Document kDJyLK2eQaRo1ZQ3Kx9Ky461y

LEAD INDUSTRIES ASSOCIATION. INC. ISt MADISON tVlMUl NCW TON* l. N. V. April , 19<5j to Xeabenof tbs Lead Industries Association, Inc.: Ve srs attaching copy of s paper presented st tbs Vinter General Heeting of Tbs Institute cf Electrical and Electronics Engineers, Jan uary 27-February X, 1963, describing 'Transforoer Seise Reduction with s Close-Fitting lias a-Lev Enclosure,' by P. *. Adkins, Portland General Electric Cccpany, Fcrtlar.i, Oregon. Tbs enclosure Is constructed of steel, sheet lead sal fibre sisse, ud vs estimate thst la tbs tranaforaer described st lesst s ton of sheet Usd Is used. hr. Adllrj hs* subsequently soundproofed tvo al-iltianal sIdler trscaforasrs sad Is currently working on s fourth, which Is larger. Xt Is extreaely Interesting to tote fro* l!r. AdiIns ' cost figures thst bs achieved tbs reduction la nai is st s cost per db of reduction which wes less then ths additional cost cf buying s transforscr sound* proofed st tbs factory. While ve bsve so relish!# statistics available at tbs Dcrdt, vs believe that there are thousands of trassforaers of varying sites throughout tbs country which sight warrant this treataeat. Vs vlU not atterpt any further Interpretation of the paper, but because of Its thoroughness sad clsrity urge that you study It. In his conclusions Jhr. AilIns states: 'In its prototype fora, this enclosure surpassed expectations. Future Installations will, bevever, incorporate several changes which should provide greater latitude for construction tolerances. Although the barrier tronsnission loss Is adequate, It Is felt that tbs proportion of lead to steel should bs Increased, vhlle alntalntng tbs sane weight.* Vs have ordered 3,000 copies of this psper and plea to sail It to a list of over kCO electric utility ccepasy engineers. Ve also plan to publish a shorter version In an early issue of cur publication ''Lead. ' Additional copies of this paper are available fren us free of chares la quantities of 25 or less end at our cost of (12.00 per hundred for larger quantities. Very truly yturs. RLZ:sk Sae. ^ IEEE Transactions Paper (Reviewed and AtcejMed f*r Publication) Dtecueeton la Duplicate Due___Ti* ru*ry__i5A_J5'il,-- -- TMxsrcnm o:sx noucrcai ra a c l o s z -f it w c h a s s -l a v ix u x w s t. K. Ai*la imur naz Portland General Electric Coopany Portland, Oregoa %*v r*w> ) A paper rec emended by the A2EE Traaaforaera Conalttee and approved by the AHZ Technical Operation* Department r<r preeentatlon at the Vinter General Meeting, Jkv York, A. I., January 27-February 1, I963. Manuscript lutmltted September 23, 1962; made available for pristine fcveaber 27, 19^2* PrW: | aTt MieWe ItJe T. Kewbn tier *rr nn 4itili--l tf Ant rite nAe tniitl (Mitlwe Bel (Mir |l Ml AB Ki|Mi lUwrwt k| TV r Elrrtrv.l KUrtnmlrt Kutirnttn, r.aiA Um H.lt tuun, Hrw Ywk II. N. T. lithe a I'M 3 feper He 63-200 "l * 11,1 ........... Ull'-n 'l mwiir.'ewwBii.iniMiwua.ii II WRaiia^inB.iip^iift htf. N 2356.01 Hi LIA185 87 iu m.j 'mo * >]: io.t! a w:r< A ci/v !>.nrr:s. p. a. AUio fvwr/1 Thla lp*r dte-uaaes the de ! jrn ind development of hlah-attenuslton, ft#l4 i,;'.i'tU acoustic enclosure for 1 re* power transformer*, teaed la -cncept u{>'/> th# 'field Incidence Ks* !j v " fro* the field cf acoustic. fre* stsntlrg e..! for* fitting, enclosure* of tali type Uh been designed to provl1# noli* reduction In C-* order of 1} to 29 deci'al* tn edlitlua to oth#r advantages inherent la neer-totel *0010*01*. jrr*oxxmo* Pol** ha* been 4*flood * unvested audible sound, sal y*t oot *li ool* e*u** eom~ pi*lot or tlr * community loto unified ct!oo. It be* bees Doted that mo / relatively intense ool*i (1** rl* to olid or ihort-ter* ennoyence, vlth d o forael coeplelnt. In coot rent, th* low frequency, continuous, *ll-per*l!n< bM* of 1* rg# trensforaer, haw rtr coafortlag to utility engineer*, nay become coepoundlng annoyance to neighbor*. "Tb* Power Ooapeny* la