NASA Technical Memorandum 1 0 0 6 3 7 I ,'
I i EVALUATION OF A MULTI-POINT METHOD FOR DETERMINING ACOUSTIC IMPEDANCE
Michael G. Jones
and
Tony L. Parrott
June 1988
AUG 1 1980
LANGLEY FtESEi\RCH CENTER C\BRAI?f PiA3h HAMPTDN, VlKClNlA
National Aeronautics and Space Adm~nistrat~on bngley Rssasrch Center Hampton, Virginia 23665-5225 AnsrrrrA(:*I- AII invcst,igation was corlductcd 60 develop and explore potsenl.ia.l irnprovcrnents pro-
vitl(vl I)y ;). M~~lt~i-l'oi111,M(~t.J~ocl (M I'M) ovc!r bllc! tristlitionsl Stoi~~~(li~ifiWit.\'(' Mettliod (SWM) i11lrl 'I'wo-Mirro1)tionc- Melthod ('I'M M) for dct.crniining scol~sl.icirn~)cda.ricc. A wave prop- ;~l:;~.l.ioli~rloclc!l, wliic.li i~lc:l~~(lc*swall al)sorpbiot~i1.1itl nlc!;l.n How, wi~stlc-vcdol)c*tl l,o rnoclc?l fell(- s~.;I.II(~~II~WH.V(! p;~.tt(*rr~ir~;HI irr~pc!da~~c(!t,ll I)(!. 'I'htt refloc:t,ion fit(-tor;~~icl ;~.co~rstic. impedancxi rbf a. l.c-sl, sl)ecirnen werc! ca.lculat+cdfrom a. 'best,' fit of this sl.a.nditig wave pa.t,tern to t,ho ~)oitit,prtrsanri! rni!;~.srlrc!tne~it,s.I)at,a was acciuired wit,li 30 t.t!st, sar~ipleschosen to cover l0llcrc-ll(!ctoion facftor triitgtiiI,~rdc!rang(! from 0.001 to 0.999. A prot)o rnicrophone was uscltl to ot)t.nir~2 tto 6 prcssurc rnc!as~~rcrncrit,spcr half-wavclengt,h of thc! standing wave, along l.llc* cc-~il~c~rlirlc*of lSllc! irripcda.ncc~t,r~l)o. 'I'hrt!c sl)a.cing di~t~rih~~t~ior~wctrcs oxa.rnined; uniforrn, r;~.~ltlor~lii.r~tl sc*l(~cl,ivt!. Sl,;t.r]tling WRVP pa.t.t.crris cnlc~~lat,cdusing the propagation rnodcl for all three spa.ci~ig clisl.rit)~ll.ionsr~latch t,h~ point, l)r(?ss~~rerneas~ire~~i~nts witohgood 1,o t>x(:cll(!ntagreement ovor 1,hc-clt~t,irc! refloct,ion factor rnagnibude range itivi!stigat,cd. Thc! tlniforrli spacirlg distributioti was prc!ferred, however, since it was the eiwiest t,o implerr~e~ilil.nd provided extremely c.o~isist,cnl~anrl rc~~)catablc!results. (!omparisons of the acoustic. inipcd a.nce dattrmincd using 2, 3, 6, a.tld 18 I~I~?~~SII~C!IT~CII~,points showed that, while two points arc! generally sufficientl . for rc!l)c!a.t,ablc~rnc!asl~rcmc?~~t,s, the most consist,cnt, results are oht,air~cvlwhen using at least, six J)~CXYII~C!II~C~I.SII~~IIIC~I~,S at points evt!nly spaced over a distance of o~lchalf-wa~elengt~h. 'I'tie cffect,s of t,urhulent rrlean flow noisc cont,amination on t81ic! MPM were simulated t)y i~tl(linga broa.tlb;~ndnoisc! sourcc to the discret,~frcquenry sourcc. Data were acquired at ~~riiformlycJist,ril)tltc!tl points and impedances wcm calculat,ed llsirig the MPM and TMM itlgori1,hrrls. r.I h(t rt*s~~lt~siron1 these two algoriblln~swere theti cor~il)a.rcdwitoh a reference sc!l, of MI'M rc~srlll,sol)t,ainod with only thc cliscrctc! frequency sol1rc.c: act3ivat,ctl. The MPM rc*sl~lf.swclrc for~~l(lto c:onvrrge to the rcferr!tice result.s with fewer a.vi:ragt.s than the TMM ' rc!st~ll,s. 'I'his oI)sc!rva.tiori indicates that t,hct MPM will bc s~rpc!riort80 t,hc TMM in the I)rc*sc*llc:cBof sig~lilic.;~.~~l,t)roil.dI)antl tloiscb Ic?vc~lsi~.ssociat,cd with Ilii!illl (low. 'I'hc* St,(zn
Over tho last, 115 to 20 years much effort has been directed toward the 'development, of more efficient nletl~odsfor dcterrnining acoustic impedance. Generally, these methods rcdy on arnplitrldc and phase information obtained at two or more locations in the stand- ing wave field. Kathuriya and Munjal [2, 31 were arnong the first to adopt a faster, but sorncwhat less accurate, impctlanct~measurerncnt procedure in which thrcc, fixed location prc*ssrlrc mensurcrneiit,~are trscd to approxirnatc the standing wavc pattern with a 'graph- icitl Icast squares' approach. Soon thereafter, several investigations were conducted with ollly two fixed Iocatioti rncasurertiet~ts,involving both pressttrc i~t~iplitudcand phase at c\ilcti frc:quency of intercst. This mctthod, called t,lle Two-Microphorie Method (TMM), is c~ssc~rlt,i;lllya t,wo paramet,cr fit of the wavc propagation model to t,hc. standing wave pat- , ti. I .his rnc!t,Ilod is l);~,sc~don a transfer fr~nctionrncasurerricnt t)c?t3wcentwo points in t,hc- ;ic.or~st,icfiolti nrltl thus irlcorporatos bobl~arrlplitutlc and phi~sc-inli)rrnat,iori. In actual ~~ri~c.t.iccl,t,lle ~t~osl,afficic?nt rlsagc of the TMM rrlakcs rise of ;L hroacl1)iind noise source 14-61 lo sirr~c~lt,itrtcotrslyilet,
'I'llt* t8ra.nsfor frrnction mcasurernents citrl hc obtained it1 c?acli frcquericy of intercst rlsit~giL (Iiscr(!tc- ~T~>(~~I(!IICYsource under corr~prr(,crcorltrol or wittll ;I broadband source ~lsitlgfast It'ortrior tri~nsformitnalyzers. '1'110 convenioncc of tlic t~roadhandsource arises fro111 (,IIO abilit8y of fast, Foc~ricrtransforrr~ a.rta1yxcr.s to proccm 111wadband signals very r;il)idly. I Iowc!vor, t,hr control of the sl)t.cdrr~rn level versus frecl~~cncyis generally limited. 'J'lcrrs, for ;L givPr1 power handlitlg capat~ility,then rnaximu~nnarrow hand lcvels are often too low it1 sot~lcrcgiolls of t,hct spcctrttni. A discret,~frcqtrency source, however, allows precise c.or~t,rol'oft,ll(! itn~plil~r~tlcat, each freqllcncy of iritctrcst 171, pertnittiiig a greater dynamic riar~gc-l,o 1)c acllicvcvl ulriforiilly across tilt! frcclr~c!r~cyriangc of ir~tc-rosl,.'L'lills, tllere arc times wltcbn discrct,t*frcclrtcncy cxcit.a.tion is dcsirahlc; srrch as dctcct,ing t,hc onset, of test specimen ~iorilirrcitritywill1 atnplit,trdc, whcrc a large tlynilrrlic ratlgc? is nc~odcd,and in the presence of rr1c:arl flow whcbn colitarninating effects of 1)roadband flow rioisc trlay hc! intolerable. On tllc ot81ier hand, the TMM with a. discrete frcqtrcricy source rc:qt~ircs computations to be conclr~ct.e(lsepa.r;it.c*ly ;it aacl~fr(lq11cncy of int.crrst and, hence, incrc*ascls the testing time.
