12.07.2015 Views

Computational Mathematical Modelling of Sound ... - FEniCS Project

Computational Mathematical Modelling of Sound ... - FEniCS Project

Computational Mathematical Modelling of Sound ... - FEniCS Project

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

N'O-PMQSRTVUWPQSXRYPMZ[PRA\I]=^`_baIcedfVc"agagc!hjiRdk_blnmomkpqa€‚§v=x„ƒ}s!z`v=x†…ˆ‡‰r,sutIv=wyx{z.s!|}x~62798:7?A@CBD8FE7IHKJML+L+L G¥§¦©¨¨¡¤ ¨£ ¨ ¡ !!"©# ¡$¢¡¤£(*)+¡,¥§-#.¨¡¤ " /0¦ 1¨2 % ! 3)54%©¡¤¦&'Š XO‹ŒN&RTP'ŽZ -RTPMZuQC‘¢’-“”QSR Š XŽ’V‹Œ’V•‘’QSR—3’-T3•KŽZ -RTPMZuQC‘•–– p=hoce˜pqdoš›PDœ1ceIceaŸž¡ q q•


]:ho_bpqa-hjiIdopgš=i,]Smo_ cea"ced„pqd agpq_ mocYdoce"ho_bpqa_ba]=cea hj_ ]:ho_bpqa !hPMpgaggdopg]=šcegmo_ agšepq^Ihj]:hj_ pqa}] ^›]:hjigc"^.]Fhj_e] ^›pDgc!b_ agš˜g]=moc"'pqa Xc!b^`igp h#"_bm3mkhgg_hoc c(bc"^›c"anhS^`c"hoigpD*)c!$%}]:ho_bpqa']=aghjiIc'&gag_pq^Ihj]:hj_ pqagm+p+MhoigcmopIagdkce"hj_ pqa-,:_ agmoc"dkho_bpqa'bp=mom*„pqd5hoigc!hjce mo_bc"aec"dŠ^`c¡]=m0gdoc"^›c"a hjm.„dop=^¢cy\19c"do_b^`cea homœS_ hji.šqpMpD2"pq_ba"_bgc"aec+)“}doc43_bm."pq^/g]=doc".hjp]=dkc dkceece'^›p=doc-_bahoigcV^›ce]=mgdkce7¡]=mkc$5Icea"_bcem]=˜p6qcVhjigc'!Mh03up=a7„dkc!$%gcea(8Imochoigchoigcepqdkc"ho_¡]+ŒmkpMhj_bp=a'gpDcemagp=h_ba(ggchji}]=a&_ba'hoigc"pq^Ihjc"pqagc˜9c(¡]] œ]9=c-^›pDgcem()Q3igc:(gd0=cemSpqm"_ ]:hoc]Fhhjigc;bp œCc"d}c("hj_ pqagm()Zua©hjigc^›ce]=mgdkce?e]=mochoig_bmYc(@9c!!h_bagšpqa©mkhj]=agg_gmkc hoigcVpqm"_b]:hj_ pqagmC]=doc-mk^›pDp=hjiIceagc"'pMh9)_bm3agp=hShoi}]:hSpq˜=D_bpIm˜c!e]ceagš:hji*Bqhoigc"hYdj]:g_gmY]=aI`hoigcC>gp œ


moiŽ]:hj_ pqa}] 9Q c"mkho_bagš›]=ag TScemoce]=di'Zuagmkho_ hIhjc+)¦=pqa}]=mkmopqa&]:hPDœ1ceg_PI]=dj]`—Cdo]=agg˜cedkš§¢¡;H©£¡Q3ig_bmVdoc(9p=dkhV_bm-^J8šqdo]=}]:hoc,hjigc"mo_ m'„p=dhjigc¤gc"šqdoc"c`p+3N&]:mkhjc"dVp 3P5e_bc"aec"pq^3PMpD_ agš'_ a”P1"_bc"aec.]:h• – p=hoce˜pqdoš&ag_ qc"domo_ hD8)Z h_bm]7gdkp`Okc!!hbc!hj_baIš¥¤dop=˜bc"^hj_ ]+b_"ce`]:hYhjigcO;ep gmkho_mkc!!hj_bp=a]:hSPnœCc"g_bmkiŽ]:ho_bpqa}]+QŒcem[hj_ agš ]=ag©Tc"moc¡]:di_bag_h#MhjcV˜=8 X]=agm§¦=pqag]=momkpqa*)Zuagmkho_Q3igc&œ1pqdol i}]=m›˜9c"cea m09c"d0D_bmkce ˜=8 f-ceagagc!hji Rdo_ lnmomop=a ]:h Š i}] b^`cedkm.ag_=ced 3hD8'p QŒc!iIagpbp=š 8]:ag • – p=hjc"˜9pqdkš.ag_=cedkmo_ hD8 B5œSigp©ig]=m_ agmg_ doc"^›c]=ag&˜9c"ceamo_p Sšqdoce]:h m0pqdkh gdo_ agš'hoigcemkc^›pqa hoigm!)§ZV]=^ ] mopšqdo]:hjc4 Y„pqd,] hjigc.ho_b^`c B]=D_ moc]=aIcy\19c"dkh¤igc( hjig]:h ZVdoc(ece_ qc"R„dkpq^ N _blF]=c!'– ’šqdoc"a ]=agX]=aImšqpMpD


GHI©C§,#+D"J§,¥61©++#BK £ELF) ž Xc! ^›igp h#"c!$%}]:ho_bpqa )[)[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[) ž.NM)TS Q3iIc“2_ ag_ hocRbc"^›c"a hN c"hjiIpM )J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[) žASM) M TSce^`pDgc!b_baIšp ŒhjigcVmkpgd"c˜c!e] gmkcp doc4>}c!!hj_ pqagm )[)[)J)[)J)[)[) ž MMUVGHXWY#+§,!©C§,©C¨55#+¥9 £C) ž •-cep=^›c!hjd08 )[)[)J)[)J)[)[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[) ž ZZ)RQ “}pqdk^›_ agš ]=aI'mkpD_baIš g_bm0edoc!hjcVm08Dm[hjce^ p c!$%}]Fhj_bp=agm )[)J)[)J)[)[) ž ZZ)TS Ragc"doš 8c4:] }]Fhj_bp=a )J)[)[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[) ž5[Z4)§,-©C1X7D©]§¥61©C+B#+K £C:\ž PD_bc"aec"d )J)[)[)J)[)J)[)[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[) ž¡[1)a ) žc¡]=m0gdoc"^›c"anhp mopIag&dkce!hj_ pqa?)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[)^O_NN) ž) ž R$%g_g^`cea h )J)[)[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[)^O_Nac¡]=m0gdoc"^›c"anhp 2] ep gmkho_V_b^9c"}]=a"c2)[)J)[)J)[)')J)[)[)J)[)J)[)[)^O8ON)dO1) ž R$%g_g^`cea h )J)[)[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[)^O8Oaž Š p=^/}]:do_bmkpqa?„pqd3moc!h#'] (epqdkg_bagš hop`Z[PI’ žqž Z Mž c ž¡ q M )J)[)J)[)[)^O Z)Š p=^/}]:do_bmkpqa?„pqd3moc!h#'] (epqdkg_bagš hop`Z[PI’b[DO8Q MCc ž = Iž )[)J)[)J)[)[)^O8[)PO¢¡G2¥ ¡TG2¥¨££ ¤¦¥¨§©© !"#¥¨$%¥'&($)¥¨§©*#+§,-¥'."¨%/0¥'1$ 23 4)¨5¥61785#+¥9 :; 578#¥9?¥'&@$A#B©C7D©E :M )PO—1pgag}]:d08?"pqagg_ hj_bp=agm )[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[) ž.NM )RQY]:do_ ]Fhj_bp=a}] -„pqdo^ ]:ho_bpqaW)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[) ž.QZ )PON cemoi'šqceaIcedj]Fhj_bp=aX)[)J)[)[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[) ž ZZ ) M PDpgag7gdoc"mom0gdocJ9c"d0„pqdk^.]=aec )J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[) ž5[[1)POc"h )J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[)^O_NTSc(>gc!"ho_bpqa']:h3hoigcVpIh#GH©E"$.©§©9`§,©I¥61$ "L2a ) ž)PON'ce]=mgdkce^`cea h˜%8Z[PI’b[DO8Q MCc ž = Iž )[)J)[)')J)[)[)J)[)J)[)[)^ODža )POa )dO1)POh )[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[)^O_QN'ce]=mgdkce^`ceaef"+#B1#¥9g¥'&hI©*D¥9§,75#+¥9"i§¥61©C X;:)RQŠ p=^/}]:do_bmkpqa?„pqd3moc!h#'] (epqdkg_bagš hop¤hoigc• ‹ŒPgN0^`c"hjiIpM¤)[)J)[)[)^O:)TSY]+b_bg]:hj_ pqa©p ŒhjigcVmk_bc"aec"d3_b^9c"}]=a"c-^›pDgc([)[)')J)[)[)J)[)J)[)[)¢QMž) M Š Mh03up=a7„dkc!$%gcea(8 )J)[)[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[)¢QDOS


ž”‹ c"agš=hji p ŒhjigcVmk_bc"aec"d)[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[)¢Q8Qž5N1)‹ c"agš=hji p ŒhjigcV"hjm¤)[)[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[)¢Q_Sž5N1)dOŒhjigcV"hjm )[)[)J)')[)J)[)J)[)[)J)[)J)[)')J)[)[)J)[)J)[)[)¢Q Mž5N1)PQ