th 11 ;***, 1* * specific corporate person who, la eddltloo to advertlsl:* ownership of tht offend!eg trsr.sforer, la locally available to hear ccasplaint* directly fro* th* annoyed neighbor, or lodlnetly fro* the courts or earloua office* of City goveroaent upon who* th* utility Kilt rely for *on* change* and other expansion privilege*. Jo order that it* obligation to provide th* blgheet level of service cosaenaurete vlth foat over a long period of tie* nay be realised, the utility oust cultivate an attitude of co-operatlca vlth thee* governing bodlee and customer* to ensure that expansion end relnforcenent vill be permitted vher* and aa re7-1!reamta dictate, rot vhere and as permitted. This paper will deaerlb* th* development of close-fitting trnnaforaer enclosure baaed on th* field Incidence Mat* Lev, (1} and the application of this sethod of Dole* control to a particular tranaforner bant on the Portland General Klectrie Company ayatea. O G coocuisicss Th* acoustic enclosure* studied aod described in this paper are free-atandleg, for* fitting, oearly total enclosure* designed to provide oolae reduction In the order of 1J to 20 decibel*. Thla order of hols* reduction la shown to be available usleg aaaa lew tteouatioo, efficient energy absorption, end oearly eoeplete enclosure. In addition to providing high noise reduction at a coat equal to or lower than other aethoda, further advent#,** of this'arthod are: 1. d o la* reduction in all direction*, 2. effective**** 1* unaffected by topography, J. doe* not require rv*ote transformer cooling, k. can be applied in th* field after coaplslnt, J. can be oondeatnictlvely disassembled, 6. iaprovea appearance of th* trenaforner. Th* nethud of noise tieataent described represent* a depart'tr* fro* aethoda cnaaonly considered for field application, and ie believed to be unique, econo*!c, end suf ficiently effective to varrant further development and application. $ LIA18586 >.* - *v * ' .. -- ------------------------U---------- --- -- - *-- I I"2~K2 Mm (* sttvl K.}u! rvmenta "" %m !- of ti'.f'nAn coot ro l schema I* to alter the charseter at sound field io Uet it la not objectionable, motl frequently If Beta* of noise reduction. The difficulty of determining the ujuat of aolee reduction thet it required of Bolt# control scheme cto better to appreciated tfUr ecnaiderlrg tne follow lrg iteas; A. loltt levels "generally considered acceptable* for representative treat trt useful tt t f>ll* only If it it racognited that lc.ey a re bated upon (roup rather than individual reaction. The lmplleetlon It Uot nolte control tcheme should incorporate pitot for additional nolte reduction beyond that which it indicated by established (roup acceptability criterlt. VMlt these crlterit are valid tt a guide la tn uodlaturted tret, they are not tecetttrily valid when applied to an individual or tatll (roup that hat been annoyed to the point of cowplalnt. B. Boise lerelt 'generally coot1dared acceptable* do not take into eontlderriion the rredsadnar.ee of one, two cr three component frequencies tt it the ceae of power t rent ferae re, l.e., the spectral dlttrlbutlcn of energy. Tbit further qualifies the ute of thete criteria by the feet that asfcle-.; nolte and transformer nolte cannot be compared on the batle of tourvd level ae measured with a Sound level Kcter. Conpari ton thould be It ted oo the dlttrlbutisn of energy la the audible apectrua, l.e., the eound level* la tie octavel ccctalnlcg 120 end A0 epa or comparable neaauremente of eatlent tod tractforaer Delta aade with a narrew band tnalyter. The difference thua determined la aore reliable for the determination of berrler attenuation requirements. C. The rate of change of nolie level la tt inportant at the amount of change in ltt effect oo the response of a (roup or tn individual. Hence, a large nolte reduction brought about gradually over e lccg period of time will be lett effective than t tan Her