'l'llt! 'l'MM is strhj(:ct, I,o two m;ijor sysltc~rnnt,icc-rrors. Onc sy~i~crni~t~icerror occurs wlictrr t,ho rr~icroplloric!scl)ariitiotl is rlcar on(! t~alf-wnvclc!ngth. 'l'l~co1,llc.r is i~ssociat~e~lwit11 ;I ~r~l)lil,r~tl(-i~rltl ~)ltnso rnc!asurc!nic~~t crrors. For cx;~ml)lc,t,o rlc hicvc. iri~l)c~(lancenieasure- III~~II~.il~cr~racies wit,ltin :I%, microphone calihration errors rrl~tst~lol cxctcd 0.1 dI3 and I .on in nrnplil,rldc and phase, respectively. The need for such precision calibration can be c*lirninatcd ~lsirig;I techni(lue int,roduccd by Chung and Popc [$I, in which measurements rnildc with oric orientation are repeated with the microphones (atitl all related circuitry) swit,chcvl. Ariothcr wity to avoid the need for prt~cisioncalibration and rrlicrophone spacing (Ii;~lf-wi~vclcngth)is bo rlse a discrct,e frequency acoustic excit,ation a.nd sccluentially posi- l.io11;I single mic.:rol)horio at prcb-sclcct,c?d locntioris. Srlcl~scq~lcntial 1)r.ol)c positioning can cli~sily I)(! accornplish(:d undcr c.ornputcr c~nt~rol.In fact, a cont,rol program can be implc- r~iclrit,c*(lt,o sarnplc t,lic st;~ndil~gwave pattern at, iltiy nrtrnber of poirits dc.sircd. Althotlgh t.hc rnc;ls~rrornc~~~tt,irric* incrcasos with tohcnurnbc?r of points s;irnplctl, bot,h systematic and rnntlorr~carrors should dccrt!afie.
l'lit! pltrposc- of ifhis investigatiori is to dc!vclop arid explore totlo pot,t:ntial irnprove- rrlclnt.s iri RCCII~RC~,precision and mcas~iremcntefiiciency provided by a Mi~lt~i-PointMethod (Mf'M), ill which fro111 2 t,o 6 prcsslrrc! rneasurenic~nt,sper half-wavclcngtli are acquired with ;I 1)rol)c. rnicrophonc~scquent,ially positionctl along the cent,crlinc! of the impedance tube. A wavo prol)agaf,ion ~riodcldescribing the standing wave pattern, iricluding effects of tube w;Jl ;11)sorl)t,ior1ar~d rrican flow, allows recor~strr~ctionof thcn standi~lgwave pattern. The rcflcct,ior~factor nrrcl, hcncc, the acottstic irnpedar~ccof the t,cst spccirnen are then deter- rrli~rcvl. 111 co~il,ritsl..blicl 'l'MM is a tlt~t,c~rrriir~ist,icapproiich iri wliicl~l.wo rnoastrrcments arc. IIS(-(I I,o (I(lt30rrr~ir~(~IaI1(l s1)ocir~1ori ir~~~)c~Ianco. (:loi~rly, tllc two rrlot,l~otlssl~ould agree whcln Itl1(- n1111ihcrof rr~c~;isrtrcn~cnbpoint,s in the. MI'M is rc~(ltrcct1to two. Mcns~irctncntswc!rc c.or~(l~~c.t~c*tlon :I0 Lc~sl,sarrrplc-s <:hosc:r~to covcBrl,hc! rc!flcction factor rrr;lgr~it~~~dc(HFM) rango fro1110.004 to O.!)!)!) ill ortlcr t,o axerciso t,htl MI'M in a bliorougll Iriilriric!r.
'I'l~c! clHi~-.l,ol' rrrcl;l.ri flow was siniulat,ctl l)y sul)c~rirnposir~g1)ro;i.cll)arid noise on the ;i.co~rst.ic:ficltl gonornt.ocl wit,ti a discrc!to freclucvlcy sortrco. It is wclll clocrlrric!t~t,ed[3, 4, 71 that f,hc* acltlition of rrrc3;rrl flow complici~t~csirrlpc*tfa.ncc? rrrca.s~~rerr~c?nts drarn;ttically. Not only ci1.11i.l~c! nlc:ati flow c.harlgc1 t,Iic impedance of t8hctcst specimc!~~,it can also cause additional sysl.crn;~.t,ica.nd ra.n ANALYSIS The Multi-Point Method (MPM) presented in this report combines the strengths of the Standing Wave Method (SWM) and the Two-Microphone Method (TMM) while avoid- ing sornc of their inherent weaknesses. The S WM is generally used as a standard against whi.cll to cornpar(*the accliracy of any new technique, sincc it involvcs direct measurement of st.arltliAg wave ratios ant1 null positions of the standing wa.ve pattern. This procedure is illl~st~rntedgral)hiri~lly in Fig. I. The I'MM uses the complex ratio of the acoustic pres- srlres it(, two 1ocat.io11sin thc standing wavc pat,tern (i.o., thcb transfc!~.f1lnc1,ion) to directly c.ornl)ut.e tohe in~pcdar~ce,so that t.he measl~ren~entprocess can hc accorrlplished without ptiysic~ltnovcr~ic~11 t, of t,ho hitrdware. Major disadvantages of the 'I'MM arc; (1 ) requirement of prc*c.isa physical positioning and arnplitrldc/phase calibrations, allti (2) systematic er- rors associat,ed with sps.t,ial scpara1,ions near one half-~avelcngt~h.'I'he MPM avoids these ciisatlvantagcs by clnploying a least squan?s fitting technique to fit a wave propagation ~nodclto thv poil~t,rr~easurcttnents. This proc.cdure should exhibit uniform accuracy for all ,, I llc! prc-ssurcBdist,ril)r~t~iorl for a plarlc wavc propagating in a tube is given by p . . 1 1) pil'rrl le--~wi I r . (1) wl~c*rc*1; is toll(*co~l~l)lc-x j)rc.sstrrc (ar~~j)lit~~tlcant1 pl~asc) rnc~i~s~~rc*tl i11, posit.ions sj, and Pi nnil 1: ilrcl t,llt~itlci(lc111, ant1 rcHcct,cd press11 rcs, rcsp~ct~ivcly.'I'llc inrirlcnt and reflected plan(*wi~vt! propilgil1,iorr cor~stant,~,I'i ;~,ntfI',, itrcn dofirled iw l', :: k, -I ini (2) itnd wtlorr! I,II(* incitlctil. itrrcl rc~Hoc-tSotlwi1vcn ~r~rrr~t)c~r.sir~rr~c~i~r~ flow ilro givc111Iby 111 tl~csc!relations w rcprest!nts the angular frequency, cl is the sorlrid specd in the tube, % nnrl M is the mean flow Mach number taken t,o be positive in thc (-t ) coordinate direction. 111g;trd and Si11ghi~1I!)) c:st,im;tt,c! t,hc incirlc~rrl,and r~flect~cdt,ttb(* wa.11 a.bsorption coef- licicnts (rx,, a,),wllich iriclutlc Chc cffixts of rnca.ri How, in thc! following rnanner: 'I'hc* (111a.rrt.ities,O,, and /lt account for viscotherrnal and turbulcncc dissipation of acoustic c1nergy at the t,uhc. walls and are calc~~latedas follows: wtlcrc. 7 rcprcscnt,~thc specific heat ratio at const,ant density i~nclvolirme, p and p are the tic-nsil,y i~ndviscosit,y of the litrid, rc, is thc heat conduction coofiicic!llt, itntl cl, is the specific hc*at. ;ita n constn~it~pressure. 'l'he ratio of t,11(' (It~ct,arva t,o th(\ p(-ri~rr(~t,cris a,), and $) is t,11(- rocfiicicr~tof friction for turI)trlent, flow IlOj, which is calculatcd nurnc-rically from the f'rarlclI,l ~~nivcrsalrcsistanro law wl~c!rcb ltc is I,hc* Ilow Ilcy rloltls rr~lrnhcr. 'I'IIo propagatioa model givcn by cqllatiorl (I) can hr fittccl 1.0 a ~listributionof N rncasllrc!cl prcssl~res,I?, t)y niinirnizing t,he,functoion wtlr*re i.tir hi~rrno~~irt,inle dc!prndencr (e jW') has been suppressrcl. '1:) ~tii~limiseF(I$, Pr) t,l~c*followir~g con~lil,iotls arc* i~riposc! S~,l)st,it,lltiosof equation (I I) into eqllations (12) and (IS) and solving for thc incident and reflected pressures yields Iri circler t.o si~t~~)lifyttir ptlysiciil clrsrripl.iot1 of 1.11~sl.anrli~lg wavr ronsidrr t,he reflectioli I(illally, ttie ircollsl.ic ilnpcduncc, q, at tlio far(*of the spccinien is givrr~by ttllr relation A ctlock on ttie arcllrwy of I1F ran hr ot)t,ai~ltldt)y comparing t.111! ~(~r~nstr~~ct~edstanding wsvc* ~)at,t,srlicalr~il;it,c~d from t,hr P, ~~~casan-n~rrit~swith ttir din.c.toly rnmsured standing wavc! pattern. ln~pcdal~ee'I'u t)c 1)escriptioti '1'110 Mtrlt,i-I'oir~t Mcl0llotl (M I'M) cjcscril)otl it1 bttc~ ANA I,Y S IS sccl,ion was irnple- rrlc*t~t,c(lir~ a scltliLrc. cross-sc*cbior~(5.08 ern by 5.08 ctri) itr~i)cdat~col,r~l)c-. A pllotograph of I,hc- tartl)(- is show11 in Fig. 2, i111(1 it sc.l~crnat~ic:ill~rstrating t,llc\ ;~l)l);tr;~t~rsit1 more detail is sliown in Fig. 3. 