¡ ¡F ¡TG¤£¢!©J¥¥¤§¢¡¥`¥9§,"Y©EA5©E_$^.]Fhjdo_ \ ¦g_bmkmo_}]:hj_ qcT"pqagmkhj]=a h§mopIagX=c!bp5e_ hD8Bg^`m©¨!hI_ ]=^`c"hoced!BI^] ^.]:hodo_ \©gc"m"do_bĨ_bagš¤hjigc-hodo_ ]:agšbccegš=cemp hoigc-hjdk_ ]=agš ]:ho_bpqap ŒhjigcVgpq^›]=_ a?epq_ ae_ g_bagš,œS_ hjihjiIc ˜pgaI}]=d08©p hoigcVgpq^›]=_ba„doc($5Icea48B9X "„p=dec+B Žgmkpgd0ecVhjcedk^„pqd"c B Ž] ^.]:hodo_ \_„pqd3hoigcVgpq^›]=_ba©p+K"pq^/Ih]:ho_bpqaœ]9=ca%g^,˜ced(B}^ ©mgdk_bagš"pqagmkhj]=a hmopIag gdkcemkmgdkcJ c(qc( Bgg—^.]:mom!B}lnšagpqdk^.] _bmkce2qc("hopqd mopIag gdkcemkmgdkc B ¤2] hj_ ^›cIc!ceaggc"a hmop gag7gdoc"momIdoc B ¤2]] O 1Ž ^›]:hjdk_ \.p 2] 5hoigc"!›]:ag$#J=]+gc"m„p=dhjigcagpDgcemSp Œhjigc-hodo_ ]:agšb]:hj_ pqa©p ŒhjigcVgp=^.]=_ a%lnagp œSa&mop gag7gdoc"momIdoc,]Fh3hjigcV_babc"hp hoigcV!h'&( U m:] gc"m3pqahjigcVagpDgcTpq_ba hjm( U mCIdop`Okc("hj_ pqa pqa ] hodo_b]=agšb]:hj_ pqa©p ŒhjiIc Ipq^.]:_baqc("hjp=dœS_ hjihjigcVc(bce^`cea hom )&:]=do_b]=˜bc_bahjigcVdo]=g_ ]+5g_ doc!!hj_ pqap hoigcV!h9B}^#dj]=I_gm3p ŒhjiIc "h!B^#+*-,/.]=doce]B}^21 0] ^.]:hodo_ \.œS_ hji pqagc'epg^`a2„pqd3c¡] ihjdk_ ]=aIšbcp+ hoigc-hjdo_b]=agš ]:ho_bpqa3p ŒhjigcVgpq^›]=_ a_bahjigcV^`cemki'm09c(e_ 8D_ agš¤_ hjmhoigdoc"cVagpMIc a%g^˜9c"dom,65 hjigc-hoig_lnagc"momp+ hoigc ]=˜gmop=do˜g_ agš¤^.]:hocedk_ ] BD^4*-798:,6; hjigc-hoig_lnagc"momp+ hoigc'9c"d0„pqdo]:hjc" ^`c"hj] BM^4}]=d[hj_(bc;=c! p1"_ hD8B}^`m ©©=:]=do_b]=˜bc_bahjigc' ceagš=hoig_bdkc!"ho_bpqap+ hoigcV"h!B ^! hjigcV_ abc!hepDpqdoI_ba}]:hoc-p ŒhjigcVmo_bc"aec"d3pqa hoigc"!›] \I_ m!B}^!1 hjigcVpMh#bc!hepDpqdoI_ba}]:hoc-p ŒhjigcVmo_bc"aec"d3pqa hoigc"!›] \I_ m!Bg^!hjigc' ceagš=hoip hoigcV!h9B ^!+*-,/.] ep gmkho_V_b^9c"}]=a"c B}Žmo^ ©A@?Z


©E©¢¡?©EA5©E_$hjcem[h ga"ho_bpqa£œ]9qc(bc"agš=hjiSB^¤]=agšb]=d.„doc($%gcea48m©¥edop=mommoc!!hj_ pqa'p+ hoigcV"h¦gceagmk_ hD8 Blnšq^ ©¢¨§© >}p œ doc"mo_ mkhj_ D_ hD8B}lnšqm>©[^ ©¢¨hjcem[h ga"ho_bpqa[


¡£¢¥¤ ¢!©GI©J¥L)¡/G¤£ ¡H £!¡F ¡ L9F ¤ ¡§¨¥¨©G2¥§¦ ¡§©¨¤£]:hoc©hjigdkpgšqi]§!h9)”Q3ig_ m`_ mœSigc"a hjiIc©œ]9qc7bc"agš=hoi_ m c!$%}] hop NB M_agdopg]=š]=^`c"hoced ¤ N M8a )hj_b^`cemhoigcV!hI__bm¤hjigcI_@9cedoc"aec'˜9c!huœCc"cea hjiIc&mop gag gdkcemom0gdoc bc(=c! m.˜c(„pqdkc4A$A©E5#+¥9¢+¥9$.$hjc"dhjigcVmo_bc"aec"d_ m3_bagm[h] bc"*)]=ag']+D¥¨$)#+,#+§,-©C1"7D© _bm-hjigcep=^/ c!\dj]:ho_bpp Choigc`c(@9c!"ho_=c›mkpgag gdoc"momIdocUhp 1]=a ] ep gmkho_^`ceI_g^ ]=ag&hoigc c(@9c!!hj_ qc^}]=d[hj_!bc'qc(bp5e_ hD8]:hhji}]Fh]:hV]_pq_baa h9B 9pq_)


hj_ ]:ho_bpqa !hjm!B Ia„pqdkhga}]:hoc! 8Bšg_bIcagp=hpqa 8 hoigc=cea hj_ ]:ho_bpqa&]=_bd˜Ih] bmkpceahjiIcC=cea hj_ ]:ho_bpqa^†]=a*B œSig_i/e]=a.˜cc!\19c"do_ cea"cemopgaI.œ]9=cem!B5„pqdc!\I]=^bc„dkpq^hj_ ]:ho_bpqa!hjm:e]=a]+bmop/gag_ anhocea hj_ pqa}] 8š g_bgc]=magp=_bmocVhjp`hjigci%g^.]:ac¡]=d()3ceapqagc1dopDpq^ hjp]=agp=hoigcedA_ a,]˜g_ g_bagš) —1c!¡]+gmocp+}hjig_ m!B+=cea hj_ ]`3mopgaI,œ]9qc"m„dopq^ hoceà c!$%g_9c"›œS_ hjì mo_ cea"cedkmYhopdkce"choigcmkpgag/gdop }]=š ]:ho_bpqahj_bp=a›"hjm1]=dkcp]=a”p 9c"aRig]=agagc(.„pqdhjiIc2qcea ho_ ]Fhj_bp=a”]=_bdhjigdkpgšqi”hjiIcm08Dmkhoce^7BYœSig_bc©l:cec(g_bagšœ') >}pcea"cedAgdop=hop=hD859c"m]=dkchocem[hjce©]:h3P ¤¦BMPDœ1ceg_ moiŽ]Fhj_bp=a}] gQŒcem[hj_baIš ]=ag.Tc"moc¡]:diPM_h#Mhjc2„pqdcedV„pqdo^›]=a"c©}]:hj])ŸP1i ]&hjcem[h¤doc($5I_bdoc"m doc"mopgd0ec"m›_ aŸhjc"do^`m p Zuagmkho_"c B ^›] ig_baIced08 B 9c"domkpqa}] ]:ag§hj_b^`c ) Q3igcgd09p=moc¤p hjig_ mœ1pqdol_ mhjpm[h#g8m}]hD8`hjp¤dkc!b] ecVpqd"pq^/bce^`cea h3hoigcVc!\19c"do_ ^›c"anhj] +hjc"mkho_bagš œS_ hoic(:] 3hjigc'pqmomk_b˜g_b_pqagmSp hjigc[9c"d0„pqdk^.]:aecVp 2mo_ cea"ced3hjiIdopgš=i ep=^/Mh]:ho_bpqa}]+5^›]:hjigc"^.]Fhj_e] }]:hj_agš)&Zua”hoig_bmdoc!pqd[h mopIag gdopg]=š ]:ho_bpqa _ a”]!h¤_bm,^`pDgc!bce ˜=8ŸhjiIc^›pDgc!b_hocc(bce^`cea h1^›c!hjigpD]=aI.hjigc_bagmkced[hj_bp=a_bp=momYp !hjc"mo_ cea"cedkm_bmAepq^Ihoce*)&}ag_h]=š=c,p Agmo_ agš]2ep=^/Mh]:ho_bpqa}]+ hopMp Kep=^/}]:docehop]=a§c!\1cedk_b^`cea h] Q3igc`]=:]=a_bmŒhji}]Fh œ1c^›]68 ce]=mo_8TD_bm0}] b_"ecY:]=do_ pgm gigceaIpq^›c"a}]hop˜9c!hohocedKIaggcedkmkhj]=agmoc"hœ mo_ cea"cedkm_ba hocedj]+"h œS_ hji hjigc`œ]9=c2gdop }]=š ]:ho_bpqaS)£¢Ÿc›^.]98 ] mop79c"d0„pqdk^ ]igpp 2]¤"hœS_ hoi ]`mk_bc"aec"dS_bmSmol:c"h#iIce_ a&“2_ šgdkc ž)Q3igc hD85cOa&cy\Dhjcedk_bpqdD_bc!œmo_bceaecedCep=agmo_ gcedkce§_ba hjig_ mdkc!pqdkh_bm˜g_ hC˜=8'mopq^`c,]=Ĩmopqdk˜g_bagš›^.]Fhjcedk_ ] Bpmkigcec!h ^›c!h] „mopq^`c.p+3_ h[ced0„p=dj]:hoce )'Q3igc/9c"d0„pqdo]:hjc"b_bl:c›^`_baIcedj]+AœCpDp1]=ag¨„pqdk^›m ](85b_ aggced-œS_ hji hoigc`mj]=^`c¤dj]=g_gm ]=mVhjigc`!h,]=aI ] ]98qc"dmoigc"c"h,^`c"hj]hjiIc.]=Ĩmopqdk˜g_bagš'^.]Fhjcedk_ ] 2_bm'Ih˜9c!huœCc"cea”hjiIc/cedV„pqdj]:hoce moigc"c"h,^`c"hj] ]=agŸ]p_baggc"d3p moigc"c"h^›c!h] BImoc"c“ _bšgdkc O1)˜g_bšqš=ced(85¡ G2¥§-¡ ¨ ¤¥LA¡G]=dkšqc-a%g^,˜cedSp ¦epq^Ihj]:hj_ pqa}] 9c!\19c"do_ ^›c"anhom†]=mkh]=ag ]:hC p œ ep=mkh9B}˜c!e] gmkc_ ahjigcVmoc!h#^O0gmkh˜=82:]=dV8M_ agš}]=do]=^›c!hjc"dom!)hjigc'ep=^/Mhjced3œ1cJe]=adoc"˜g_“2_ šgdocž c¥¤§¦©¨§ &), ¨ &)( ¡G¤£¦¥§ ¤¥LA¡G ¡H © £KL ¢ ¡TG¤£¡T§


c!$%}]:ho_bpqa _ m?b_ agc¡]=d`œCc§^›]98


pqagc!"ho_bpqaS)Z œ1cIhhjigc,] epImkhj__ ^/ceg]=aec ? hop §¨ Bhjigc,p_bm hjigcmo]=^`c©_b^9c"}]=a"c©]=m,]=_bd 1 B_baŸhoigcTSpq˜g_ba epqagI_ hj_ pqa +Q hoi}]:hœS_œSig_ih _ a "pq^bc!hjc hjdo]=agmo^`_bmkmo_ pqa§p _ aep=^›_ agš©œ]9=cem^`pDgc!b_baIš›hjig]:hVhjigc`!hdocem0¤¥ , &)( & * 0 2 34§¦ž=ž


¡¡¡¡¡hj_ a%gcem() epqaho_bpqa BQ _bm1] mop[gmoc"2„pqdYhoigcmkcešq^`cea hCpqa.hjiIc˜pgag}]:d08¤œSigcedkcQ3igc-TSpq˜g_baep=agg_*"pMp=dog_ a}]:hjc"m!B Xc!b^`igp h#"c!$%}]:ho_bpqahji%gmSdoc""cemhopgdo_¡]ž#abcc¡ £¢ & ¨ * , ¨ * ¥¤ & ¢ ¨ ¢ ¢§¦ ¢ &©¨ ¤ * *¨ * ¢§¦ &©¨ ¦ ¢, 0 * ¦ ( , *,¨ ¨ “2_bšIdocfQ¢ * ¨ *, & ¦© &¨ * *, *, * ¢ ¤ ¢ * ¨ ¢ ¦ ¨§¢§¦ &¨-*, ¨ & *cea"ced`_bm¤m9p=moce


! N p=a mkcešq^`cea h ž„hjiIc["cea hjdkcp+ hoigcV"h „m08D^›^`c"hod08_ a©hjigc # g_ doc("hj_ pqa , N p=a mkcešq^`cea hO „hjiIc p Ih# c"h ? §¨ $#S _bm3^ hj_b_ ce©˜=8 # ]=aI&] hjc"mkhC ga"ho_bpqa RY$%}]Fhj_bp=a=cedhoigc2# !&gpq^›]=_baSB¦"pqdodkcempqagI_bagš hjp&^ ho_ 8M_ agšXc(b^`igp h#"¤c!$%}]:ho_bpqa O p ]=ag _ba hjc"šqdj]Fhj_baIš p =cedShjigc'481 _bagIdo_e] 5"hqp g^`c )Q3ig_ mSšq_=cem˜%8,< # "! ! # !


