f A mi-mpiricl formul givn y mkin cn u o clcul h rl n imginry pr of h wv numr [8]. g Somim known rnmiion mri [6-7].

4 h qunii i which r frquncy-pnn qunii my ircly rl o h couicl propri of h mpl [].. wo-lo implmnion Equion 5 rprn wo quion in four unknown. In orr o l o olv for h rnfr mri lmn wo iionl inpnn quion my gnr y inroucing con rminion coniion: i.. 6 whr uprcrip n no h wo iffrn rminion coniion. h rnfr mri lmn my hn ily rmin y invring h lr prion o oin. 7. On-lo implmnion Whn h pln wv rflcion n rnmiion cofficin from h wo urfc of h mpl r h m i i poil o k vng of h rciprocl nur of h lyr o gnr wo iionl quion in of mking con of murmn h :. 8 By comining Eq. 5 n 8 h rnfr mri lmn for mpl ifying h ov coniion cn pr ircly for on rminion coniion: i Drminion of h rnfr mri lmn From Eq. h prur n pricl vlocii h wo urfc of h mpl my ily pr in rm of cofficin A o D: c D C c B A D C B A k k k k ρ ρ h irc no h rciprociy rquir h h rminn of h rnfr mri uniy [6]. Ingr h no h h lr conrin i gnrl propry of piv linr four-pol nwork [9]. Allr h lo hown h hi coniion follow ircly from h rquirmn h h rnmiion cofficin of plnr rirrily lyr couicl ym h m in oh ircion []. Furhr irc no h for ymmricl ym.

5 whr h uprcrip no h h qunii r rmin for n rirry rminion coniion. Afr uiuing Eq. ino Eq. 7 or 9 h rnfr mri lmn r hn plicily rmin in rm of cofficin A o D. Aiionlly no h y uing Eq. n Eq. 5 n fr om lgric mnipulion omi hr i cn hown h: A B ρc ρ c ρc ρ c k k ρc ρ c ρc ρ c k k C D. I houl no h cofficin A o D r pnn on h rminion coniion. On h conrry h rnfr mri lmn i r inpnn of h rminion coniion. 5 DEERMINAION OF RANSMISSION LOSS h oun rnmiion lo of priion i fin : W i L log W whr W i n W r h irorn oun powr incin on h priion n h oun powr rnmi y h priion n ri from h ohr i rpcivly. ypiclly h oun rnmiion lo i rmin ccoring o nr procur [-] whr h pcimn i po o iffu oun fil. In h c of h primnl up cri in Scion wih prfcly nchoic rminion h i D h oun rnmiion lo i: nchoic A L n log nchoic C whr h ucrip n inic h h mpl i po o normlly incin pln wv fil. Whn Eq. wih h coniion D r uiu ino Eq. 5 h norml incinc oun rnmiion lo i foun o : L n log ρc. ρ c No h h oun powr W rnmi y mpl in u pn in gnrl oh on h propri of h mpl n on h rminion coniion. For mpl in h rm c of prfcly rigi rminion h pln wv cofficin C rigi n D rigi r qul in mgniu n h oun powr rnmi y h mpl i in principl zro hu cuing h rnmiion lo o pprnly infini. Evn whn u rminion i nrly-nchoic mll rflcion from h rminion my hv noicl impc on h rnmiion lo if i nrlynchoic nrlynchoic i clcul imply log A / C : Rf []. On h conrry h norml incinc rnmiion lo givn in Eq. i pr in rm of h rnfr mri lmn which r propri only of h mpl n no of h