'I'hc t111)ct is 58.4 em in Icngt~h. Two 75-watt, 1)11ascmatched acoust,ic drivc?rs ger~erai~csigtials ovctr it frequency range of 0.3 to 3.0 kHz, with SPL's up to 140 dH irt, 1,hc- tc>st spccirnen stlrfacc. The tcst specitnen is carefully clanlpcd to the exit plane of tohc: irnpcdancr! tube with the aid of a rubber gasket. The georrietry of the appara- t,~lsis slrch that plane waves propagate dow11 tohe tube to the face of the test specimen. 'I'hcsc plane wiwcs arc reflected by the test specimen and create a standing wave pattern Iohatrlriiclrlely chitraclcrizcs the liorrrlal incidence acoustic in~pcdancc~of the specimen. An 0.S:IS-crn condc~tser-type rnicrophonc, fiush mounted in the top wall 0.635 cm from thr I.c*sl,spccirncn face, is nscd to rncasllrct ttica rc.f(!roncc levels to irls~lrt.tallat the desired test cwviror~rncwtis prosct~f,.A tri~vc*rsirigrr~icroi)l~orlct prot)e can he ~)osit,ior~eclat the ccnterlinc ovc8r irl)l)roximat~cly28.8 crit of t8hct~lt)c Icngtli to acquire acotlstic prcassurcldata along the sl,;rrtclir~gwiivc8. r l3 ravcrsing I'rol~c!1)cscription '1'0 i~(:c~lritI.(!lyrtlc?n.surtB '~)oint,' 1)rc.ssltres it) iI, sta,ri(ling wava field by rneans of a probe I,~ll)o,spurio~ls sound itrisirtg frorn transrnissiot~through tha prohc 1.11bc walls must he trtit~i~r~ixc(l.Tlto 1,ravcrsing probc (Fig. 4) was fabricated fro111 a 8:<.82-crri long stainless st,c*c*l t,r~t)c. wit.t~o~~t.c!r itnd innc!r diamct.crs of O.l(i and 0.08 crn, rc!sl)cct,ively. The probe wi1.s c:ortl)l(,cl bo i\rl 1.27-cni condenst?r-type rnicrophonc! via a flexible tuhe, and could be pnsil,ionctl wit,hil~0.025 rnrrl of bhc spccific!d lo~ittiori. The four 0.071-cm-diameter probe 1.111)(* ~)orl,s,('cl~~il.lly sl)il.cc*d itro~lntl t,hc prohc* in ir single n~cvisrrroll~c!rttplnnc located 1.42 crlt frorrl I,II(* 1)rol)(lI,il), c.orrltl I)(* i~osibior~c*dovcnr ;I. rilllgo of 1.78 to 30.58 crrr frorn tl~otoest sl)(v.itrrc!tr file('. '1'0 cl(~lec*rrr~ir~c*I,hc- trlliv:l.s of t,ra.ttstt~issiont.l~ro\lgh t.hc ~)rot)owi~.lls, rrlc~itstrrcrrierits werc! I.i~.k(-l~wil,l~ 1,11(~ l)roI)(-1)orI.s Ioc:at,~(Iill i1. (I~t*l)111111 pro(i11(:(~1I)y a rtc-itrly pcrfoct reflector (st.(-(-1i)Ii11.(-). Sill('(*I,hc% 1)orls wcarc! loc;lt,c~dirt the: 1)lit11(!of a (I(!(:P 111111, a.ny so~tndtrans- rr~i~siollI,l~ro~lgl~ 1,he ~)roh(!t,~lt)(b walls wi)~ll(lt,(-11(1 to irt(:r~as(!lOlic a.pparent signal level at, 1.11~r~~lll locations and, th~ls,tlccrcaso thc? dyna.rrlic rango of the rrtca.surernent system. The ~I~C~LSII~(!IIIBII~~Wits c.o~~d~~cI.c~cI a.t a high itrx~plitu(Ic!(approximately 1:XI dB) for six frequen- cies frorrt 0.5 t~ 3.0 klIx. Mea.srlrcrnent,s were condircted with the ports open and closcd (multipla Iaycrs of tape uscd to seal rncasuren~cntports). The cffccts of wall transmission or1 Lll(* prol)c: ~)c!rforr~iaricc!were dotermined frorr~the ra.tio of the opc!n-port to closed-port rcnsl)onsc!. 'I'll(: rcsl~lt~sof this ~nc!a.sarernenta.ro ill~lst~ratedin Fig. 5, in which the ratio of ~.hc:opcln-port. prol)c. rcssponsr!to thc closrd-port rcsponsc is plotted ir~c1H vcrsus frequency. Sillrc* I,I1(! ol)cn-porI, rc*sl)orlsc!is al, lcast 32 dl3 i1.hovc that of thc closcxl-port response, it, is c.l(-i~rl,l1;1t cor~t,ii~nir~itt~ir~gcuff(!cts drlr to sol~ndtrnnsrnissio~~ ISl~rol~gl1 bhc t111)cwalls arcD t~o~ligil)lc!over t.hc frc!cllroncy riitlgc of ir~l~crost~. A hlock diagrarrl of thc signal conditiotling ilist,rtrrr~entat~iotland data processing sys- f.cnl for tohe aco~~st~icsignals is show11 in Fig. 6. At cach test frcclllellcy, an SPC was set ;it t,ha rcferenrc rnicrophonc- via it cotnptttor-controlled frequency syntlicsizer. Acoustic j)rcssllr(:s were tl1t*11obl,ainotl at a nu~rit)erof axial locations. Tliest~axial pressttres were tlicr~insert,ed as 1; into the nppropriat,e cxprcssions in eq~~at~iori(16) in order to compute t,hc~incident atld reflected pressure levels, as given in equations (14) and (15). The re- flccbion factor and acotrstic in~pedariceof t,lio test specimen wcBrcxthen computed at the test froclucncy using equations (17) and (18). Contributions from broadband noise were rnininiir.ct1 by band-pass Ciltming and signal enhancement. The arnplitude and phase of t,hc cxcitation frequcncy wore obtained with an on-line fast Fourier transform routine. Meast~rc?tncntPoi tit 1)istributions 111 orclcr to rlctcrrnillc bllcl opt,inlr~rndist4ril)tltOion (spacing and nr~rnl)cr)of measurement poinl,s ovc!r tho st,;itldirlg wavv pabt,crn, three! tlistril)~rt,ionwenb c~xarni~~t*d. The: cli~tribut~ions rhosc911 wcrc (I*) rrnifor~r~sp;lcing, (2) random spacing, a~lrt(3) srlcctivc spacing ba9t.d r. or1 loc.i~t,iotlof rrl;txirnn ant1 rriirlitrra of t,ho st;tntIing wave patbcrrl. I hc! rlriiforln spacing clistri t)l~l,ionis t,llct sirnplcsb t,o inlplrrnent,. t lowcver, it, may not, y icld the rnost uniform ilrcurncy over it wide rnngc of wavelengths and test, specimen rcflcction factors. Since srlch rrrliforrrl acc.llriicy is a tlcsirable goal, tllc? other two more con~plcxrrlcasurement point d isl,rihrt ,,ions wc*rcl itIso ir~vcstigated. t.I II(I trnifortr~sj)ilcirlg tlistribrrtion was ernployed to o1)tairi diit,a for all of the available t,(*sI,SI)(\C~~~I(-IIS. 'I'11(- goal was to ot)t,ititi 6 ~rniformlyspaced points per half-wavelength (tr~iixirrl~~tr~of :I I~i~lf-wilvc-lcngt\~s)in ortlor t,o obtain an arcuratt~Icast squares curve fit. Sit~rc-I.Ilc8 W~~VCIPII~~IISit~~o~iii,t,~'~tI with kh(* lowor fr(vll~c~ltciesilrtD grc*ilIcr t1li111 the availa1)le i~xi;~lrr~r-~~s~~rcrnc~tlt, rango, a rninirntlrrl of 10 tlitta points (n~liforrnlycti~t~ribnted over t,he , il~i~iliil)I(!ratlp(-) Wits IIS~VI. I .IIC IlSitK(' of t~lor(~tOlla~~ two ~)oilll,sper Iia.lFwavelength also . itvoicls t,hc ill-co~iclitiolldsolutior~ for tht! rcflt-rt.ior~fart.or, viil c~cl~rnt~ion(I), which occurs wllc*tl ot~lytwo rr~ciis~rra~r~cntpoints arc! 11sc*clthilf. arc war orlo II;II~-witvelcngthapart. Irr a sirr~ilarrrlanner, acoustic irnpcdanrr!