,,# ! ! # ! ,# , .N ¥ §? 9! #+* , . ! # *-,/. 6 ! ,#+*¢ ¤£ &)9&B'¦¥ ( )*¨§ J' E¡hjiIc&}aI_ hjc¤c(bce^`cea h^›c!hjigpD hjigcgdoc"mom0gdoc _ m]+gdop¡\M_b^›]:hoce ˜%8 ] ga!hj_bp=aZuaœSiI_i _ mJg_ c!"c"œS_bmkc_ _bagce]=dV_ba #- !'pqa”] hodo_b]=agšb]:hj_ pqa§p hoigc_"pq^Ih]Fhj_bp=a}] (]=mVmoiIp œSa _ba “2_bš gdoc Z )`OhVhjigc`agpDgcem ] pqagš˜pgag}]:d08 moc"šq^`cea h Z œ1cgpq^›]=_badoc-hjig]:h ( c!$%}] m % œSiI_iœCc"docVhjigcVšq_ qcea ˜pgag}]:d082:] gcem3p )doc!$%g_]Fhj_bp=a Z Bdoc( ]+e_baIš ˜=8 ( B]=ag igpDpqmoc £© „pqd ] mi hjig]:h £©^h Z BIœSig_iœC]=mSdoc($%g_bdkcep _ ahoigc-gc"do_:]:ho_bpqa=]:ag_bmki']+bpqagš˜9pIag}]=dV8moc"šq^›c"a Z ) pšqc"h]^:]=do_b]:hj_ pqa}] -„pqdk^ ]Fhj_bp=a©]=mS˜c!bp œ')¢Ÿc-hoigcea“2_baghoigc'gdoc"momIdoc ( ]=m]=˜p =cm0i'hoi}]:h„pqdS]+ £ £©# ( ! £ ! # !


¤ &£¢


]Fhj_bp=a}] \„pqdk^b]:hj_ pqaR„p=d›hjiI_bm`^›pDgc!_bm`hji}]Fh©c!$%}] 3Q3igc§g_@9cedkcea"c_bahjigcX=]:do_B[ i}]=mhuœ1p.^`pqdkchjc"do^`m!B}pqagc:„dkpq^ hoigcVagc"œ mopgd0ec-hjc"do^ B}]=aI'pqaIc:„dopq^hj_bp=aagc"œ ˜pgaI}]=d08"pqagg_ hj_ pqa ]:h˜9pIag}]=dV8moceš=^›c"anh Z ]:ag'hoi}]:hShjigcVhjc"mkhC gaZ3hjigcpqa}] }Ipq^.]:_ba._ m1m09c(e_ &}ce˜=8/b_bm[hj_ agš hoigc ! ]=aI #J"pMp=dog_ a}]:hjc"m


¡ ¥P)F §¡G $¡ "$%'&(*)¡p-c4=]+}]:hocChjiIcc ?e_ cea48 p ]mk_bc"aec"d œ1c3mkhg8,hoigcceaIcedoš+8bp=momA_ ahjigcCm08Dmkhoce^7)Q8]:h,hoigcpIhbc"h"dopqmkm¤moc!!hj_ pqa p hoigc!h¢Ÿcep=^/}]:doc©hjiIchop=h]+1œC]6=c'c"agcedkšhjiIpIhhjiIcmk_ cea"cedAhjpV]T"pq^/Ih]:ho_bpqa,œS_ hji hjiIc3mo_ cea"ced_ agmkhj] ce*)ŒQ3igcSceagc"doš 8œS_pqa}] hjp _bmgdkp9p=dkhj_¡p+2hjiIc "h!)_bmhjiIc["dopqmkmmkc!!hj_bp=a_bm ^`c¡]:mgdkce _ba }]:m¡]+bm¥ ¤ ] B˜Ih`mk_ba"c©hjigci%g^›]=a c¡]=d^e]=aPMpgagRgdkcemom0gdoc O8N! (" _ mS]`dkc(„c"doceaec[gdoc"momIdoc[epqdkdocem09p=agg_baIš`hop N)B "9)EFL!MM"FL F ¦ F $¡)HJ¡pq^/Ih]:ho_bpqaIm p Mhoigcmop gagIdocemkmgdkcYœC]9qcY_baV!hjm œS_ hoi ]=ag-œS_ hoigpIhŒ]3mo_bc"aec"dŠ¢ ( ¢1 / 1 OR4# ¢( ¢1 #- !œSigcedkc ¦doceš=_bmkhoced.Idocemkmgdkc_ a.hjiIcœS_bgcdo]=agšqcp !O8N ¤2]hop O8NDN ¤ ]Bg_ h3_bm


[ c &©(+&)* ¦ * ( ¢¦¥ ¨ ¢ ¢§¦ ¦ &¨ ¢ ¦ ,¨ ¦ ( & ¦ (+& , * ¨ ¦©¨ &), ¡ 0 3 ¢ *,¨ *“2_bšIdoc*¨ ¦© ¢@¥£¢ 0 2 ¢ (¢ 0 2 ¢ 1.510.50−0.5−1−1.50.10.080.06r direction0.040.020024z direction681.510.50−0.5−1−1.50.10.080.06r direction0.040.020024z direction68“2_bšIdoc ac & ( & * "¦ * ( ¢@¥ ¨ ¢ ¢§¦ ¦ &¨ ¢ ¦ ,¨ ¦ ( & ¦ (+& , * ¨ ¦ ¨ &©¨ &/, ¨ &/( & &), ¨ &)( &/, ¢ 0 3 ¢ 0 &¨ ¦©¨ &¥ ¢(+& *,¨ *¦¥ &/( & &), ¨ &)( *( & ¢ ¥¤ 0§¦ ¢ * ,¨ & ( *¨ ¦©§ž a


BA ¦ K!H L&() $% ' "#' ¡p=dhjigc^gdpqmoc¤p A"pq^/g]=do_ mopqa&œS_ hji§cy\cedk_b^`cea h]+Adoc"m hjmœ1c`ig]6=c`] bmkp2epqa53“hjigc/¡]=mkc©p 3hoigc_qc"a hj_b]:hj_ pqa "h,ceagg_ agš_ a ]&˜g_ š&dkpMpq^7)Q p] !"pga hmo_bIcedoc"Shoigcœ]9qc"m›c"a hjcedk_bagš§hoigcpIhbc"h¤p+]§"h¤ceaIg_bagš _ a ]=a„pqd,hjigcdkc(>}c("ho_bpqagm¤phjci}] m}]+ec a"pqdodkcem09pqaIg_bagšhjp ]Ĩ_bš,dkpMpq^ hjigc˜9pIag}]=dV8_"pqagg_ hj_bp=agm]:h_ba&}aI_8:; 7 8 §¨ ž , O #+* , . ¢#+* ,/. 1 £œSigcedkc§¢ _bmhoigc —Ccemkmoc( ga"hj_ pqap ŒhjigcT&}dkmkhpqdoIced!)¨ ¨ ¡:©£¥¤§ ¡TF ¡:G?¥ F ¡;¥©*¡ ¨¤£pqa}] Sc4=]+}]:ho_bpqaIm.p -hoigcmop gag gdoc"mom0gdoc doc"!hj_bp=a p -hjigc&mo_ 3Q3igc¤epq^Ihj]:hj_ _b}]Fhjce ˜=8 "pq^/g]=do_ mopqa hjpcy\cedk_b^`cea h]+1}]Fh])Q3iIcedoc©]=doc›moc(=cedo] bceaeced_bmJ:]hjm2^.]=Ic]:hP ¤ ]=ag,pqaIcC_bm gcem0edk_b˜ce ˜c!bp œ') O ^`c¡]=m0gdoc"^›c"anh2p }hjiIc^›ce]=mgdkce^`cea § $M"FL )* ¡ M"9)E FL!EK"H L&(*)©[DO8Q MCc ž = IžVmopgaIdoc""ho_bpqa _bm^`c¡]=m0gdoc"&˜=87epq^}]=dk_bagš hjiIcO;!"pqdoI_bagš`hjp`Z[Pg’c($%g_g^`cea h7„pqd^`c¡]=m0gdo_ agš mopgaI doc"!hj_bp=a p ,]”mo_ cea"cedep=agmo_ mkhjm p ]Q3igcB1] mk_ cea"ced!Bhuœ1p "hom`hodj]=agm09p=dkhj_ agš§mop gag œ]9qc"m›hopmopgd0ec7gdopD"_bagš§aIpq_bmkccea"ced!Bg] hodj]=aImo^`_bmomk_bpqac(bc"^›c"anh {] igpqdka ceagI_bagš _ a'],dkc(=cedo˜ced 3]=ag?„dopq^¢hjigc-mk_ $'&)(+*,-&/.1012)3546hjigcVpIhbc!hS_bm3^`pMg_ &}ce?„dkpq^ §¨ hop¦NS4