reduction effected in e short period of tine. Tide Introduce! the psychological effect which say be used to advantage to increate the effectiveneta of treatment. Ideally, the scat pronounced effect w-uld be achieved by allowing the nolte to continue unabtted until the last bolt vat to be interted, at which tiae the r.olte would be ihut off suddenly. Thlt eaphsslzet the lnportance of scheduling work for the thortest tout-down period, and returning a trantforaer bank to aervice at toon tt pottible. It followt that considerable benefit wight be achieved from trtlfleiilly augmenting or tuaUlnlng transformer nolae during the work period. D. A nolee cowplalnt nay be en objection to the existence of t tubttatloa rather than an objection to trantforaer nolte, in which cate no amount of nolte reduction will satisfy the complaint. Although t complaint nay be tuspect, one alternative to immediate treatment la to await legal ectlcn at evidence of a ter lout nolte complaint. Since this alternative Involves unfavorable publicity and is detrimental to the Interests of the utility, the possibility of this type complaint can only be considered at cause for a conservative approach. The nolae eosplelnt which reo-ilted in the treatment developed in this peper, wet vehement from the beginning. It necessitated the use of neaeurement end comparison methoda vhlch, at baa been pointed out, are not strictly valid, but were consistent ' * LIA18589 - 3- with approved techniques and vtthln th* capabilities of IK* aeaturlng equlimaut availibl* * The object of coaplatnt vaa * bunk >.f thr* single-phase 115->7 kv autotrenaform r* each rated 2}/J3.J/kl.7 KVA, CA/ftA/rJA, standard acla* lavaj. !> standard iv -1m level for **ch unit 1* 7* do* (db, A scale, ba-i on 15,VDO K7A-(mrt*), end field measurements according to tfiXA Etandard method* Indicated thl# vaa U, Oo! leva! of *eh unit. A cursory sound level aunray wee ut4 to determine th* validity of the various complaint* M further define t-he problem. That ur*#y, mad* between twelve o'clock *wA four la th* morning, Indicated that several cviUatn had Juat cause for complaint. A second, more extensive aurwy vs* than k !< and from It, for analysis and con trol, a map of sound lavcl cootoura wea drawn. A cceperla'-o of that mcp with contour* calculated from the transformer sound laral and physical dimensions shoved no rorrellatlca because of tbs topography end raflactloaa from oearty buildings. Typical sound lavala at varloua resldeocta ar* ihwn la Tati* 1. TABU I Sxcaaary of Sound Level Survey Results Min. Antleot Trans. Boise Beaui tent Customer Dlatanc* (2-h a.a.) Level Only Level A lbO ft. 30 dbA B 200 30 C 3*0 30 D 500 *9 dbA U *7 39-5 *9 db bb * *7 bO Incrvete In level 19 db. lb A 17 10 Th* column headed "Increase la Level* Indicate* the aaouat by which the minimum ambient oola* laval vaa lacreaaed by lnatallatlon of the tranaforaer tank. The minimum aabi at level shewn la a condition occurring only momentarily and la approximately 5 db below the normal for that time of night. from thla It vaa Judged that a traniformer aousd leval reduction of at least 10-15 db would be required. A reduction of this order would not render It Inaudible, but should sufficiently reduce th* probability of future complaint. In consideration of plans for future system additions, and recognising the proba bility that noise problems would arise vlth Increasing frequsccy In the future, the decision via made not Just to solve this problem, but to become familiar enough with transformer noise problems In general that analyzing and prescribing treatment for future problems would be relatively painless. After estimating the costs of various methods of achieving the necesaary oola* reduction*. It wa* decided that the knowledge and experience to be gained by constructing a barrier of nur own deaign would more than offset a reasonable Increase In cost over that of a manufacturer`a design If such