~wcrc! obtained l~sit~grandomly selected mcla- srrrc-tr~c~titlocilt,iotls. Again, thc! t,ot,al nrlrr~hcrof dat,a points rntlgotl from 10 to 18. Also, for tollisspacing ctist,ribut,ion an ad(lit.ional co~~st,raintwas irnl)oscd such that at least two I tt~c~;~s~trottrct~lspclr i; w:~v(~I~~t)gl,hw(*rta l.ak(!r~. 111 ot,htbr worcls, (-RCII I~iiIf-wnvclengtlt was tlivitlctl int,o 3 c*qu;~lscgmcnts, and a randorn r~rrrn\)ergetic!rator was 11sot1to determine two rr~c;lsrrrc*~ncntlociibians within tach st:grricnt,. 'I'll(: solcct,ivo spacing distrib~ttionwas I.hc! s;trnc as t,he ~rriiforrnsl)acing distribution, wit11 adclitional cl;iba acqllircd at c*ach peak iultl rir~llc~icot~ritcrcd ill the staridirlg wavct l);~t,t,c-rti. I1 was t.xpc*ctcci tliat significant data quality improvernerit could be obtained by iricl~ttlirigrncas~trcrrlctrts at prcssrlrc* nnlls, which tend to ho very sharp and deep for sl)c*c.irncnswith large rcflc*cbion factor ningnit,trclcs (c.g., steel). In tile prcscnt, cotlfiguration, sc*lc*ctivt*upacing has two limitations; (1) sp;it,ial rc*sol~rt~iondrrtx to tall(> finite area of the prot~c~port,s, aticl (2) finite step sizc* in the scarch procedure* algorithm. I)uc to t,hcsc lirrlilaI,iorrs. rirrll loc.atiolls rrray riot. I~avo~)(~(BII Ioca1,tvI as prc(:iscIy BS iritendcd. In [act, whc!ri t,lic~standing wave 111rll is very sharp, (lafa acq~liredin these) sensitive regions may act,r~;lllydcgrrtdc t,hc iicCtIracy of t,lic ovc-r;~IIrosl~lts. 1rril)cdanco Mcasrlror11c*ti1~Valida.t,ion 1t;irigc 'I'llc 30 diffc!rcnt t,(-st,spccirncns incl~ldcdrnost,ly rcsonant type al)sorl)crs, whose struc- t,trr;tl foatrlres clifrc*r in clctail to covc:r a wido range of reflection factor rrlagnitudes (0.004 .: It ICM 6 0.999). '1'0 obtaiti bile srnallcst possit~lcR FM, a foam wedgc was used, whereas t,hc. largc I?, FM's were obtairicci with a steel spc~c.irncii.'rhc intcrtncdiatc range of RFM's was ol)ba,itlcd via cerarnic honeyconlb, a rigid str~lrtureof isolated, srriall diameter parallel c.h;lnnt!ls wliich providcd a very st,ablct and linc~arilnpedance. This variety of test speci- trlc-11s ;tllowc*d tI1ct ~)rop;tgationrnoclc-I, dcscril)c*tl in tile A NA1,YSIS sc~clion,to bc exerciseti for ;c witlc rang(* of irr~potl;~nc.cs.Obviously, if the irnl>cdarrc.cb v;ilrrcs ot)t.ained using the M I'M icrc! stiow~i1.0 1~ r(!l)(n~ti~bl(b,corlsist~rlt,, ;ltld convorgc ~triifor~~llyto previons results oi)t,itit~oclI)y ot,ti(!r tri(!t,hods, th(! MI'M will be validat,t.vl. Sirrirrl;~ljctlFlow Noisc 15ffccts 111 sotnc8 icl)l~lic.ittioris,;~coust,ic irr~l)cdanco r~lc~i~sr~rc~rncnts ;I~Ptic~c.c3ssary in the presenccl , of 1i1low. I .II(* prc~sc~ric't-of rrlcmn flow will tc\ti(l t,o cx;lggcrat,o rlifrcrc-nc.c.s in t,hc measured irril)c*di~rlc.r~rsirig I.hc* tliflitrcvl, spacitlg disbril)~rtioris. 'I'hus, it is of iritcrcst to determine t,hc* c-lrc~cl,of flow tloise or1 the! accrlracy of tJ10 MPM. Mean flow cfft.ct,s on impedance dlrc- to I.11o rliclil.rl flow or as a dcletcrious cffttct on t,lio rneasrrrcarnorit process itself, such a.s I,hc* ii~ercascdhackgrollnd rloise level generat$ctl i)y flow t,urbulcncc. It is critically impor- 1,;i.nt I,h;tl, t,hc- I,wo c:ffccts bc? separated. Many trlaterials exhibit nonlinear behavior in the I)rclscricc! of rnciirl flow, which c;tust\s changes in tlic acor~sticirnpodaricc of a test specirricn 11 1-12]. / 111 I.l~isinvc%sligation, the tloisc! ror~l.arni~i;ll,ior~i~spccts of tl~rl)ulcr~l,flow wc!re sirnulat,cd 011 Il~rcv!sl)ccinrc~rls t8I~at c!xhil)itc?d litlcar I)clla.vior ovcr the SI'L riitlge available in the ,. r* . tfc-st,;~l)l);trntus. I Ilc! three* t,c!st, spt:cirnens invcstigatc!d (steel, foarn wedge and ceramic I~onoyrornb)wcro chosen to sblldy the cffect, of sirnulatoedflow noise on the measurement, process ovc8r it Iargc~KFM rstlgc. A sctries of tests wcrc tondrrctcd in wl~icha broadband tloisa I);lckgroutid was int,rocIrlcctl too'contarninatt~' the discreti! test, frequencies. This was ;~cro~nl)lisllcdby exciting oil(! of the two drivcsrs with signals .fro111;t broadband noise gr~nc-ri~tor.'rile cliscr~~t~c*frrlcjl~cncy standir~g wavc! pattern was thcnll c!xtracted from the cornhinod rcsporlsc by 11si11gat1 cnsernblc a.vcr;lging f,cchniqric, and thc acoustic impedances wclrc*clc~t,c~rrnincd with t8ho MPM. 111 1.11i.q s~ctiont,hc tcrnis acorrstic irnpedanct?,reflection factor, and standing wave ratio arc rtsc(l sornt!whaf, inl.crchar~gcably.This is dllc to the fact thi~tthe three j>ararneters are ~lirect~lyrelated. As will be seen in the discussion, certain topics car1 he more conveniently clcscri1)ed in terms of a ~);trt,icularchoice of orle of these parameters. Curvo-Fitt8ingCornparison Via. 7 drpicbs Sl'f, nncl phase clist,ribr~t,ior~sversus axial clist,ar~cc. These data wen? ncclr~ircdl)y apl)Iyirlg oi~chof t,hc t,hrcc rnc;tsurc\rl~c*ntpoint sp;lcing clisbributions to thrcct I,c*stsj)c~c.itlic!tls wlioscb SW 11's varied froril 0.2 I,o 40 (1 13 (0.00~1. 11 IZM .' 0.1)09). Fig. 7(a) sl~owsrosr~lt,s for an int.orrt~c!tliat,c~SWI1 rntlgcs, itntl Figs. 7(1)) al~(l7(c) show rcsr~ltsfor ,l Ii~rgc*;III(~ small SW ll's, rc~sl)c~ctively.I Ilc rtic;~sr~rt!dvallres ;trcBrcprc~scntc*tl by thc circles ;111cl 1.110 solitl lillc. rcprcscr~tsthe I~astsclrlaros wa.vcbprol)agat,ior~ rriodcl fit, to t,he data. The S;IIII~*t,t*st frc?rll~otlry of 2 kk1z is shown for ;ill bhrcvl t.cst, spccirr~clris.'I'llo rosr~lt,sarc plotted fro111:r - -.90.5 to rr: 0 rtn, wit,l~thc spc*cirrlrr~plarcd at 7 O crll ancl the upstrean1 sorlrcc* loc;~t,edi~b ;~t)or~l, n: 63.5 rrn. Fig. 7(a) d(-rrlot~st,ratcsthc i~1)ilit~of t.Ilc1 t,l~t.c-cnlcastlrc!rilcnt pbirit clist,ributions to rt~c.o~~sl~rr~ct,tl~c*sl.andi~~g wavc pattfcrr~rlw.ritc.t,crist,ic- of a silrnplc with a I0 clH SWR, (RFM ncvitr 0.6). For s;trnl)lcs of this typc!, the thrco rnt!asurcmcnt, point, dist.rihrltions provide n(*;~rIyicIvt~t,ic.a.I r('s11l1.s. 'I'II(~s(! r(~s11I1,sWO~CI rcy)cat,nhlc! for virltually all of t,l~esamples wit,11 S W It's I)c*t,wcc-rtn t)otc t 1 itnd 25 tltj. 