^.]=l:c&hjiIc§mopgaI gdoc"momIdocgdpqmkchjp”doc"^›p6=cdoc4>}c!!hj_bp=agm]:h.hoigcpMh#bc!h]=aIho_ba%gchoigdop gšqi›hoigciIpqdoa]:ag._ anhophoigcdkc(=cedo˜cedo]:hj_ pqa©dkpMpq^7)2Q3iIcigpqdkaœ]9qc"mepqaagšhopZ[Pg’H[8O8Q Mc ž q Iž B i}]9qc-]-hjp=hj] ]=agš cSagp=h1šqdoce]:hjc"dYhoi}]=a&ž M©¨ hop^gmkh!BI]+!ep=dog_pqa ¡~D| v=w©‡~F| =… x†…ˆ~F|I‰4)]=mS_bamoc("hj_hoigc doc4qcedk˜9c"dj]:ho_bpqa dkpMpq^7B5œSigc"doc hjiIc igpqdoa§hocedo^`_bag]:hjc"m!B+hjiIcedoc¤]:doc mo_ \§^`_"dop+3Zuagigpqagc ^`c¡]=m0gdoc"mhjiIcmop gag¤gdkcemom0gdocp =ced-]ec"dkh]:_ba'ho_b^`c Bgigpqagc"m!)RY]+i§^›_edop8¦QDN.mkc!"pqaggm(B ]=aghjiIc docem0 h_bm:Idocemkcea hjc"Ÿ]:m-].^`c¡]=a :] gc,p6qc"dhj_ ^›cagpqdo^›]\^`_edkpgigp=agcem()]=aghjigcVmo_41232c¡ £¢ ¦©¦¢ &), ¥ ¢( ¢ & * ¦ ( , ¢ ¦ ,¨ (+&¨ ¦ ¨¢,¥¤ 2© ¢ ¦ ( ¨ & ¦ ( ¢ ¨ ¦©¨ , ,5¢ &0 ¦“2_bšIdoc¦©¨ ¦ ¨ , & ¢ ¦ ,¨ * ¢ & 0 ¤ &), ¨ &)()0 §¦ ( * , ¥¢ ¢5, & & ¢ &), ¨l=cec(Ÿc4qcea h}] Y]=_bd >}p œ ]:^›_ a}]=d]=ag ]=a pIhbc"h ]:doc¡]p 1]:h' c¡]=m[h=O.^ 1 hop ^›]=l:chjigcVmop gag'œC]9qc"m]=`O0ImkhShjp`]^ ]=dkšqced.=pI^›cœS_ hjiagp¤doc4>}c!!hj_bp=agm!)YZuahjigc ^.]Fhji13ce^›]:hj_¡] „pqdo^ ]:ho_bpqahjiI_bm_ m^›pDgc(bc"'œS_ hjihjiIc¤] epImkhj_,_b^ce}]=aec ? §¨ BQ3igc'mkpgd0ec7gdopD"cem`] m09c("hodg^ p C„doc($%gcea"_bc"m„dkpq^ M N XC"hop ž.N N8NDN X " )15 o“2_bšIdoc,ž5N c© & ¢(+, ¢ ¦© * ¢ & * ¢ * *, & ,5¢ 5( & * &)( *, 2 ¦ GH©E"$.©C§,©C¨ W ¢g4 \ 93'F+£C:9:6£2+£I_@9cedoc"a h c!\1cedo_ ^›c"a h] 1moc"hgm¤]=dkc©agc"cegc"hop§šqc"h¤]+!ec(Ihjc" docem0 hom¤] 43Q3igdoc"cepqdkg_bagš§hop Z[PI’ [DO8Q Mc ž¡ q Iž) ’-aIcœS_ hji”hjiIc mk_ cea"ced _baImkh]+bc"*Bpqagc©œSiIcedochjiIcODž


cea"cedY_bmdoc( ]+ece`˜=8›][g_ c!"cp 5!h]=aI›hjiIc b]=mkhYpqagc3œS_ hji¤hjig_ m


žqž c ¢ ¦ ¦¢ &/, ¥ ¢5( ¢ & * ¦ ( , ¢§¦ &©¨-* , ¨ & , ¢ * &/( * ¤ 2© * ¢§¦ &0 ¦ ¢ ¨ (£¢¤£“2_bšIdoc¢,-& 0 ¤ ¦ & * ,¨ ¦ ¢ ¦ ,¨ ¢ ¦ ( ¨ & ¦©2 _b˜gdo]:hjc"`]=agIhY_ba hopVhoigc3h#g˜c] mk^.]+II_bmkhj]=a"cQ3igc^`_"dopIigpqagc"m]=docgi}]:moc¡]ce] i p=hjiIced!) Q3igcCmo]=^bcœSig_i,_bm ] g_ c!"c1p Ihjigc1^.]:hocedk_ ] „dkpq^ hjigcYmo_bc"aec"d„dopq^hSgc"m"do_b˜ce _bamkc!"ho_bpqa ¤‚ sovF‰Dws!z.s!|}x~ €‰ ~D| ›wjsgmoc"&_ba©hoigcV^›ce]=mIdoce^`cea ‡!x†…ˆ~F|_bm'Mh ]:hVhjiIc›c"ag p 1hjigc`h#g˜c )Q3igc¤hjc"mkhoce ^›]:hjc"do_b] epqaImo_bm[hjc"Ÿp S M]=˜gmkpqdoĨ_bagš'^.]:hocedk_ ] B2]'hoig_ba &}˜gdkpgmb]68=ced]=ag”] cedV„pqdj]FhjceŸmoigc"c"h¤^`c"h]+ )^›^h_ a?„dopq^¢hjigcVmop gd"c )¤Yb]=agc-œC]6=cem]=doc-mkcea]=ag&mkh]:agg_baIš›œC]6=cemV]=dk_bmkc )3Z agp›ceagc"doš 8'_bm]=˜gmkpqdo˜ce*BQ3igcœC]6=cemV]=dkcdkc(>}c("hocem1hop=h] dkc(>}c("hj_ pqa*BDhjigcmkpgag?IdocemkmgdkcV_bmA"ecedkp _ba.hoigcagpDgc"mœSig_i^`c¡]=aImChjigc"doc_3hjigcm[h]=aIg_bagš'œ]9qc"m¥„hjiIc©mop _b !gdVqc_ba “2_bšIdoc žO ) ¢ igcea”hjiIcedoc._bmmkpq^`cpIc_bà hjigcagpMIcem hjigc}]=moiIce]=˜gmop=dIho_bpqa.hoigcmkpgag2IdocemkmgdkcVšqc"hom]agp=a"ec"dop:]a“2_bš gdoc žO ) !gdVqc_agšŸ^`c"hoigpMWgmoc"m]Ÿ^`pq˜g_bc^`_edkpgigp=agc hoi}]:h_ep’-aIc&^`c¡]=m0gdo_)›Q3igc&}dom[h^›]F\M_b^g^ ]=aI ^`_bag_ ^g^ p Yhjigc`mopIag gdkcem 3hjigc`_b^9c"}]=a"c,h#g˜c_ m„pgaI^›]=a%}] 8 ]=ag ˜=8Ÿhoigc2:] Ic©_ba hoigcemkc7pq_ anhom,hjigc]:˜gmopqd0Ihj_ pqa”_bmmgdkc!b]:hjc"*) ¡]huœ1p.^`_"dopIigpqagc-^`c"hoigpMgmkcemShjigc ^`_edkpgigp=agcem"U}]=˜g_b_ hD8 Bg]+ hocedSmo_ šqa}] Sgdop+3Q3igcagšBChop ^`c¡]:mgdkc'mkpgagWgdoc"momIdoc&p+œC]9qcem._ba ˜9p:hjig_bdkc!"ho_bpqaIm,hjp šqc"h¤hjiIcecemkmo_ŒhjigcVmo]=^/bc )]=˜gmop=dIho_bpqap1234¢¡¢¢¡¢¢¡¢GH©E"$.©C§,©C¨˜c Mh©_ba hopO_Q


c & * ¢ ¦ & ¢ ¦ ,¨ ¦ ( & ¦ (+&¤£¥¦£ , *, ¢§¦ &©¨-* , ¨ & ¦ &!¥ ¢( * ¢5( ¦ ¢, ¨-* &©¨“2_bšIdoc-žO,-&© *,¨ ¢ * (+&¨§ & ¨¢5, & ¢ ¨ , &© * & * ¢§¦ & ]=doc hjigdkcec'hD85cemp c!\19c"do_ ^›c"anhj] moc"hgm?gmkce ]:hP ¤¦)YQ3igcI_@9cedoc"aec"mQ3igcedkchoigce^ ]=dkchjigc mopIdec moc!h# ]=ag hjigchjdo]=agmk^›_ momo_ pqa”c! ce^`cea h9) “2_ šgdoc˜9c!huœCc"ceaœSmVhjigc mkc"hŸ]+!ep=dog_ agš©hjpZ[Pg’ žqž Z Mž c ž¡ q M )-Z hVi}]:mV]©doc(>gc!"ho_bagšmkpgd"cž5Q©moigpceagIm _ a ]©i}] m}] "c ),Zua “2_ šgdkc©ž.S]©moc!h# ] (epqdkg_bagš©hopZ[Pg’^[8O8Q Mc ž q Iž]=agœSa*)Q3igc mopIdec _bm dkc(>}c("ho_bagšB1˜Ih¤hjiIc "hoce mk_ cea"ced¤agp œ c"aggm`_ba]_bm¤moigph9)Q3ig_ m3moc"hœ]=mImoce _ba©hoigc-^`c¡]=m0gdoc"^›c"anhSIcem"do_ ˜9c"'_ ahjdj]:agmo^`_bmkmo_bp=ac!bc"^›c"ašgdkc›ž M _bm]=˜gmop=do˜g_ agš]=ag'hjigc,"hoce§mo_bc"aec"dceaIgm_ba].i}] m}]+ec )Q3igc_ba§“2_c!\19c"do_ ^›c"anhj] moc!h# _ mJe] ce hjigc©• ‹ŒPgN ^›c!hjigpD ]:ag^›c!hjigpDŸ˜}]:moceŸpqaŸhjiI_bma PDœ1cegc"a˜9c4„pqdocVZ[Pg’ žqž Z Mž c ž¡ q M œC]=m_ a hjdopD"ce*)œ]=mCgmkce&_p`^.]:l=cV]:] b_ }]:hj_ pqa.p+ hoigc'epq^Ihj]:hj_ pqa}] ^›pDgc(5œCc'"pq^/g]=doc-^`c¡]=m0gdoc"^›c"a hQhomK„dop=^*hoigcChjiIdocecCc!\19c"do_ ^›c"anhj] Imkc"hgm]=ag p=agcp }hoigc3] "pgmkho__ ^/ceg]=aecdocem0hji7ep=^/Mh]:ho_bpqa}]+9dkcem hjm3œS_ hjihjigcVmj]:^›cT}]:dj]=^`c"hocedom()œS_€¡~FwFv¢ … v=x†…ˆ~F| ~ €-x ƒ}s z.~DsD_baO;ceaIg_ \U)œ¢docemk_bm[hj_D_ hD8Ÿ_ m,]&mkceagmk_ hj_ qc2g]=dj]=^`c"hoced()§Z h¡]:a”c(qc"aR:]=dV8 ˜9c!huœCc"ceamo_ 3Q3igc2>}phji¤hjigcSmo]=^›cSgc"mo_ šqa*)AQ3igc:] Ic3gc!ceagIm]=^`pqagšVp=hoigcedhjiI_bagšqmpqà igp œbceaecedkmYœS_hjigc ^›]:hjc"do_ ]+ _bmepq^gdkcemomkce*)3Q3iI_bm=]+gc _bm3œSdo_ hohocea&_ a hoigc'&}šgdkc hoc!\Dh;„pqdi}]=do|p|¡¢¡¢¡¢¢¡¢¡¢¢¡¢¡¢¢¡¢¡¢¡ ¢¡¢¡¢¡ ¢¡¢¡¢¡ ¢¡¢¡¢¡ ¢¡¢¡¢© © ¢9L Ï©[¥LA¡G ¡H ¥© ¡ h¡/F ¤ ¤ ¥K©J¥¨LA¡GI© ¢RF ¡ ¨ ¡ ¢moc!!hj_ pqa ‚ sovF‰Mwjs!z.s!|}x ¥ § § )ŒQ3igc3mop gd"c_ ahjiIc3moc"h`moigp œSa8_gdkcemkcea hjc"&_ba.pqagchjiI_bdop5"hj]9qcemigc"doc BI˜IhSmop=^›cV]=dkc-c(=ceaQ3igc'bp=hom3]=dkc-^›pqm[h#hoceŸ_ ap5"h]9=cem!) Q3igc^}]:dj]=^`c"hocedom]=doc _bm[hjce&_bamkc!"ho_bpqa v=wov=z.s!xus!wj‰gdoc"moceac¡] i7&}šgdkc )OS