lu creaa* did, In fact, matarlalli*. Deaign Consideration! To data, the most reliable method of achieving substantial sola* reduction In an existing lnatallatlon has been to Insert a masonry barrier between the noise source and critical observer. The primary effect of thlw treatment la to distort the sound flald by reflection and la always accompanied by a noise level Increase In a non-crltlcal me -e*- ' !, LI A1 .k . area, Application of this ewth-d, tn thU ca, It often -'-t 1 Uffleult by the ph/al-tl rrnr-if^cnt f the i.tiOtl n and 1 '*1 t<*rrtri featuM-a, If 11* r.;l r-Jurtion requi recent* *urh ti.t tnfc* or f ur v*lla *r.d pja*:biy a fail or per' *! r*>f re required, It e*/ be ne -is*ry to Install Cooling #qvl|nt ct*:ie the soflctire. Pfhllt the obstacle! re oot Insurmountable, th*y do add curtail* rally to tJ* coit of treatment. Thee* and other considerations prvmpted the eearch for tvthoi of treatment which w effective, compact, end economical and did not require idltl r.*l cooling or revote lntallatlon of cooling equlparnt. These re pulreaenlo c old te fulfilled ty * barrier ecnttructed between the radiators *M the transformer tan* If: 1. high enough transmission loee could be built into the terrier, 2. the Increase la sound level betveca the berrler end terJi (buildup) could be Halted, J. It did oat lapcir the function of the transformer, k. the cc*t of treatment by thli acta* was consensurate with noli# control requlresent*. To conelder the Ileal situation, the nolle reduction that would be achieved by covering a uniformly radiating towice with perfectly attenuating terrier v.uld te flvea by equation (1), In which K represents that friction of the total area which le covered. This function 1 plotted In Figure 1. Development of tlili equation will be found In Appendix II. db 10 log (i - *) (1) Aa night be expected, covering half the radiating area results In a reduction In radiated puwer of 3 db (or half power). However, no barrier ll Infinitely attenuating, and *o It 1 deal ruble to nodlfy aquation (1) to Include the effect of finite barrier tranaaiasloo loai (aee Appendix III). Thla nay be dene la effect, by replacing that pert of the original *ource "re moved" by a perfect barrier with a aounce equal in area, tut whose strength la equal to the original aounce level nlnu* the barrier transmission loaa. The reaultlng at* tenuatlon nay then be given ea a function of the part of the original acurca area covered, and the barrier transmission loaa aa In aquation (?). db 10 log (1 K (10*.l(Tl.)_ijj (?j where: db reaultant nolte reduction K fraction of original area covered by barrier TL barrier tranaalaalon loaa in declbela A fsmlly of curves (bowing soma aolutlona for thla equation la given In Figure 2. With reference to Figure 2, It can be aeen that the benefit that night be attrib uted to Increasing the barrier transmission lcaa la lcat unleaa great care la taken to provide nearly perfect coverege. it will later be ahown that It la not difficult to attain a barrier tranaalaalon loaa of 30 db, henca the aound level reduction achieved la prlaarlly dependent upon the extent of Coverage with tne barrier tranaalaaloo loaa a a Halt. It ahould alao be avldent that the laat few per cent coverage would be lncreailngly expensive. LI A18591 5 Jo practice, several thlrgs contrllule to licit tlw effvctlver,**# of thia ldeallied enclosure. Th* phyalcai Configuration of the tramf >ror, the location of *l'f#, guagea, and other device# for which access cuat le privllei, an1 cJo#c prualelty of radiator* ell #erv* to Increase the physical complexity of the er.cloaura. In aome ce#e, fixture# muat p# through the wall of U* enclo#ure anl muat be Isolated fro* It #li>ce anything thet bridge# the apace between the enclosure wall end transformer tank will tranamlt acouatle energy. The cloie pro#laity of the barrier wall to the tranafervr tank caute# adiabatic axpanaloo and coapreaalon of the encloaed air. It haa been noted by other# that If a,t controlled, thia phenooenen aey be reaponalble for an a;p*rant alx to ten decibel 1'.craaae in the aourcc aound level. Control of thia fora of Buildup may be accompli .hed In an tncloaure of th.