'l'his was expe(:ted, sinccs t.hc discrete frcqllency sound sortrcc- wits vcvry st,i~blc!nr~(l a siaablt! nl~rnbcrof averages (500) wcrc.'ilsed to determine the ;~co~tsl,ic.I)rclsstlrct at, c*iich 1)ositiorl.. This IIII~II~)~~~of iiV(?riiaCS was tlot rlccessary to attain i~c.cc-pl~i~l)lt!rc~sr~lts (tlricl thr~s,a good signal-to-~~oisc.ratio), l)r~bwas 11sc~1t~ecause of thc? Ii'ig. 7(b) shows t,hc rt!cor~struct,ed st.ar~(ling\va,ve pat,ter~~for a steel sarnple charac- t.c?rizt!ti by large SWR's rangirlg fro111 30 t,o 40 (11-I (H.IPM nea,r 1.0). Again, hot,h t,he SPTl and phase mat,cl~iilmost all of the? data poil~tsaccurately. Son~cwhat.: . surprisingly, the rlniforrr~spa.cing dist,ribut,iori provides a more tyl)ical represcnta.tion of the standing wave ~);l.t,tc~rr~(nt~lls gra.cl~rally incrossc! ;is so1111dj)ropilga.t,cs a.way from t811(- facc? of the specimen) I,II;LII (Iocs 1,11es(!I(!~t,iv~ spil~ir~g dist,rit)l~tio~~. 'I1his III;LY 1)~duc, in p:~rt,,too t,hk difficrllty of actr~;i.llylocating ant1 rneixsuring t,hc absoltitc rr~inirnawith the scllcct,ivc?spacing distribu- ti or^, ;I.S diucussetl 1)reviorisly. Overall, the three? c:rlrves appear quit(! similar and, as will be tliscr~ssc:rllater, providc nciirly ide11tic;tl rcll(~c:t~iortfacttors. Icig. 7(c) sl~owsrcsl~lts acquircd with ;I foitrn wcclge test sl)ccir~ic*ncharacterized by very low SWfl's of ahoat. 0.2 dn (ILFM of 0.004). This spccirlleri was elloscr~to exercise thc MI'M a.1, srr~irllR.lcM's. <:ont,r;try toot,hc rtsrllbs frorri s;t.rnplcs with Ii~.rgcr1l.VM's the math tr~o(l(!lloitst S(III;L~(~Sfit ~)roc(!(lrir(!docs not fib t,h~i~t~~plil~tld~ <1ati~a.s wc11, ir1 cvntnst with fahc?pttil.s(* dalai~, which is st,ill dcscril)cd vcry wc?ll by thc rnath n~otlel. This dcgradatiori of thr? i~rnplitrrdcfit is belicvc!d tluc! to t~u~ncricalproble~ns asso~ial~cci with small reflected WR.VC ;trr~~)Iit~rtd~s.Howt!vcr, tlit! ovcra,ll qi~alityis st,ill good (see Fig. 8(h)) in that the clcwia.t.iorls bct,wc:c!tt tllc rncasurcd data and thr curvc fit are no rnorc: than about 0.05 dl3 for il.ny of tht! ~rica.stirerr~ct~t,point, distrib~t~iotls.Also, it shoul(l be t1otc.d t,hat.curve fits to (!itel1 sc:l, of phirsc' ilata. iu-cBcor~sistc~t~t frorr~ ~IIV spacing distriht~tior~to the other. Corr~l);trisot~of M I'M wil,l~'I'MM and SW M A clirc*cl,c.ort~l)itrison of toll($ MI'M witall t,ho 'I'MM can I)(! oI)t,itir~t-dl)y cornl)ut,ing the irr~~)cvlil~lcc-11sirlg !.II(- 'I'MM ;tIgorithrr~on illly SII~)SO~,of two III(~;~SI~~OIII(~II~poit~l~sof the MPM tli~l~;~for it givcw si~rnljlc. Fig. 8 clc.pict,s aco~~st.ici~r~podnrlccbs (rt~sist,;~ticc* and reactance) i~ccluirc*(lfro111 tlniforlr~, ri~nciorn ar~cl sc%l(.ct,ivc- sl);u:ing tlistrib~rt,ior~s.It, also irlclr~desresults ol)t,air~c~civia th(*'I'MM itlgorithtn frorr~l,hc two riniforrn spacing rnc;lst~rotnct~tpoints nearest I,II(* I.(-st,sl)ccirrtc-r~ ((lcrlot.cd with diarrlonds). 'Fhcsc: tr~cast~rcrncnt,points were chosen to i~voitl1,I1o ill-co~~tlil~ior~it~gwl~icll occrrrs ill t,l~c-'I'MM algoritl~rrifor sl);~ci~~gsnear one half- , w;tvc~l(*trgl,I~.1. ypiciil rcwr~ll,sarc! sl~owr~frorrt c~1c.11 of six ty1)c.s of tctst, sl)ccimens to frilly clc-rr1or1s1,ritl.c.1.110 MI'M c;rp;~))ilit.it~s.III atldilion, Fig. 8(f) iriclr~clc~src*srilts which had been ot)t,ilirtc*tl c1;trlic!r wit 11 then SWM (cl(~~~ot.odwith x's). Iligl~lyrc*ll(*c.bivc~ rr~i~t~eriills arc* ofton chosc~11to sirr~ulat.c!groll~tcl sr~rfaces in scale model ~)t.ol)i~g;~t.iot~sl.r~tlics II:{I. Whcr~st,~~dyir~g trlittc~riills which t~i~vctritbh(!r large SWR's it is ~(~tl(ari~llytr~or(~ ~~~(si~t~ir~gfl~l t,o conll)arc rc\sl~ltst);tsc~cI or1 t,h~rcllcct,iot~ factor. This is illus- I,r;~t,cvlit1 Fig. 8(i1) for a st,c!c!l spc~cinic?n,it1 whir11 l)ot,h the roflc,ct,ion factor and impedance corrlltilrisot~s;IrcD i~~clrttlcd. As sccr~in this ligrlrcn, highly rcflcc1,ivc. n~iltcrials ger~crallypro- dtrcc- sip,~~ific;tnt,scatt.c!r on ;It1 acor~sticir~il)c~d;irlc.c* plot,, whilc cot~vorgingquite well when depirl~odin t,ho rollcc-t,ior~fi~ct~or rcgirnc?. On the* ot,llor hantl, rn;lt.c~rii~lswith S WR.'s less than ;I IBO~II 25 (1 1) I,c*tltl to I)(* Ivss scansi tivo l,o srnii ll cl~;lngesin t,li(\ st.ai~cling witvcBpararnct,crs itll(1, II(>IICC,ca.n I)(\ cor~~l)ilrc%clvcDry wc!ll on bhc* I)asis of acollst.ic itnl)(vlance ((..a. Fig. 8(b)). Vig. 8(c-f) Ml'M - Ilow Many I'oil~t~st'cr FIalf-Wavclc~igt~h'?, Ariot.llc!r goill of I,liis invcst,igntioti was 1.0 rlcltcmr~incthc! relat,ionsl~ipl)et,ween the num- 1)c.r of tI;l,bil. poi11t.s i1.11cl t,lic: clr~alit~yof irripetliltlcc~tneiisr~rerncnt.~. 'I'llr: rltliforrrl spacing dis- f,ril)r~t,io~~(Iiit,;~ (l(~srril)(vl ill l:i~. 7 wits rts(vI Sor l,l~iss1,rtcIy. AS IISII;I~, tnl~(l(litlait st-1' cot~t,;iil~o(l I ;I trrirrirr~lrtr~of six l)oirlt,s l)(~cyrlc (5 w;tvc~lrr~gbl~),with r11) l,o bhrc~c*c.yc.les ir~cluclc!(l. 'I'IIO r 7 r(*sr~II.sof l.hose I~I(*;ISII~CIIICTI~.Sarc8 rcprc~sc~nbc~clI)y sc1aarc.s in I'ig. 10. I hct second set of rc*si~lt,s(tlopicted witl~circlcs) was corr~l)ut,ctlusing only t,htb six rnc~;isrlrcrricrltsclosest t,o I,llc* sp(*cirncn. [pinillly, two i~ddit,ionalsc6s of rcsitlt.~ivcre (:ornprtt,cd by usirrg t,hree (first,, a 1,11irtlnt~tl fifth points) ancl two (first ilntl Fotrrbl~points) points frorn lohofirst cycle, depicted with 1,rinnglcs and dintnonds, rc~spc~ct,ivc!ly.If sho~~ldho rloteti t,llat tho rrsage of only two rnc8;isrlrc~mi*ntpoints rcdrrccs tllc algorithm to il dctcrtl~inisticcalculat~ion of the impedance, sitr~ilart,o t,hc 'I'MM. As slrown in Id'ig. 10(a,l,), the rirlrnber of points per cyrlc clops not significantly affect I,hc* rcs~llt.~for s;~nlplcswilsh RFM's wlrirh ;trct not Iiirge. This is a very i~nportant,observa- t,io~~,si11c.(8 it, ilt(lici~t,os1,l1;11. (~r~if,(%rol)c;~l.;t\)l(~ rosr~lln c;tri I)c oI)t,;~irlcvlSor ;I vast majority of s;l rnplcs wit, h as fc*w ;IS t,wo properly posi tionctd ;~corlst,icpresstrrct rrit~;~surcrricntsper cycle. As prcwiorisly tlisrr~ssc-(I,sa~r~ples with Iargtl ItFM's an*getlerally <:orrlpared directly on the* I);lsis of rc*floct.ion filct.or~. When st~~dicclin t.l~ismantlcr, Fig. 10(c) further sub- xt,;ltl t.i;l I,(-s t,llc rot~clrlsion1,11aIt two pain t,s 1)c.r ry rlc arc gencxrally srlfficicrlt for accurat,e rc-sr~lts. Ilow~vcr,I,h(vr(* is R sligllt irn~)rovcr~~~r~t,whcrr addit,ional pressure rneasr~rement~s ;lrc inclr~dcd.'T'hrts, sincc cacl~prcssllrcl rneasrlrc*rr~entreq11irc.s a minimal amonnt of timc, il, is rc*rorr~r~~ct~d(s(lt,l~;lb six points (or~c!ryclr t,ot,aI) bc rised whorl possil>lc. Sinlulntcd Iclow Noise Rc.sults ,I .II(~ final port,iorl of t.his invc~st,ig;it,ionwas 1.0 exrlrnine on(. cff(>c-1,of flow noise on tohe III(*~ISIIr(-t~~cr~t~ 1)roc~ss. '1'0 i1(:~0111l)li~ht,llis goill, ii 1111r~it)~rof ~rii~i~s~~r(~rn(~rit,s were nlatfca wil,ll ;I I)~~i~cll)i~~ltliloisc- solrrc.cB coi~~hir~ccl wif.11 t,hc. cliscrc!tc! frc*clr~c*r~cyso1trc.c to sirnulato P. 1.11~rloisc* conL;~r~~irl;ll~io~~~)rc*sc*nt wit,l~ rrlc*;~rl flow. 1 he \)roacll);~t~tlnoiso sorlrce was set, I,o ;I I(*vc-l wtrc~rc-cliff(~rcwcos I)c~twcc~~l 'I'MM ;~tltl MI'M rcsrllbs al)pc~arcd,which occurrt~d ;II, ;I I(nvcl srtcll t.l~ntt,llcv r;lt,io of disrrcf c frc~clrtonc'yIcvol to ovorall t)roadl)and noise Ievcl w;ls ;I ~)l)roxini;~l.cbly 2 d 11. Fig. I 1 sllows f l1c1 I)ro;ldl);i rrcl r~oisc-spc*c.t,rtt rrl at !,he refcretlce rr~ic-rol)lloli(-wil,l~ ;I 1,yj)ic;~It,c*sb frc-clrtorlcy I(~vc1lsr1l)orirrij)osc~t1 ;~b I .5 kllx. Icig. 1 l(a) shows f.hc- corrlt)inc(l sl)c*ct3rr~tnfor ;I higlily at)sort)ing tcst nlatcrinl, wl~crcasFig. 