¢¡¤£¦¥¨§©! #"%$'&( *)+,".--0/.1++23 */4(57698:88:?@8=:=!ABC¡D£¦¥¨§©EGF¨! #"%$H&*0 *)>I".--/:#1>2J /K4(56ML%N%O.A+?88:BQ7Q7Q7Q P7P7P7PQ7Q7Q7Q P7P7P7PQ7Q7Q7Q P7P7P7P¢¡¤£¦¥¨§©>RS! #"%$H&*0 *)>T".--0/.1++23 */ U+JVXWY5+Z[ *U+/1'B\ R


c© &)* ¦ (+&¨ £ * ,¨ ¨ ¢ ¢§¦ ¦ &¨ £ £ ¢ ¦ ,¨ ¦ ( & ¦ (+& & ¢ & (+&¨ ¦ ¨¢, ¥ ¢5( & & ¦¦“2_bšIdocVž[¨ ¨ ¢( ¨ , ¢ " 22 63 2¤ 2)33 ¦ 0 & &/, ¨ &/( &/, ¢ 0 ¢ *,¨ & (+*¨ ¦ ¢-0 ¢6 ¦ ¦ ¢ &*¡ * $F &(M) ¦F M L" $HJHJFLEK&)¨§ '£¢¤¥¤ ¡¦ ¦§¨ ¦ Z ]:ag ž[&_bagI_¡]Fhjcemhji}]:hœCci}]9qc˜}]:R"pq_bae_bIcea"c©p hjigc^`c¡]=m0gdoc"“2_bšIdocžh„pqdYhjigc-mkc"h#&] (epqdkg_baIšhjp Z[Pg’ žqž Z Mž c ž¡ q M ]FhhjigcT p œCc"d]=agepq^Ihocedkcemcem˜IhšqpDpM ]:h3hoigcV^›_ g c;„doc($5Icea"_bcem()„doc!$%gc"ae_605040Reduction, dB302010010 1 10 2 10 3 10 4Frequency, HzZc© &)* ¦ (+&¨ £ * ,¨ ¨ ¢ ¢§¦ ¦ &¨ £ £ ¢ ¦ ,¨ ¦ ( & ¦ (+& & ¢ & (+&¨ ¦ ¨¢, ¥ ¢5( & & ¦¦“2_bšIdocVž¨ ¨ ¢( ¨ , ¢ " 22 63 2¤ 2)33 ¦ 0 & &/, ¨ &/( &/, ¢ 0 ¢ *,¨ & (+*¨ ¦ ¢-0 ¢6 ¦ ¦ ¢ &*¢ (+& ¢ ¤ ¤ ¢ ¢ ¢¦ ¥¢ ' *,¨ & ¨ ¦ £ ¢,#¥ ( & ¢ ¦ &/, ¨ ¤ 2 ¦ 4 §605040Reduction, dB3020100−1010 1 10 2 10 3 10 4Frequency, Hz§ ¢ (+& ¢ ¤ ¦ ¢ ¢ ¢ ¢¦ ¥¢ ' *,¨ & ¨ ¦ £ ¢,#¥ ( & ¢ ¦ &/, ¨ ¤ 2 ¦ 4 O Z


¡ * $F &(M) @ F M '" $HJHJ FLEK& )¨§ ' ¢¤¥¤ ¡ A¡ §¨ ¦ BApq^/g]=do_ mopqa ˜c"huœ1cecea hjigc^`c¡]=m0gdoc"


c © & * ¦ ( &©¨ ¢ & * ¦ ( & ¢ &/, ¨ & ¨ ( !&¨ , & ¨ ¢, ¢¡¤£¦¥¨§©§§¨“2_bšIdocO8N!"$#% £ * ,¨ ¨ ¢ ¢§¦ ¦ &¨ £ £ ¢ ¦ ,¨ ¦ (+& ¦ ( & & ¢ & ( &©¨ ¦©¨¢5, & &/, ¨ &/( &), §45403530Reduction, dB252015105010 1 10 2 10 3 10 4Frequency, Hzc© &)* ¦ (+&¨ £ * ,¨ ¨ ¢ ¢§¦ ¦ &¨ £ £ ¢ ¦ ,¨ ¦ ( & ¦ (+& & ¢ & (+&¨ ¦ ¨¢, ¥ ¢5( & & ¦¦“2_bšIdocVž¨ ¨ ¢( ¨ , ¢ " ¦ ¤ ¦ ¤ 2)33 20 & &/, ¨ &/( &), 20Ž¦ ¢ * ,¨ & ( *¨ ¦© ¢-0 2]¦ ¦ ¢ &*¢ (+& ¢ ¤ ¦ ¢ ¢ ¢ ¢¦ ¥¢ ' *,¨ & ¨ ¦ £ ¢,#¥ ( & ¢ ¦ &/, ¨ ¤ 453¦ §40353025Reduction, dB2015105010 1 10 2 10 3 10 4Frequency. Hz¢ 0 3 ¢ *,¨ & ( *¨ ¦© ¢ 0 2 ¢ &§R¢ ( & ¢ ¤ ¦ ¢ ¢ ¢ ¢ ¢ ' * ,¨ & ¨ ¦ £ ¢,¥ (+& ¢ ¦ &), ¨%¤ 3546 O a


\¦\ XZ,".&()+1¥¤§¦©¨ "%>1 -/:+) 1¤§¦¦¨ &*/:)+71+*1)7- *@/: /. U+¢&*0 )+C¡¤£¦¥§-C$+2% U = ":>1 #":1+)>& .A TB U>".--/:#1>2¡ * $F &(M) @ F M '" $HJHJFLEK&)¨§D L ¢¡ § L Epq^/g]=do_ mopqa „p=dhjigc mkc"h ] !"pqdog_ agš.hop©hjigc`•V‹ŒPgN ^›c!hjigpD§šq_ qcemšqpMpDI"pq_ba13ŠhT„dkpq^ hoigcepq^Ihoce ]=ag ^`c¡]=m0gdoc" e]=moc^„pqd:„dkc!$%gceae_bc"me_bIcea"c`p+1hoigc¤docem0hop ]=˜9p Ih-hjigc^(Ih03 pqa „doc!$%gc"a(8 B mkcec`“2_ šgdoc ODžBO8Q]=ag,O_S),“2_bšIdoc ODO©i}]:mae_ gcea"cT„pqd3mc!!hjdj]hjp›]=˜pIh(O8NDN8N X " )epq_302520Reduction, dB151050−510 1 10 2 10 3 10 4Frequency, Hzc© &)* ¦ (+&¨ £ * ,¨ ¨ ¢ ¢§¦ ¦ &¨ £ £ ¢ ¦ ,¨ ¦ ( & ¦ (+& & ¢ & (+&¨ ¦ ¨¢, ¥ ¢5( & & ¦¦“2_bšIdoc(OMž¨ ¨ ¢( ¨ , ¢ &£¢ ) © ¢ & ¢ ¨0 & &/, ¨ &/( &), ¢-0 6 ¢ * ,¨ ( *¨ ¦© ¢-0 2]¦ ¦ ¢ &*¢ (+& ¢ ¤ ¦ ¢ ¢ ¢ ¢¦ ¥¢ ' *,¨ & ¨ ¦ £ ¢,#¥ ( & ¢ ¦ &/, ¨ ¤ 453¦ §706050Reduction, dB403020100−1010 1 10 2 10 3 10 4Frequency, Hz /&*@&( *G & ! !#"¢&(%$'&":>1 *U+ -) (¦ /:) *+*!)+>- &X8=L N#,.-:B\0/


c© &)* ¦ (+&¨ £ * ,¨ ¨ ¢ ¢§¦ ¦ &¨ £ £ ¢ ¦ ,¨ ¦ ( & ¦ (+& & ¢ & (+&¨ ¦ ¨¢, ¥ ¢5( & & ¦¦“2_bšIdoc(O8Q¨ ¨ ¢( ¨ , ¢ &£¢ ) © ¢ & ¢ ¨0 & &/, ¨ &/( &), ¢-0 3 ¢ * ,¨ ( *¨ ¦© ¢-0 2]¦ ¦ ¢ &*\ F¨XZ,".&()+1¥¤§¦©¨ "%>1 -/:+) 1¤§¦¦¨ &*/:)+71+*1)7- *@/: /. U+¢&*0 )+C¡¤£¦¥§-C$+2% U = ":>1 #":1+)>& TB U>".--/:#1>240353025Reduction, dB20151050−510 1 10 2 10 3 10 4Frequency, Hz§ ¢ (+& ¢ ¤ ¤ ¢ ¢ ¢¦ ¥¢ ' *,¨ & ¨ ¦ £ ¢,#¥ ( & ¢ ¦ &/, ¨ ¤ 453¦ 605040Reduction, dB3020100−1010 1 10 2 10 3 10 4Frequency, Hz /&*@&( *G & ; ! !#"¢&(%$'&":>1 *U+ -) (¦ /:) *+*!)+>- &X8


¡$¡&E9$%'&) 'M'&)HJ!F & =!E9$¡)HJ E9pqa "pMc@?e_bc"a h †“2_bšIdoc O M ]=agŸ] dkc(>}c("hj_ pqa "pqagm[h]=a h,_ mš=_qc"a „pqdOa”]=Ĩmopqd0Ihj_iI„dkc!$%gcea(8'˜}]=ag_ a'hoigcdo]=agšqc M Ǹ hop&ž Z NDN›XC",]=m]›dkcem hp AhjiIc^`c¡]=m0gdocZ3c¡]^›c"anh¤p+hoigc ] epImkhj__b^9c"}]=a"c©gc"medk_b˜ce_ba ‚ sovF‰Dws!z.s!|}x~ €vD‡~n‰!x†…ˆ‡zt}s v=|5‡s4)AQ3igc docem0 h]=aI']ep=^/}]:do_bmkpqa©œS_ hoi&]:a']+epgm[hj_ _ ^/ceg]=aec-^`pDgc!… a _ a moc!!hj_ pqa …bs!|5‡s!w _bmAmkigp œSa›_ a¤“2_bš gdochO Z )2Q3igcS]+epgm[hj_†moc"cRY$%}]Fhj_bp=a v=wkv=z.s!x s!wj‰ €¡~Fw Fv¢ … v=x{…ˆ~F|§~ €x ƒ}s-z.~Ds _ a_b^9c"}]=a"c_bm