6 murmn nvironmn.g. h u rminion hu proviing n prion h i unmiguou. I houl no h in Eq. hr r no rm h rfr plicily o h mpl hickn or poiion. 6 REMARKS h ignl from microphon my convninly u h rfrnc o clcul R R n fin in Eq.. Oviouly hll qul o uniy in h c. R owvr whn h pproch i follow h ignl-o-noi rio my no ifcory crin frqunci in priculr whn h mpl unr invigion i highly rflciv. o ovrcom hi prolm ihr fifh microphon poiion clo o h loupkr or h ignl provi o h loupkr my u in. I houl no h in h lr c i mu um h h loupkr i prfcly linr which my confirm y n inpcion of h cohrnc of h rnfr funcion im funcion of ourc lvl. h mho o no rquir imulnou murmn of R lhough hi woul conirly p up h murmn proc. Murmn cn conuc y h u of ul-chnnl FF nlyzr n ingl microphon provi h h ignl o h loupkr i u rfrnc. Conir Eq. which rl h compl mpliu of h pln wv componn for oh h uprm n ownrm u cion. o implify h noion w wri: A C. 5 B D nc nc I houl no fir h A / C in h c for D. Equion. 5 rprn wo quion in four unknown. In orr o l o olv for h mri lmn wo iionl quion my gnr y inroucing con rminion coniion: i.. A A C C 6 B B D D whr uprcrip n no h wo iffrn rminion coniion. Afr om lgric mnipulion omi hr i cn hown h: A D A D R R 7 C D C D R R whr R D / C i h rflcion cofficin cr y h non-il rminion n A / C. Clrly prolm wih ingulriy occur if h wo mur rminion prouc lmo inicl rflcion cofficin on or mor frqunci. h prnc of nrly-nchoic rminion in l on murmn coniion cu h oun fil in h ownrm cion o lmo purly propgionl in h c hu mimizing h ph iffrnc wn h oun prur h wo ownrm microphon locion n hu minimizing h ffc of microphon ph-mimch on h ownrm rnfr funcion im. No h microphon wiching procur my prform clirion g o ruc h ffc of microphon n murmn chnnl mimch rcommn for mpl in Rf. [-5]. i R

7 7 CONCLUSIONS In h prn ricl w hv cri quick n convnin mho for rmining h norml incinc rnmiion lo of mpl plc in ning wv u on h wllknown rnfr mri rprnion. Alhough h oun powr rnmi hrough h mpl pn in gnrl oh on i propri n on h u rminion coniion h procur provi h norml incinc rnmiion lo if h mpl wr ck y prfcly nchoic rminion inpnn of h cul u rminion coniion u uring h murmn. Morovr knowlg of uch rminion coniion i no rquir. Boh on- n wo-lo implmnion hv n cri n h coniion unr which h on-lo mho my u hv n pcifi. 8 REFERENCES [] M. L. Munl n A. G. Doig hory of wo ourc-locion mho for irc primnl vluion of h four-pol prmr of n rocouic lmn J. Soun i [] Z. o n A. F. Syr A Rviw of Currn chniqu for Muring Mufflr rnmiion Lo rocing of h SAE Noi & irion Confrnc n Ehiiion. [] B.. Song n J. S. Bolon A rnfr mri pproch for iming h chrcriic impnc n wv numr of limp n rigi porou mril J. Acou. Soc. Am [] J. S. Bolon R. J. Yun J. op n D. Apfl Dvlopmn of nw oun rnmiion for uomoiv ln mril SAE chnicl pr Doc. Nr [5] J.S. Bn n A.G. irol Enginring pplicion of corrlion n pcrl nlyi John Wily & Son Nw York 98. [6] A. D. irc Acouic: An Inroucion o I hyicl rincipl An Applicion Wooury Nw York Acouicl Sociy of Amric 99. [7] L.E. Kinlr A.R. Fry A.B. Coppn n J.. Snr Funmnl of Acouic h E. John Wily & Son Nw York. [8] S. mkin Elmn of Acouic Wily Nw York 98. [9] K. U. Ingr No on Soun Aorpion chnology Noi Conrol Founion oughkpi NY 99. [] J. F. Allr ropgion of Soun in orou Mi Elvir Appli Scinc Lonon n Nw York 99. [] Snr rminology rling o nvironmnl couic ASM C 6- ASM Inrnionl W Conhohockn A USA. [] Snr mho for h lorory murmn of irorn oun rnmiion lo of uiling priion n lmn ASM E-9- ASM Inrnionl W Conhohockn A USA. [] Acouic Murmn of oun inulion in uiling n of uiling lmn r: Lorory murmn of irorn oun inulion of uiling lmn ISO -:995 Inrnionl Orgnizion for Snrizion Gnv Swizrln 995. [] Snr mho for impnc n orpion of couicl mril uing u wo microphon n igil frquncy nlyi ym ASM E-5-98 ASM Inrnionl W Conhohockn A USA 998.

8 [5] Acouic Drminion of Soun Aorpion Cofficin n Impnc in Impnc u-r : rnfr-funcion Mho ISO 5 :998 Inrnionl Orgnizion for Snrizion Gnv Swizrln 998.