11 (b) shows I,llc. corr~l)itlc-(lsl)c~c.I.rrrt~l for ;I highly rc\fl(v-t.ir~gI(>st, nl;ittnrial. It, sllo~~ldI)c r~ot,edthat the lor~gif.r~clir~;tlrcnsoriirnccw of thc irnpocIanc.c! t.111)(. tctncl bo acccnt,uat.c corresponding frequen- civs it1 1,l1(* l)roiitll);~t~clc*xc.itat.ion, t,hl~s gcnc~r;rt,it~g ;I ~~rtrnhcrof sl)cct,rrirri pcaks other than 1,11ilt ;lssociabcd wil,ll f hcl discrctcl frcclt~onrysot1rc.c.. 'I'his t)ro;i(lI);~lldriois(? prodtlces the siirr~c*cfFr*c.t as ol,sc~rvctl wit.11 low voloc.iby rrltl;ltl flow, i.t~. if, tcnds toosubmerge the test, frc*clrlc*nryspc-c.t,r;il lint* ir~l,trc! bro;ttlband ~loisc.. 111 t,llc caso of l,ho sinall RFM material (Itig. 1 1 (;I)) totic*cliscrcl~,c* frc-c1ricnc.y I(~volwas wtall al)ovc t,hc I)roatlt)nntl levels (from about, 15 to 30 (It), tlcpc~r~(Iitlgon choir(\ of cliscrotc~frctclllc~iry), whcrcas for t,hc large RFM ma- 1,clri;lI (Ieig. I 1 (I))) Srclcl~rc-ncicwc.orrcwj)o~ii 1.0 1,111- rc~sori;lnc.cnswc!rcb a.lso prcscnt a.t levels of 10 lo 15 tlb al)ovc~tohc8 I)ronclb;~ntlnoiso. , I .II(- r~niforrnsl);tcing dist,rihut,io~~was again r~sctllo ncqnirc. cI;tt,;t Tor Ihc three samples clr*scril~c~tlin Fig. 7 (rr~;lt,c~ri;llswil,ll t.ypical, srnilll a.11(1largc! IIFM's), wit,li tllle! usnal number of ~)oir~l,spc1r cy<:l(!. Icor coriiparison pllrI)oscs, ;l roTt~renccdata set (rc!prc:sctlt,ed by square syrr~l)ols)was ac.quircd wit,hout tht! hroaclhancl noise included. 'I'he 1)roadhand noise sourcc was then act,ivat,ctl and tlie pressure tIat,a wcrc accl~rircdwith t,he rnaxirritlrn possible number of data. points. '1'110 rcst~lt,sof this dat,n sclt, artxdcy)ict,ed by tht! circlcs in I'ig. 12. Two data poi11t.s wtve then takt~~~from t,llis sarnc? dala. set (broadi)and r~oist'S~II~CC! activated) and inpr~tinto lohcrnit1.h propagation rriodcl (rcq)rcscntcvl i)y triangles) to compare with results fro111tr~t~ltiplc tlal,;~ points. *.1 Ilcsc! 1,wo points wcrc! c:hoscvi frorr~thc tolal data set such tllat I.llcy w(In1 f w;i.velcrigtli apart. Siricr t.llc MI'M rriatl~propagiltion triodrl redeces to the 'I'MM i~.Igorithrnwith t,lic rlsagc of only two data ~)oints,thcsc! two-point results represent 'I'MM rclsults tlnd~*rblic l)est, possiblt- conditions. I3y rlsirlg a single t,ra~lsduccr,calibratiori crrors II;LV(~ ~OCII(~lir~~iri;ti,~d. Also, 1)y choosil~gi,hc spacing of the nlc!a.s~~rc~rr~cntsproperly, t,11(- I)c-sf,~)ossil)lr- rcstr 1 ts frorr~t,hc t,wo-point, da t,il, shot~ldbo ;~chicvc!d. The overall effect, of t,llis j)rocedrlrct is 1.0 (lctnonstrat,e! the capahilit,ics of t8ho MPM vcrsrls the best available with i.hc! 'I'MM. A nt~r~il)r-rof cor~clrrsiollscan bo dr;rwn fro111t,hc rosults of Fig. 12(a,b) for materials wil,l~I.yl)ic;rl i~r~tlsrriall RFM's. 'I't~eMPM rtw1il1.s with t,hc 1)roadharid noise fall very closcb t.o t,hc- rc~sr~ltsol)t,air)cd wittiout, hroatlband t~oisc.In gcncml, tlic I'MM resr~lts(with I)roa(ll);t~~drloiscb) illso corllcl rcasoriat)ly close. to tl~cot.hcr data. ITowever, the TMM results (lo nol, rr~i~t~cliwit,l~ 1,11(~ 'c.lc;lrll rosr~lt.~(discrttlc- frc-clricbncy sorlrct. only) as well as toheMPM rc~sr~lls.I~~trl.t~c*r 1.1~~1s with 1.11(\ s;lrncBrn;ttcrials, which ;trc not s11ow11in t,hc figlircs, indicate 1.11;11. 1,11(* 'I'MM rc-s~~llsgr;td~~;tlly i11)l)ro;l~h f llc MI'M rcs~~lt~s;IS I,hc* n~lrril~crof avcragcs is irierc*;lsc~tl(ilr~cl hor~c.c-,;IS tho signal-to-r~ois(*ratio is inereas(-(I). *l1hcrefor(:, for this ilrr;t11~(~111(~11t.,I,l1(8 rr~;l,ior i~r~l)rovo~~l(~rit, of tli(b MI'M o\~P~181~c 'I'MM is t8l1o r~c(?(lfor fewer ilV(8ri\gOS1,O i1~~1~ilill(l(~ll;l~~~ ('Oll~i~~~(~l1~~ ~(>SII~!S. 'I'll(* reslil1.s of' Icig. 12(c) arc1 for ;L 11;trcl SII~S~IC(!(largct 1Il:M). Agilin, these types of tt~;tl~c~ri;~larcn corril);rrc~cl or1 1,110 bitsis ol' rc~fic.ct,ior~factors. As wits rlot.ccl in the resrilts of Icig. I2(;t,l)), l,hc- 'I'MM is rlob ql~it,oas c.or~sistoutas t,llc blPM, I)crt is tlot dramatically clilfcrc!~~t.. 11, is cxpc-clcd t,hi~tthis iriclusion of ;u:tunl rrlc:;lri flow (as opposc:d to the simulated mean flow r~sotlin t,l~isst,tldy) will cotriplicate t,llc! rnc*asurc?rnentI)mcc.ss to such a degree that tsI~(-tlispi~rit~y I)c~t,wcon t hct Ml'M and the I'MM will be sigriifica~it~lyincr~ascd. In thc? ~~siral i~ 1) J)I~C;LI,~OJI of 'r MM, lixccl trlicro1)honc. loci~1,iorisarc c!rriploye:cl 1.0 ;ivoi J tllc mechanical incotivc!r~icncx*oS l)rol,cl rnoverr~cnt~.'l'hc1 ~~clcsdfor prctc.is(: caIi\)rat,iot~(:a11 I)celirninatcd by tr~ic:rh~)l~o~~oswil,c.l~i~~g. Ilowovc!r. tl~iswill r~ol.likely l)roclr~c:cI.llc1 si~.rr~c!cl;l.b;i. cluality as i1 sit~glvprot)(! Inr;~,v(~rs(vlI)(~I.w~!(~II two l)oiril,s. 011 l?h(!o1,Iic:r II;I.I~(~,ir l)rol)(! rr~ov(:rr~(!r~t,is ii.vi~.il;tI)l(~,~,IIC~(B 110 r(*il.SOll1101~ la() (IS(! ill, I~'~I.S~~:! ~)()~II~~S ~i~~~lill lell(n,firS1, ~li~.~f-~il.~~!~~!ll~~~~l loo;i.voirl t,hc! ill-co~~ilitior~il~gprol)lc:rr~. 111 ordor to void calibrabiot~dillicr~Il,ies, 'I'MM data. c.;ln l)c taken witoh ii singlet microphonc~scqllcntially positioned to 1,wo dcsircd locations. (:lt~il.rly,f,hc a.c(:llrilc.y of 'I'MM rcsl~lt~sis lirr~it~cltlI)y thc! tra1)ahility of prc.ciscly determining thc n1c;t11 flow velocity, whcrc!a.s the MPM iterntivc! schcrne corrccts for possiblc deficiencies ill bl~isrrlci~sttrerrlonl,. Also, whilc the rct-positior~itigis occurri~~g,slow drift in the mean flow, if present, will likc?ly cause tohe result,s of tho TMM to be dist,orted. 