O Zc & ( & * *,¨ ¢ * , * ( ¤ ¦ *( ¥ ¢5( & ¢ &)* ¦ (+&¨ £ * ,¨ ¨ * ¨ ¦ * &¨ * ¨ ¢ ¦© ¨“2_bšIdoc¢§¦ &©¨-* , ¨ & & § ¢ (+& £¢ ¤ ¢¦¥ ¤ ¢ ¢ ¢ ¢ ¢ ' *,¨ * ©¨ . ,-& ¢¦¥ & * ¢( ,* &/( * ¢¦¥ ¡ ¦ ¨%¢ *,¨ £ £ ¨ ¢ ¢!b]:hj_ pqa&gp=agc )-Q3i}]Fh-_bm ¡] gmkce ˜=8m[h]=agI_bagš.œC]9qc"mVhoi}]:hV]:doc"doce]:hjc" ˜=8'docZ3¡]1œC]9qc"m,]:h'„pqd-cy\g]:^/ c,hjigc¤_ abc!h-p Yhjigc¤mo_bc"aec"d!)¤Q3igcemkc`œC]9qc"m,]=dkc>}c!!hj_bp=agmVpa˜9pIag}]=dV8epqagI_ hj_ pqagm()YQ3iIcc4@5c("h_bmSagp=hShoi}]:hpq˜=D_bpgmS_ aedoce]:hjc"&˜=8i}]=aIšqc_2000REAL PARTAcoustic impedance, Nsm −510000−1000−2000−3000−400010 1 10 2 10 3 10 410000IMAGINARY PARTAcoustic impedance, Nsm −580006000400020000−200010 1 10 2 10 3 10 4Frequency, Hz¡ "#£¢ ) ¦FL! #")H GBi}]9qcJ ]=aIcVœC]9qc"m;„pqd„doc($5Icea"_bcemC hjp›]pq_ba hSœSigc"dochoigc-œ]9=cbc"agš=hji _bm¢Ÿcc!$%}] 5hop%NB M8a ho_b^`cemYhjigc"hg_ ]=^`c"hoced¥¤ ¤ N M8a )AQ3ig_bmA„doc($5Icea48©_bm


c & ¢ ¦ ,¨ ¦ ( & ¦ (+& (+&¨ ¦ ¨¢, (+&¨§ & ¨¢5, £ *,¨ ¢ ¦ ( & § & ¨ ¢, * &“2_bšIdoc@OD[¢ ¦ ( ¨ & £ £ & &/, ¨ &/( &/, ¢-0 3 ¢ * ,¨ & ( *¨ ¦© ¢ 0 2 ¢ & ¨ ¦ £ ¢, ¥ ( & ¢ ¦ &/, ¨ ¤ 3546 a ]¤mkc¡]=d0iX„pqdS]:a&]=mSpMhj_b^›] gcemk_bšqa']=mpqmomk_b˜ c )]=ag=]:d08?}]:dj]=^`c"hocedom3_mkc"h# ] (epqdkg_bagš©hophjigc›•V‹ PIN ^`c"hoigpD œS_ hji ]=a ]=˜13Q3igc›m[h#g18¤epqaecedkagmVhjigc )¨§' ' M& ()HJ!F©a “2_ šgdkc`O a hjigc2 ceagš:hji p 3hoigc.mk_ cea"cedig]=m ]&˜g_ š&_ ^/}]+"hpqaOmœ1c?¡]=aŸmocec_doc"^›pDgc(b_ agšhoigcSmopgd0ecS_ba¤mkc!"ho_bpqa ¡ Ss!z.~Ds … |£¢¤~ €Sx ƒ}s3‰ ~Mwj‡s !s‡ov ‰ s-~ €—


A )¨§' ' EK"H M©i}]=agšqcV_ ahoigcTbc"agš=hoi p+ hoigc-!h˜c"huœ1cec"a&hjiIc-mopgd0ec]=aghjiIc mk_ cea"ced3^›]=l=c"mŠhkh# cg_@9cedkcea"c1_ ahjiIc1dkce!hj_ pqa*B=mkcecC“2_bšIdocJO= )ŒQ3igcCdkce"hj_ pqa_ m mkhjdkceagš:hjigc"agceb_gmkc p+2m[h]=agI_bagš œC]6=cem_bahjigcV"h9)¥¢ igc"a hoigc'bc"agš=hjip ŒhjiIcpqdœCce]=l=c"agce§˜c!e]hjigc mo_bceaeced ]=aI hoigc pIh# c"h _bm2:]=dk_bc"*Bhoigcemkc gigc"agpq^`cea}]]=dkc"h'˜c"huœ1ceceapqaIc;„doc($5Icea48.hjp,]=agp=hoigced †“2_bš gdoc(QDN )AZ hjigcc!\19c"do_ ^›c"anhj] moc"h^›p6qc"2„dopq^hjiIc©hjdj]:agmo^`_bmkmo_bp=aŸc! ce^`cea h^i}]:agšqc_ba hjig_ mg_bc(ec©p+"h,œ1p ”agp=h ig]6=ci}]="h!) _b^}]60Variation <strong>of</strong> the length <strong>of</strong> the silencer5040Reduction, dB3020100−1010 1 10 2 10 3 10 4Frequency, HzO ac© & &/, ¢¦¥ & &), ¨ &)( ¢ * ( &©¨ !& &/&), ¢ 0 2 ¢¡ ¢-0 ¤ ¢¡ ¢-0 6 ¢¢“2_bšIdoc£ ¢ 3 ¢¢ ¢ 20Ž¦ ¢ *,¨ £ £ 250 ¦ ¢ * ,¨ &©( *¨ ¦© ¢ 0 2 ¢ & ¨ ¦ £ ¢,¤¥ ( & ¢ ¦ &/, ¨ ¤ 3546 45403530Reduction, dB2520151050−510 1 10 2 10 3 10 4Frequency, Hzc & &), ¢¦¥ & ¨ ¦©¨ !& &/&/, & ¢ ¦ ( ¨ & *,¨ & &), ¨ &)( ¢ *( &¨!& &/&),“2_bšIdocO=£ £ ¦-0 ¢ ¢¢ 0¦ 0§¦ ¢¡ £ £ ¤ 0 ¢ ¢ 0 £ ¤ 0 ¦ ¢ *,¨ ¡ ¦ 0 ¢ ¢ 0 & &/, ¨ &/( &), ¢-0 3 ¢ & ( *¨ ¦© ¢-0 2 ¢ & ¨ ¦ £ ¢5, ¥ (+& ¢ ¦ &), ¨%¤ 3546 *,¨Q_S


40Variation <strong>of</strong> the length <strong>of</strong> the duct after the silencer353025Reduction, dB20151050−5−1010 1 10 2 10 3 10 4Frequency, HzQDN c & &/, ¢¦¥ & ¨ ¦©¨ !& &/&), & &), ¨ &)( * ,¨ & ¢ ¦ & ¢ * ( &¨ !& &/&),“2_bšIdoc ¦-0 ¢ ¢¢ ¦-0 ¦ ¢¢ £ £ ¤ 0 ¢ ¢ * ,¨ £ ¤ 0§¦ ¢ 0 & &/, ¨ &/( &), ¢ 0 3 ¢ * ,¨ & (+*¨ ¦ ¢ 0 2 ¢ & ¨ ¦ £ ¢5,¤¥ ( & ¢ ¦ &/, ¨ ¤ 3546 ©¦ $EK& "M ' EK"H Mdj]=I_gmp+Yhoigc,"hVi}]=m]=a§_b^}] !hpqahoigc,mop gag gdoc"mom0gdoc¤doc"!hj_bp=a*B5hjiIcQ3igc ceddo]=g_ImhjigcV˜c"hohocedSdoc"!hj_bp=a †“2_bšIdoc QIž )mo^›]1008060Reduction, dB40200−2010 1 10 2 10 3 10 4Frequency, HzQIž c & ( *¨ ¦© ¢¦¥ &¨ ¦ ¨ ©¢ * ( &©¨ !& &/&/, £ £ ¢-0 ¢ ¦ ¢¡ ¢ 0 ¢56§¦ ¦ ¢¡ £ £ “2_bšIdoc0 ¢54 ¢¢ £ ¢-0 2 ¢ ¢¡ ¡ ¢-0 2]¦ ¦ ¢¡ ¢ ¢-0Ž¦ ¢ ¢ * ,¨ ¢ 0 ¤ 2 ¦ ¢ * ,¨ & &/, ¨ &/( &/, ¢-0 3¢ & ¨ ¦ £ ¢,#¥ (+& ¢ ¦ &/, ¨%¤ (+& ¦ & ¨¢ & ¤ 6 ¦ 50 3456¦ 0 2 ¦ ¢53¦ ©* ,¨ 2)3 ¦¦ ¢Q M


¢ =!F ¦FL$%!E M'! J$¡©igcea hjigcigp bcdj]:g_gmp hoigc9c"d0„pqdo]:hjc" moigc"c"h`^›c!h] C_bm:]=do_ ce œ1cmocec7b_ hohbc¢_badkce!hj_ pqa ]:h3hjigc' p œ1ced„dkc!$%gceae_bc"m †“2_bš gdoc QO )i}]=agšqcmj]=^`c_bm›hjdIcœSigcea hjigc ]:^›pIanh©p igpbc+BSdoc!Idocemkcea hjc" ]=m©hoigc§igp cIcedV3Q3igch!BI_bm:]=dk_bce {“ _bšgdkchQDQ ]=ag›mo_ ^›_ ]=d08VœSigcea›hjigcShjig_lnagcemkmCp 9hjigcC9c"d0„pqdo]:hjc"ecea+_ m.:]=do_ ce {“2_ šgdkc Q8S )moigc"c"h^›c!h]40Variation <strong>of</strong> the radius <strong>of</strong> the holes in the perforated metal353025Reduction, dB20151050−5−1010 1 10 2 10 3 10 4Frequency, HzQO c & ¢ & ( *¨ ¦© ¢ *( &¨ £ £ ¢-0§¦ ¢ ¢¡ ¥20 ¢ ¢ ¢¡ ¡ ¦ 0 ¢ ¢§¢¡ “2_bšIdoc¢ ¢§¢ * ,¨ £ 20§¦ ¢ ¢ 0 & &), ¨ &)( &/, ¢-0 3 ¢ * ,¨ &©(+*¨ ¦© ¢-0 2 ¢ & ¨ ¦ £ ¢,¥¦-0¢ ¦ &), ¨%¤ 3546 (+&50Variation <strong>of</strong> the percent hole in the perforated metal4030Reduction, dB20100−1010 1 10 2 10 3 10 4Frequency, HzQDQ c¡ *( * ¢5, ¢@¥ & ¢ & ¦ &)( ¨ &/, *&%¢¦¥ & ¦ &)( ¥ ¢5(+* &©¨ &/& ¢ & * £ 3 ¢£¢ £ £ “2_bšIdoc$ ¥¦ ¢¥¢ $ £ ¤¦ ¢ £ £ ¤ ¢¥¢ *,¨ 2 ¢¥¢ 0 & &/, ¨ &/( &), ¢-0 3 ¢ *,¨ &¢¤¢*¨ ¦© ¢ 0 2 ¢ & ¨ ¦ £ ¢5, ¥ (+& ¢ ¦ &), ¨%¤ 3546 (Q Z


c & ¨ ., & ¢¦¥ & ¦ &)( ¥ ¢5(+* &©¨ ¢ & * ¢ *( &¨ £ £ £¢ 0 ¦ ¢§¢¡ £ ¢-0 ¢§¢¢“2_bšIdochQ8S 250 ¢ ¢ ¢¡ £ £ 20§¦ ¢§¢¡ ¨¦ 0 ¢ ¢§¢ * ,¨ ¦ 0 ¢ ¢§¢ 0 & &/, ¨ &/( &/, ¢-0 3 ¢ *,¨ £ ¦ FLM&M L&#& G $¡)E ' L9&(H¡ )M M ¡ ' $ ©M F © ¢©)¨§ $%'!F &($¡ &œ docemk_bm[hj_D_ hD8©]=aI©hjigchoig_lnagc"mom3p hoigc-]=˜gmkpqdoĨ_bagš,^›]:hocedo_b] ]=docmoc"agmo_ hj_=cQ3igc:>}p{“ _bšgdkc0Q M )Q3igc"doc _ m-]_ec"dkhj]=_baI:] gcp >gp œ doc"mo_ mkhj_ D_ hD8„pqdce] i}]=dj]:^›c!hjcedkmagš ^›]:hjc"do_ ]+hji}]:h.šq_=cem›^.]F\M_ ^g^ doc"!hj_bp=a