< type by lining the cavity with d-na* blanket! or block# ol glass fibre to provide vlacoua loaaea. In the deacrlbed enclosure, a two-Inch thickneaa * denae flbreglas vaa acunted approximately one Inch from the terrier. . It waa estimated to be adequate to Halt the apparent Increase of aource no He level to 3 db. Subaequaot meaiurement# Indicated that thia nolae level lncrtaae waa no more than 3 db. The phyalcal Irregularity and non-ur.iform radiation of the tranaformer tank cauaea beoding wave# (2) to be act up In the surfaceof the ancloaure, which lo turn re-radiate aound. The Introduction of bending wevea alao cakes panel resonance#poaalble at fr*qurnciea other than thoae characterlatle to transformer nolae. The preaence of bending wave# sake# It neceaaary to provide damping to dlaalpate energy transmitted In the wave, Halting the aaplltude of atendlng wave# aet up on the aurface. Thia daaplng can be obtained by uae of barrier aaterlal laving high Internal loaaea (mechanical hy* terra la) auch aa lead. Oeneral or a pot application of- daaplng after construction could alao be used. If the nolae source vaa a uniformly radiating flat aurface it would radiate plane waves. A barrier constructed parallel to the aurface would encounter aound wave# lapinging norally on its surface, and no bending wave could be aet up. If, In addition, the fundamental self-resonant frequency of the barrier panel ware sufficiently 1<V, it would not be excited by a sound wave of the frequencies encr red in tranaforaer nolae, hence daaplng treatment* would be unnecessary. In the absence of resonances, a panel attenuates sound In proportion to the logarlthr of the squared product of frequency and panel aurface weight. Bence, at a given frequency, doubling the aurface weight would Increase transmission loss by six decibels. By the saae token, doubling frequency would have the aaae effect. This la the field Incidence Hast Lav 1, 3, reduced to equation (3). TL - -5 10 log (1 *(1.4 x lO'tyfrf)2) (3) where; TL diffuse field transmission loss in db f frequency in epe - tf aurface weight of lenel lo //ft* By equation (3), barrier having a surface weight of ten pounds per square foot would have a transmission loss of 28 db at 120 epa (the fundamental transformer nolae frequency), 34 db at 240 epa and 40 db at 3^0 epa (the second and third harmonic fre quencies reapectlvely). Applicability of thia equation does, however, rely upon "limpneat" and Internal hyatereala to prevent devlatloni In transmission lost which vould result from resonance* at Integer multiples of the basic panel resonant frequency. In view of these problem* and in consideration of the reatrleted apace available, the barrier section used was composed of 1/16 inch lead sheet laminated to ten gage frflnrtriMTthnrrrr LIA18592 o I \ 0 .6. te*l with eposy r*oln ei-ainund. A two Inch cvrtaln of prund density flbergla# wat mounted i proxlo*t*)y ona Inch from th berriar to pr\.vlJ# vltcoua lot* within th* cavity. Th* tarrler and supporting atruclure ' fr* (tending *n<l Isolated froa th* transformer. The*# pip** and fitting* which, of necessity, p------ i V..uugh ` arrler wtr* Isolated >M staled with c..apllant neoprene gasket*. A lined, iht metal roof wn extenled from the edge of th* tank top anJ fatter.eu with sheet-aetal screw* to th* top rig* of the terrier, ensuring a permanent, weathertight enclosure. T). roof la th* only Intentional bridge tetv**n th* tank and terrier, an4 we* cuntldered acceptatl* because of th* flexibility of th* roof, and the vltratloo nod* at thla point on th* tank. Th* top of th* particular trar.afcraer being treated w* not considered to be an actlre nola* tourc# for four reason*: 