011 the other I~anrl,t.lle MPM, which tcnds to itvcrage over oscillations of the rricarl flow, is designed to rr~inirr~izctho i~tlversecffc!ct,s of thc rrlcarl flow clriff, and, hence, shol~ldprovide a more i1cc.llri1t.c- rcsnlt,. II, is int,cnrlcd that this prcmisc will ho inves1,igatcd in fi~t,~irctests. CON(:I,UDlN(: REMARKS An t.xperirr~cr~twas condllcted to c.ornpartNn Multi-F'oint Mcf.hnrl (MPM) for determin- ing ;lco~~st,i(:irrll)odar1~~~ ~it~l~ two rclii~blc rr~(\t,l~ods, t,hc Stsanding Wilvc M<~tliod(SWM) i~t~tl1#11(. 'I'wo M ic.ro~)l~o~~c~M(:t hot1 ('I'MM). A significant nl~rnhcrof t,est, rrlatcrials were st~tdiotlto tost. 1,11(- MI'M over a r;lrlgc of RT'M's frorn 0.004 lto 0.00!). Aco~~st,icpressures i~lor~g1,11(~ c.c?r~l,cirli~~cof t.l~ca inil)rtlar~c.t~t,r~t)t! woro rnoas~~rc~~lwi1,ll three rncasurement point sl);lc'il~gclist,ril)~~t~ior~s; ~~tiiforrn, rand on^ and si~loc.l,ivc~.A leasf, scluarc>sfitti~~g method, with I,hc t,~ll)(-wall i~l)sorl)t.ior~iltitl IIIC~IIflow inclllclotl, was used t,o r~lodclthe* standing wavo 1)id(.I~r11.Icrotn tallisst.itl~ding wiivc patt,c*rnthc- conlplcx refiection factor of tdhctest specimen Wits (l(-I4(*rrr~iricd.SOIII(* COII~.~IIS~OIIS fro111 this ir~vcstigationarcb l)rc~sc~~ll,cdin the following sclc.l0iol~. St.nr~clir~gw;lvcb ~)ilttc-rr~sc.irlr~~li~fr~rl wit.11 t,l~clpropilgatiori rnotlc~lfor ;dl three spacirlg tlisl,ril)~~t,ior~sw(wb roll11(1loo ~r~ill,('l~11i(- rri~*as~~r(~~r~t!~~l,swit11 gootl to oxc:c.llent agreenier~l, ovcnr I,II(B c*r~l,irc.It I;M ritngc. Mar~~~ally~)osit.ior~c~rl ac.o~~st,ic. I)rtBssrlrtb rrlcws~~rc~rnents were ~lsc*tl1.0 sllow I.II;II, t,hc* MI'M is corr~~);lrnl)l(~l,o t,l~c SM'M. III adtlitiori, ;I, two-point suhsct, of ~~t~iforrr~sl);lcir~g lilt,;^, ~ilrc~S~llychosol~ 1.0 i~voitlspacings tl(lilr ;I half-wavelength, was inpl~l,ir~t~o ;I 'I'MM itlgoril.hrr~. Acor~st~icirr~l)cda~~ccs, rornpl~tcvl frorn dnt,a for each of 1.11(~SI)~LC~II~ rIist.rit~~~l~ior~~, or(^ ~,IICII cornl)iir~~(l \vil.h r(*sltltsof tho 'I'MM and SWM. The rilnrlorr~ar~cl sclccf.ivc spacing irnpcdanccs wclrc for~t~dt,o ;igrclo with t,hc 'llMM and SWM with iiccc~l)t,itl)l(~consistc!ncy. Thc ~rnifornls1)ilcirlg tlistrihtrt~ion,howevor, was observed to provi(lc ox1,rcmc-ly consistcrll reslllts. 'I't~ct t~niforrr~spacing irny)cdar~c.editt,a was also shown t,o Iw vc-ry rcpcal,al)lt~and, t.llns, a sr~pcriorrr~c~asurcrncnt poinl, distrib~~t~ionto be used with t8I1(* M I'M. Noxt, n sfucly was cor~clrrct,c~tlt,o clctcrrrlirlc* t.l~ci~r~n~l)or of datil ~)oinl,snc%cessary to prop(-rly define then itcorrstic prelssurc distril)ut,iorl. (:o~nparisonswerc rrladc t)ct,ween results 11sit1g2, 3, 6, all(! 18 di~bnl)oint,s whir11 sliowotl tal1;~b,ill general, only tswo properly located t~l(-i~~r~rc~rrl(~rlt1)oint.s arc rcclr~ired for rcyc*itt,aI)lc ~~~casr~re~ne~ll,~.I~owove~r,ii, was show11 I,Jlnl, 1,Ilcn trlost ror~sistc~rltMI'M rc-sr~ltsiirct ot)t,nir~c(lby sing at lcasl, six ;lcorlst,ic presslrro rr~(*;is~~rc*trrc!nt~sevc*t~ly sl~iwctcl itcross on(*hitlf-~i~~(!l(!r~gt,h. Finally, at1 ir~vc~st,igatiollwas col~tlucl,edbo tlt?t,t:rrr~int!tllc effc~c.1,~of corll arnination due I,o l,I~eturbt~lenb rllca.11 flow noise on the MPM. 'Li, sirrirllate tllis flow rloise, a broadband noisc sourco was atldetl to 1,hc. discrete! frequclncy source. A set of ciat,a was then acquired wit,h t,he r~niforrnsparitla distrihilt,iorl and input into the MI'M. In addition, a two-point, :;r~l)scf,of t,hc* silrrlc ditt,n was inpr~tirlt,o a I'MM algorithrrl. Tllo rcsr~ltsfrom these two 1rlc1,hotls were then cornpilrcd with a refcrencc sc.1, of MPM rcsi~lt~sobtaincd with only t,hr discrctse frc 111 eor~rlrlsior~,1,11(b overall purpose of tllis invest,igation, whicl~was to develop and c*xl)lolc-I.tlc* pot c.rll,ia l irrl,)rovernclrlt.s on accrlracy, precisiorl, an tl rnc~asrrrc?mbntefficiency ;~ffortlc*cll)y bllc- M I'M, I~irsI)c:cl~ si~t~isfiecl. 'i'1lrc.c. accepta1)lc rrlcasrlrorncnt point spacing tlisl,ril)rlt,ions havc. l)clt~n tlcrrlor~st~ratcd,but, t,llc. t)~st,apptaars to I](. tht! ~lniformspacing. Sitlec- tol~cMt'R4 is filst, i~ndctfficicnt,, cs1)erially wht-n rlscd in conjl~nctionwith the ltniforrn sl);~eit~gIII~~~IS~II'~II~(!I~I, poit~t,(list,ribr~t,iol~, it, fr1ii.v well I)(? a prc*f~rat)I~!rrlethod for future cxl)(*rirrlc~~ll~s. . . I{ Kl~KlI.l~;N(:F;S I . W. I(. 11.. Ilil)l)(!rlt 1!)5:i Aq.us,!.ic:;t 3, 153- l fi0. 'I'hc! 1)rilc:bicir.l rc!l)rc!sc~~t,iltionof standing w;~.vc~sill i1.11 ir.cor~sI,ic.i rr~l)c!d;t~~cc~ 1.11I)(!. 2. M. Id. f(i~(~lll~~i~i~.;III(I M. I,. M tltljnl 1977 .Jor~rrlalof l.hc* Acolrs!.ic So!:irl,y .of.Atn.e-rka 62, 751-754. M(!ilsr~rc*rrlc!~lt,of l,t~c!i1c:o11st.i(.;11 irnpc!clar~cc? of it l)ln.ck box at low frequen- cic.s rrsi~lg;I. shorI,c!r irrl~)c!danc:c: tor~\)c. 3. M. I,. Knt,h~~riyitar~tl M. L. M~~njal1977 !l~),j~rt!nl_ of-&l!y Ac:~~ust,jc-S~ci_c,Q.-ofAmeric?~ 62., 755-759. Mc!i.hod for c?v;llt~ationof t,hc acollstical itnpcdarlcc? of a. black box, ,with or witl~outrrir:an flow, rrleasrrrir~gpressrlros at fixctl posiI.ions. 4. I). A. Illnser ant1 J. Y. Chung 1978 blhe~~Noisc,901-!)OF(. A transfer frlnction technique for dat,c*rrr~itlingthc ;~.co~~st,icchara.ct~erist.ics of dlrct sy~t~crnswith flow.. . 5. A. I?. Seyhcrt atid 'I'. I,. I'arrott 1978 NASA 'J1MZ78J8Fi. Irnpcltlance measurement, tlsirlg ii, two-micropl~onc,randorn-cx~itat~io~~ n~etllod. ti. .J. Y. <:hl~ngii11d .J. Y. llla~flrI !)HO ,Jorlrrr;il of tht* Arou,stjc: Soc-icby or Ar~lclr-i~a(jg, 907- 92 1 . 'I'ransfvr f1111ct~ior1tnc!tt~otl of rnc!;tsl~ring in-dt~ctacortstic 1)rol)clrtic:s. 1. Theory ~III~II I. l~;xp(*rir11(!111~. 7. A. b'. SoyI)crt. ;LII(I I). It. Ross 1977 .l-~urr~;tl.~ff,l~-A<~rrsI,ic Soei(:jfy._oL:-A!ngr-ic~ . ti I, I :102-1370. I~xpc~ritnc~ltaldcternlil~atiot~ of acoustic: ~>rol)erticsusing a two- micropflone, riinclorn-c*xcit,at,iont,echniquo. 8. .I. Y. Chung and J. I'ope 1978 Intery-Noisc,R!):l-899. Prilct,ical nlcasurcmcnt, of acous- 1,iciil intensity - tht- two-rnicrophonc cross-spoct,ral method. 0. il. Ingard iit~clV. I(. Sir~ghill1974 Jo!~~Igf-_ttie~-c<)~tjccS~~-cigjtyY c_?f-America 55, 535- 538. Sound alotcnl~iltionill t,r~rhr~lentpip(! flow. 10. S. W. Yuan 1!167 J"~~~!(l;ltio~g-Ofpluitl Mccha-nics. pp. 383-384. Englewood Cliffs, Ncw .Jersey: f'rcr~t,ictl-IIall, Inc. I I. W. It;. Zorr~rnskiand H. .J. Tester 1976 NASA '~M-X:~:i~I~l.Prediction of the acoustic itr~l)ctlancc*of tlt~ctlitlcrs. 12. A. S. Ilc~rshiit~tl TI. Walkcr 1978 NASA (:I1-2!)51. F;ffects of grazitlg flow on the sloi~dy-stiil,c*flow rc\sistilncc allti i~c.ousticitr~l)c*dar~ce of 1 11ir1 porous-faced liners. 13. '1'. I,. I'i~rrotl~,<:. I,. McAnir1c.11itl~tl 1. A. (hrl1)crg l!187 NAS-A 'L'M--2748. ICvalnatioll of $1 scii,!