Mc *( * ¢5,¡¢¦¥ & §R¢ (+& ¢ ¤ & ¢ * ¦ & 2 ¢ ¢ ¢-0 ¡ ¤ ¢ ¢ 0 £ £ 2 ¢ ¢ ¢ ¢ 0“2_bšIdocJQ£ ¤ ¢ ¢ ¢ * ,¨ £ £ 2 ¢ ¢ ¢ ¢ ¢¦ ¢ ' ¥ ¢5( ¦ ¨%¢ * ¢( , ¢ * &/( * & &/, ¨ &/( &/, ¢-0 3¢ * ,¨ & (+*¨ ¦© ¢ 0 2 ¢ & ¨ ¦ £ ¢,¤¥ ( & ¢ ¦ &/, ¨ ¤ 346 90807060Reduction, dB50403020100−1010 1 10 2 10 3 10 4Frequency, Hz40Variation <strong>of</strong> the thickness <strong>of</strong> the isolating material353025Reduction, dB20151050−5−1010 1 10 2 10 3 10 4Frequency, HzQ Zc© & ¨ ., & ¢¦¥ &©* ¢5( , ¢ * &)( * ¢ * ( &©¨ !& &/&/, 2 ¢ ¨%¢¡ £ £ ¤ ¢“2_bšIdoc¢¡ £ ¦ ¢ ¨%¢ * ,¨ 2 ¢ ¢ ¨ ¢ ¥ ¢( § ¢ (+& £¢ ¤ ¤ ¢ ¢ ¢ ¢ ' & &/, ¨ &/( &/, ¢-0 3¨* ,¨ & (+*¨ ¦© ¢ 0 2 ¢ & ¨ ¦ £ ¢,¤¥ ( & ¢ ¦ &/, ¨ ¤ 346 ¢Q a


_bagš hjiIcmopIag gdkp}]=š ]Fhj_bp=a _ba ]Ÿ!h˜=8 hoigcX&gag_ hoc&c! ce^`cea h©^`c"hoigpDN'pMIc!p+]›š=_qc"ašq_=cem]ep=^/Mh]:ho_bpqa}]+5hjpDp+hjp„pqdSc!\I]=^bcVm[h#g8hoigccedV„pqdo^›]=a"ccea"ced gcemk_bšqaS)©Q3i}]:hšq_=cemVhjigc9p=momo_ ˜g_ _ hD8'hjp7epq^}]=dkc›cy\cedk_b^`cea h]+Ydkcem0 hommo_ mopm[h#g8Ÿhjigc_ ^/}]+"h,p+g_ @5c"doc"anh}]=dj]:^›c!hjcedkm pqa hjiIcmopgaIWgdkcem 3¢Ÿc^›]98”]hœC]=m moc"cea hjig]:hhoigc©!h^bc"agš=hoi*B2hjiIc©!h dj]=I_gm]=ag hjiIcmgdkcdoce"ho_bpqa*)&Zœ dkcemk_bmkhj]=a"chjpqšqc!hjigc"d1œS_ hji.hoigchjiI_lnagcemkm3p hjiIc^›]:hjc"do_ ]+_ a›hoigcmo_bc"aec"d]=dkc>}pgmocp hjigcmo^›] +œS_ IhjiXepq^}]=dkce&hop›hoigc ceagš=hoi&p 2hjigc"h ,:mo_bc"aec"dgp+3—Cc!e]a›hoigc^`cemkig_bagšhjceaIgmChjpedoce]:hjc „c"œ c! ce^`cea hjmC_ba›hoigc #Vg_ doc!!hj_ pqa*)AQ3ig_ m\"pq^3^.]=_hoiŸhjiIc.igpq^`pqšqc"agcep gm,Žc!g^›]=aga "pqagg_ hj_ pqagm]:h # N&]=ag # #+* , .%B˜g_bagc"ŸœS_gceš=docec"m2p „docec"gpq^ _ba hjigc #Sg_bdkc!!hj_bp=a*B+Iabc"mom hoigcY^›c"moi,_ m &}aIcCceaIpgšqi*)šq_=cem¦„c!œSœC]9qc¤ ceagš=hoi œSig_i doc($5I_bdoc"m] &}aIc&^`cemoiSB]:agX_bš=iQ„doc($5Icea"_bcem.i}]9qc§mo^›]pqmkhocedo_ pqdo_3c"dodkpqd.]:a}] 8Dmk_bm›]=doc']9=]:_ ]:˜bc2„pqd hoigcX&}aI_ hjc c! ce^`cea h›^›c!hjigpDW„pqdO^›iIp h"c($5g]:hj_ pqa )-Z hœ1p hjigc"doc(„p=doc,˜cpqmomk_b˜ chjpš=c"hV].˜pgaII„pqdhjiIcXc!pqa}] Scedkdopqd.pqa ]Ÿšq_ qcea c(=c!hoigdopIšqi ]=}]+Ihj_ qcdkc(&}agc"^›c"a hjmp VhjiIcepq^Ihj]:hj_a5I^›c"do_e] ^›c!hjigpDgm hji}]:hJep b ˜9c/gmoc" hjp&mkp=c©Xc!b^`igp h#"Q3igcedkc]=doc›p=hjiIced“}pqdc!\I]=^bcpqaIc?ep gmoc$%}]=gdo]:hj_c! ce^`cea hjm¤_baImkhjce]= p hjdo_b]=a13c!$%}]:ho_bpqa*)]:dpqddj]=_ mochoigc,pqdkgcedp+Y] gdkp \M_ ^.]:ho_bpqaIm˜=8IImo_baIš©ig_bš=igcedIcešqdkcecg_ c!"c"œS_bmkcš8Dagpq^`_ ] m!) ’agc7epb] bmkp gmoc'] ˜pgaI}]=d08 c!bc"^›c"a h›^`c"hoigpD ˜}]:moce pqa]9p( ¢,0!2 3353 ¡)*2¡/G¤£¢ ¤£¨L)¡/G_bagmkcedkho_bpqa bpqmkmœS_ hoi¤epq^Ihj]:hj_ pqa}] Œdoc"m hjm!) Q3ig_ mmoigp œ1ce šqpMpDI"pq_ba"_ 3„pqdhjiIcœ hjigc'(Ih03 pqa7„dkc!$%gc"a(8 )gcea"c]FhhoigcT„doc($5Icea"_bcem˜c!bphoi,mo^›] 5i}]=aIšqcemi}]=mĨ_bš_ ^/}]+"hAp=a,hjigcdkce"hj_ pqa¤p mop gag}]=dj]:^›c!hjcedkmAhji}]FhAœS_) gdoc"momIdocm›]+bmop ]¤pqmomk_b˜g_b_ hD8 hjp šqc"agcedo] 8Ÿm[h#g8”hoigc c(qp Iho_bpqa p mopIagQgdkcem 3Q3igcedkc'_hoigdopIšqi ]`mk_bc"aec"d!)mgdkcL9£K ¤£¨£KLA¡Gepqagmkc!$%gc"anh8 ^`pqdocT"pq^/Ih]:ho_bpqag] 5dkcemop gd"cem!)pdkceec.cy\Mc!!Mhj_bp=aŸhj_ ^›c¤pqagc/epbŸp+epIdomoc/gmoc/}]=do] c!ep=^/Mhj_baIš'mk_ba"cQ mop gag7gdoc"momIdoc_ mepq^Ihoce moc(}]=dj]Fhjc! 82„pqd3ce] i7„dkc!$%gc"a(8 )hjigcVdoc"!hj_bp=a'p^›c"moi*)Q=


pqa©p ŒhjiIc š=_qc"a'˜pgaI}]=d08_=]+gcTgdkpq˜ ce^ ]:m]:a'_ anhocešqdo] +c($5g]:hj_ pqa*)doc(„p=do^b]:hj_p gd[hjigc"d_b^gdkp =choigc^`pMgc(9_ a.hjiI_bmCdkc!pqdkhpqagc;"p doce^`pDgc! hjigcmopgd0echopQhoiagpqa13u]F\M_ ] ^`pMgc"mhjp šqc!hS˜9c!hohocedS]=šqdkcec"^›c"anhCœS_ hjicy\cedk_b^`cea13edoce]:hjc-œC]9qcemSœS_ dkcem hjm]:hSiI_bšqigc"d.„doc($5Icea"_bcem()h]hœ1pb ˜9c›_ba hjc"doc"mkhj_ agš'hop "pqa hj_ba%gc`hjigc/}]=do]=^›c!hjc"dm[h#g8 hjdV8D_bagš hjpX&gagŸhjiIcZp Œhjigc¡ cedV„c!"hmk_bc"aec"d¢ )gcemk_bšqaSDN


!#"%$&')(+*-,./021./3*-./5476%$&& \ 98;:=A@CBEDF:G@CHJIGLKM-*-./IONAAI./*QPRSTHVUXW- .YI¥Z;[]\u m‹‰zXA@CBEDF:G@2{lÉ€j%BQjGzCo¤Dœi u BEDE¥is u C@GA}tBEDF¥is¾ 4-%9¥†“.!??%`b0R§LLM-MXL#A…VM96%$$&Apqj u @=>¥z-jGo2jGiBh


!#"%$&')(+*,&-.(0/213/546-78:9 /2;¢=?-0&-.(0/21>&'@;A/B*C8',EDF:;#(GHDJICKMLN&O&;A8-+OP(09RQ-+=*S#T'HGHUFWVX(HZY#[#R‚xG„ƒ…TB ÎZ†2‡5ˆ3͉ D!F ˆ†Š‡Uˆ‹ GHD Œ EŽ!{"r$&')(+*,&-+(0/21 /54M- 78€x/2;¢=?-0&-.(0/21>&'‘;A/B*C8')[9‚xG„ƒ… ÎZ†xV!’HR“R”•Š”–J—,˜Z—•‚xG„ƒ… Ί‹xV!’HR“R”•Š”–J—,˜Z—•¢¡£¥¤¦¤®¡¨¦§¦¨©\^]6_T\`badcafehgjigkclnmPopcrqsaftTu5vwaxiu5opyzom{i|Rg}eho~vwgtš:”›.œk—GH’„BDŒB’HDƒž ‰Ÿ‹ R…Œ¡EFGH…ž ‰ ž †,ˆ¢ ‚x’HZY£BTGHUG„¤CG¥§¦¨ ‹ žžžM©¡WªC«¬§’HEG„Dƒ­G„Œ ®DBTÎ žMŒB€BTŒBD¢’„wGHD¯ŽXT5[d’¨ Í°±’jG„Œ ®DBTž ‰Ÿ‹ ²6’„wFG„…ΉŸ¢ ³ …! ‡ D´TBµ…DŒ¦ Ί¢‹ ²6·š:”›.œk—GH’„BDŒB’HDƒž ‰Ÿ‹ R…Œ¡EFGH…ž ‰ ž †,ˆ¢ ‚x’HZY£BTGHUG„¤CG¥§¦ˆ žžžžM©¡ ªC«¬§’HEG„Dƒ­G„Œ ®DBT Œ€BTŒBD¢’„wGHD¯ŽXT5[d’¨ Í°±’jG„Œ ®DBTž ‰Ÿ‹ ²6’„wFG„…ΉŸ¢ ³ …! ‡ D´TBµ…DŒ¦ Ί¢‹ ²6·Í,ˆ


‚xG„ƒ… ÎZxV!’HR“R”•Š”–J—,˜Z—•‚xG„ƒ… Î ¡xV!’HR“R”•Š”–J—,˜Z—•Î ͉ žMR…Œ¡’HDƒˆ¨ ‰Ÿ¢ R…Œ¡’HDƒE…TBBD, FBTŒBTGHV>BF GHD ŒGHD£¢¥¤ I¦¤¨§©%8&WBŽ>B2…TWF…G„Dƒ¦WI,",",I:YN Î ¡ ³ EDF3 …GHFG¥§¦¯YN ˆÎ [ Ž ‡Q=?O8;A81-BS§¥¥¦‚xG„ƒ… ˆ žxV!’HR“R”•Š”–J—,˜Z—•š ”›+œ^—GH’„BDŒB’HDƒÎ‰ ˆ R…Œ¡EFGH…ž ‰YΊˆ¢ ‚x’HZY£BTGHUG„¤CG¥§¦† žžžž ©6WªC«¬§’HEG„Dƒ­G„Œ ®DBT¢ ŒB€BU5[f6 ’DD³ …! ‡ D´TBµ…DŒ¦ ‹ ¡ ²¡·š:”›.œk—GH’„BDŒB’HDƒÎ‰Ÿˆ R…Œ¡EFGH…ž ‰œÎZˆ¢ ‚x’HZY£BTGHUG„¤CG¥§¦¢ žžžžM©¡ ªC«¬§’HEG„Dƒ­G„Œ ®DBT¢ Œ€BTŒBD¢’„wGHD¯ŽXT5[d’¨ Í°±’jG„Œ ®DBTž ‰Ÿ‹ ²6’„wFG„…ΉŸ¢ ³ …! ‡ D´TBµ…DŒ¦ ‹ ¡ ²6·BYpBTš:”›.œk—GH’„BDŒB’HDƒž ‰ ¡ R…Œ¡EFGH…ž ‰œÎ ‚x’HZY£BTGHUG„¤CG¥§¦¢ žžžžM©¡WªC«¬§’HEG„Dƒ­G„Œ ®DBT¢ Œ€BTŒBD¢’„wGHD¯ŽXT5[d’¨ Í°±’jG„Œ ®DBTž ‰Ÿ‹ ²6’„wFG„…ΉŸ¢ ³ …! ‡ D´TBµ…DŒ¦ ¡ † ²6·E[Í ¨


‚xG„ƒ… ˆÎxV!’HR“R”•Š”–J—,˜Z—•‚xG„ƒ… ˆˆxV!’HR“R”•Š”–J—,˜Z—•‚xG„ƒ… ˆ ¨xV!’HR“R”•Š”–J—,˜Z—•š:”›.œk—GH’„BDŒB’HDƒž ‰ † R…Œ¡EFGH…ž ‰œÎZˆ¢ ‚x’HZY£BTGHUG„¤CG¥§¦Í žžžžM©¡WªC«¬§’HEG„Dƒ­G„Œ ®DBT¢ Œ€BTŒBD¢’„wGHD¯ŽXT5[d’¨ Í°±’jG„Œ ®DBTž ‰Ÿ‹ ²6’„wFG„…ΉŸ¢ ³ …! ‡ D´TBµ…DŒ¦ ‹ ¡ ²6·š:”›.œk—GH’„BDŒB’HDƒž ‰ ¡ R…Œ¡EFGH…ž ‰ ž ¢ ‚x’HZY£BTGHUG„¤CG¥§¦ žžžžM©¡ ªC«¬§’HEG„Dƒ­G„Œ ®DBT¢ Œ€BTŒBD¢’„wGHD¯ŽXT5[d’¨ Í°±’jG„Œ ®DBTž ‰Ÿ‹ ²6’„wFG„…ΉŸ¢ ³ …! ‡ D´TBµ…DŒ¦ Î ¡ ‹ˆ ²6·š:”›.œk—GH’„BDŒB’HDƒž ‰ ¡ R…Œ¡EFGH…ž ‰œÎZˆ¢ ‚x’HZY£BTGHUG„¤CG¥§¦¨ ‹ žžžM©¡WªC«¬§’HEG„Dƒ­G„Œ ®DBT¢ Œ€BTŒBD¢’„wGHD¯ŽXT5[d’¨ Í°±’jG„Œ ®DBTž ‰Ÿ‹ ²6’„wFG„…ΉŸ¢ ³ …! ‡ D´TBµ…DŒ¦ ‹ ¡ ²6·ÍAÍ


‚xG„ƒ… ˆ3ÍxV!’HR“R”•Š”–J—,˜Z—•‚xG„ƒ… ˆ†xV!’HR“R”•Š”–J—,˜Z—•…’¥¦ J B…TBBD,¦FŒGHV>BF G„D ŒG„D¢¥¤¨§ © 8&2Q=CO8;A81-±/54/2=Q-+(09¯( ;¢B’„ŠY#[ !´G„ Ž>BFDŒB{…V>´F D GHDDMFG ‡&C9: Î žž¯ zEDF ¯’HDƒ Î žž ¢ ´[AGHŒBTŽDB#Y~BTAŽ…?¡ ‰ T BŒ ±EB[Íš:”›.œk—GH’„BDŒB’HDƒž ‰ ¡ R…Œ¡EFGH…ž ‰ ž ‚x’HZY£BTGHUG„¤CG¥§¦† žžžžM©¡WªC«¬§’HEG„Dƒ­G„Œ ®DBTÍ Œ€BTŒBD¢’„wGHD¯ŽXT5[d’¨ Í°±’jG„Œ ®DBTž ‰Ÿ‹ ²6’„wFG„…ΉŸ¢ ³ …! ‡ D´TBµ…DŒ¦ Ίˆ ¨¨ ²6·š:”›.œk—‚x’HZY£BTGHUG„¤CG¥§¦¨žžžžM©¡WªC«¬§’HEG„Dƒ­G„Œ ®DBT¢ EDF ‹ Œ€BTŒBD¢’„wGHD¯ŽXT5[d’¨ Í°±’jG„Œ ®DBTž ‰Ÿ‹ ²6’„wFG„…ΉŸ¢ Í,¢


‚xG„ƒ… ˆ†xV!’HRk•Š—¢¡jœk—¢£¥¤§¦‡ ¨ ‰ ž † ž¨ Ή ‹†3Í Gˆ¢Î‰ ¢ ‡5ˆ?‰ ¨ ž ¨ ‰ ¨ ‹†ˆ G¨ž ‡ ž ‰ ¡ ¢ ¨ ¢ ¨ ‰ ,¢ žGÍž ž ‰ žžžž}¨ ‰YÎ ¡ ,ˆ G¢¨ ž ‰ ¨ Î ¡ ž ˆ?‰ Í‹ˆ žG†ž ž ‰ Í¢ ¡¡ Ή ‹ žGžž ž ‰ †bÎZ†‹ Ή ¨ ˆÎŠˆ GΞ ‰ † ¡ Í Î‰ žžž ¡ GΊˆ¢žž Ή žž ¡ Î }ž ‰ ˆAÍaÎ G¢¨ž ž ‰ ¡ Ί‹‹ }ž ‰ ¨ Í‹Î G†žž ž ‰ ž ‹E }ž ‰ ¨ž ˆÎ Gžžžž ‰ ‹¢¢ ¡ }ž ‰ ˆ¢ ž¨G΂xG„ƒ… ˆ‹xV!’HR“R”•Š”–J—,˜Z—•¨©¤>œ˜¤+–d—¢k”£¥¤—.©6T¯ªC«ÎZ† žž ‰ ‹3Í¢¢ }ž ‰ ‹‹ ¡ ˆ Gˆ žžž ‰ ,¢ ž Í }ž ‰ †bΊˆ Gˆ¢ žž ‰ ‹3Í¥ÍAÍ }ž ‰ ††AÍ‹ G¨ Ί¢ž ‰ ††,ˆ ž}ž ‰ ˆ‹† ¡ GÍ žžž ‰ ¡ Ί‹¢ }ž ‰YÎZ† žžGΊˆ¢ žž ‰ † ¡ ‹‹ }ž ‰YÎ ¡ ˆ‹ GÎZ† žžž ‰ ††bÎ † }ž ‰YÎ?Í ¨ Í Gš:”›.œk—GH’„BDŒB’HDƒž ‰ ¡ R…Œ¡EFGH…ž ‰œÎ ‚x’HZY£BTGHUG„¤CG¥§¦¨ ‹ žžžM©¡WªC«¬§’HEG„Dƒ­G„Œ ®DBT¢ Œ€BTŒBD¢’„wGHD¯ŽXT5[d’¨ Í°±’jG„Œ ®DBTž ‰Ÿ‹ ²6’„wFG„…ΉŸ¢ ³ …! ‡ D´TBµ…DŒ¦ ¡ † ²6·Í†


FpfwF…ŒfDFG„Dƒ~ŒBŽ…!EG„DsG„DTBŒGHDbICK¢L&OT&;A8-+OP(09Q-.=!*S~! …ŽŒŒBTFGHD!ƒ¢¢ °GHDM¢’„@TŽŒBNDF­Y~G„M¢T©¨ŒG„Dƒw…ŒCF [d!wŽE BT G„D¯‚xGHƒ…!B ˆ2‡ ¨ † ¤RRŽEB ¤E’„…BNG„DA!V’„#VX’HZY …!D’H~ Ž GHT…FG„BF3EDF´BTT ¤ETGHFj[f Ž ‡‚xG„ƒ… ˆ2‡ ¨ †xV!’HR“R”•Š”–J—,˜Z—•\^]6_¡ `badcafehgjigkclnmPopc i|Rg£¢Radcafe gji!gkc li¥¤Rv§¦BN¤E’H…!B¡#FŒGHV>BF´GHDWƒ…T#C [š:”›.œk—GH’„BDŒB’HDƒž ‰ ¡ R…Œ¡EFGH…ž ‰œÎ ž ‚x’HZY£BTGHUG„¤CG¥§¦¨ ‹ žžžM©¡WªC«¬§’HEG„Dƒ­G„Œ ®DBT¢ Œ€BTŒBD¢’„wGHD¯ŽXT5[d’¨ Í°±’jG„Œ ®DBTž ‰Ÿ‹ ²6’„wFG„…ΉŸ¢ ³ …! ‡ D´TBµ…DŒ¦ ¡ † ²6·Í,‹

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!