~rrlo(1~1 cxj,c!rirncnt l,o invostigalc lor~grangc acorls1,ic propagat,ion. ratio of cll~ct.arc;l 1.0 dllct, poriniol cr frrv sl);~r(*S~IIII~ sp(lt~l sl)(v:ific. Ilc~~t.at, c.onsLant prc '~sllro :. so~~nrlsl)occl in t11l)c. fr(v~ll(~ll(.y d I a/(:,WiIV(' ll~lllll)(~t'ill f~()(~Sl)ilc(' rrlcniln Ilow Marh r~urnI~c*r 1,ol;r l 1111 rr11)cr of diih points i~col~sl,ic.prc. *ssl~r(! . rr~c~as~~rc~tlacoust.ic prcssrlrc. wit11 open ports rnc*i~.sr~rc~tlacorlstic prcssurc. with closctl ports Hcy nolfls 1111nlI)c!r S W M SI,;I11cIi11g M{;IV(* kl(~l,I~o(l -SW It Sl,i111cIi11p,W~IV(* lt;il,io 'I'M R/I 'I'wo blic.rol)l\or~c*M(.l,l~o(l .? . . . i . . +* I I . - I 120 I - 1 - I SWR+ RFM I I m I 9 I I - I XI+ 8 I I I RF = RFM I - I - i SWR mk - L 9 -m I 90 -- - - X1 I I I I I - I - I -I.. 80 - I I I I I I I I I -1.0 -0.8 -0.6 -0.4 -0.2 0.0 x, normalized Figure 1.- Reflection factor determination from continuous plot of standing wave (face of specimen at x=O.O). ------.- .------.--- . _ 1.27-cm Microphone 0.635-cm Reference Microphone 7 \ Measurement Ports Acoustic Driver L~estSpecimen \LTraversing Probe Figure 3.- Schematic of impedance tube apparatus. Measurement port plane (symmetric locations) Figure 4.- Traversing probe sensing port location. 30 I1 I 1 1111 1111 1111 1111 IIII 0.0 0.5 1.O 1.5 2.0 2.5 3.0 frequency, kHz Figure 5.- Probe port insertion loss as measured by relative responses with ports open and closed- ports located at pressure null. Reference Band-pass amplifier I - $ Frequency Amplifier Computer synthesizer b . Signal averager . . Ag~~re6.- Electronic instrumentation and signal conditioning schema tic. - x, crn 115r 200 - - Q3u 110F SELECTIVE SPACING a (J) 100: -100- - C -30 -25 -20 -1, = -10 -5 0 x, cm ' X, Crn Figure 7.- Least squares fit of propagation model to discrete SPL's and phases for three measurement spacing distributions (2 kHz). a Typical SWR sample (approximately 10 dB). Figure 7.- (b) Large SWR sample (30 to 40 dB). SELECTI'JE SFkCltJG Figure 7.- (c) Small SWR sample (approximately 0.2 dB). frequency, kHz UNIFOf?tbl RAPlD@f,1 SELECTIL'E TM kl frequency, kHz frequency, kHz Figure 8.- Comparison of reflection factors and/or impedances for a variety of measurement and analysis methods. (a) Steel plate. .4 4 O.~llllllllI1llll~IIII~I~II~~~~~~.5 1 .O 1.5 2.0 2.5 3.0 0. .5 1. 1.5 2.C) 2.5 3.0 0. freal.lenc\~, kHz frequency. kHz . (b) ' (c> 0 UF~IIF15RF.1 0 RAI 4GOt~1 a SELECTIVE *ri TFw4fwl .5 1.0 1.5 2.0 2.5 3.0 frequency, kHz frequency, kHz Figure 8.- (b) Foam wedge. (c) Ceramic honeycomb. frequency. IcHz frequency, kHz (~j! (5) a U 1.~1I FO R h,I 0 F?~PlEOl~il a SELECTIVE 2. ThI tv! frequency, kHz frequency, i4-t~ ~i~ure8.- (d) Fibermetal sheet on honeycomb surface. .. , ,I : - (e) Porous metal plate on honeycomb surface. frequency, kHz frequency. kHz (f) - 740 .45 ;50 .55 .60 .65 .70 -frequency, kHz frequency, kHz Figure 8.- (f) Aluminum plate with 4 holes. Figure 9.- Demonstration of repeatability (uniform spacing). L 0 0 G tltI1tlliql!~l~~lllllll/~~~~I .5 1 .G 1.5 2.0 2.5 3.0 f req;.~ency, kHz I ;freqi~ency,kHz L .6 - .4*-1111111111111111111111111111110. .5 1.0 1.5 2.0 2.5 3.0 frequency, kHz frequency, kHz frequency, kHz frequency, kHz . . Figure 10.- Comparison of MPM results using various amounts of uniform spacing data. (a) Typical RFM (ceramic honeycomb). (b) Small RFM (foam wedge). (c) Large RFM (steel). .5 , 1 .O 1.5 2.0 2.5 3.0 frequency, itHz b frequency, kHz Figure 11.- Comparison of spectra for discrete frequency (1.5 kHz) with superimposed broadband noise. (a) Small RFM test specimen. (b) Large RFM test specimen. .. 0 0 '0. .5 1.0 1.5 2.0 2.5 3.L' frequency, kHz frequency, kHz GG- .zoo .5 1 .O 1.5 2.0 2.5 3.0 frequency, kHz frequency, kHz frequency,' kHz frequency, kHz Figure 12.- Comparison of MPM and TMM results with broadband noise included. (a) Typical rJ;M (ceramic honeycomb). (b) Small RFM (foam wedge). (c) Large RFM (steel). Report Documentation Page 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. I 1 NASA TM-100637 I I I_ --. I I I~TxndSt~btitle 1 5. Report Date EVALUATION OF A MULTI-POINT METHOD FOR DETERMINING June 1988 I ACOUSTIC IMPEDANCE . I 6. Performing Organization Code ... .------8. Performing Organization Report No. l4ichael G. Jones and Tony L. Parrott 10. Work Unit No. -- Organizat~onName and Address 505-61-11-02 Langl ey Research Center 11. Contract or Grant NO. tlampton, VA 23665-5225 13. -- Type of Report and Period Covered Agency Name and Address Technical Memorandum National Aeronautics and Space Administration Washington, DC 20546-0001 14. Sponsoring dgency Code I 15. Supplementary Notes t I Michael G. Jones, Planning Research Corporation, Hampton, Virginia. Tony L. Parrott, Langley Research Center, Hampton, Virginia. 16. Abstract An investigation was conducted to explore potential improvements provided by a Multi-Point Method (MPM) over the Standing Wave Method (SWM) and Two- Microphone Method (TMM) for determining acoustic impedance. A wave propagation model was developed to model the standing wave pattern in an impedance tube. The acoustic impedance of a test specimen was calculated from a 'best' fit of this standing wave pattern to pressure measurements obtained along the impedance tube centerline. Three measurement spacing distributions were examined; uniform, random, and selective. Calculated standing wave patterns match the point pressure measurement distributions with good agreement for a reflection factor magnitude range of 0.004 to 0.999. Comparisons of results using 2, 3, 6, and 18 measurement points showed that the most consistent results are obtained when using at least 6 evenly spaced pressure measurements per half-wavelength. Also, data were acquired with broadband noise added to the discrete frequency noise and impedances were calculated using the MPM and TMM algorithms. The results indicate that the MPM will be superior to the TMM in the presence of significant broadband noise levels associated with mean flow. - 17. Key Words (Suggested by Authorlsll 18. D~stributionStatement Acoustic impedance measurement Unclassified - Unl inited Reflection factor Normal incidence Standing wave method Multi-point method Mean flow Two-111icrophone ciethod Subject Category - 71 ----- 19. Secur~tyClau~f. (of thls report) 20. Security Classif. (of this page) 21. No. of pages 22. Price Unclassified Unclassified 35 A0 3 NASA FORM 1626 OCT 86