1) th* asall area, 2) th* direction In which It radiated, }) effective mast do* to buahlcga, etc., b) th* ,gat-fllled cavity under th* top. A typical panel section and other vleva of the en- cloaure tre *bown In rigurea J through 9 Appendix 2. Detlgn Evaluation After the completion of th* flrat of thre* encloturea, eound level **aaureB*eta vere made flrit without radiator*, and then with radiator* In piece. Measurement* In* dlcvted th* aouod level of th* tank bad been reduced 22 dbj to 52 dag (k>XX method) with good unlfwralty. Felnatallatloo of th* radlatort raleed th* eound level to 57 dbg giving a net reduction of 17 dbg. Th* loading effect of th* radiator* on th* tank la not known quantitatively, but th* retult we* that of adding to th* transformer tank nola* level a aecond tourc* whot* level vtt 56 dbg. It can b surmised froa thla that to aebdeva any further algnlfdcant nola* reduction, th* redlator* autt b* laolated froa th* tank. There wat no Indication of panel reaonance, nor did aaeple aeaaureaenta Intide th* ndoture indicate n tlgndf leant buildup of nola*. Bated on the** findings, th* two remaining traoaforaera of the bank were alallarly treated. Similar aeatureoent* Indicated sound level* three to five decibels higher than thtt of the first unit, and were characterised by vibration antloodea. Performance was laproved by subsequent relief of spot cootact*. Prolonged surveillance of to^oil temperature In thee* transformer# Indicated that theraal Insulation of th* tank resulted in earlier application of second and third stage cooling, but did not increase th* peak load temperature. It ws therefore not Mceeaary to derat* th* transforacr bank. Aa wna aentloned previously, construction clearances wtr* extremely Halted. De tail design and fabrication was done la the field for th* flrat unit, and was closely supervised. Fabrication of the second and third units was don*, without codification, froa th* original pattern* and aeaaureaenta with only node rat* supervision. It 1* be lieved that aanufacturlng and construction tolerance* were th* caus* of th* troubl* experienced with thee* units. Installation of thla typ* enclosure la now planned for a three phase transformer of the tea* total rating a* haa been described. Th* tremforaer hat been purchased with additional clearence between the tank and fixtures in expectation that construction problem* will b minimised. Header arrangement of coolers on th* new transformer prom ises considerably less nola* froa thla tourc*. Coat of Treataent Th* cost of treating this tran*former bank va approximately $21,000 or fklO p*r db per transformer end represents 0.8) per db bated on the traneforaer cost. By eoaperlaon, an offending traneforaer may be replaced by e new on* purchased with reduced T itfM ?*-r-irirurt "g^aPIH --1*1 wap Li A18593 7 nouhd laval. TM eholc* v i.]4 r|r**nt an UlUoml cut of 14 to 1.34 l'T d: ; lot tbaniaoul eotl# (ani filed charset oo lha eilill:,} Lank until It can t* uted in i< rant It 1* nad* ill*). further coapurlton it provlJed by the vttlaaled eotl of O.T4 ir Jb for t frtt wall Mtoiiry terrier, ecouttlc trettnent ,t th* barrier, arul coaaaarclalljr avaiittle panel* applied to the trantforner to achieve the aaaa Delta reduction. Hunairr Cone lut lor t Tnlt pajar hat briefly deicrlbed Iht developaent of a compact, demountable ind affactlra ecouttlc ancloaura built by Portland Oner*! Electric Coapany. Id It* prototype fora, thli enciotur* turp*f*#4 aipeetatlont. Puturt tratillatloo* will, however, Incorporate i*ver*l change* which a'ould provide ureater latitude for coo*tructloo tolerance*. Although tba tarrlar traoialu loo lot* it *4*30*1#, it it felt that tha proportico of let! to deal thould t# locrened, while aaintalr.ing the %ae valjht. Thlt would provide treater lta;r.*i, reducing the effect of atlff Joint* be tween plate*, and re-lucth* the lUtellVood of atavdlnt wttet do# to vibration *r_i tending wtvtt. It la alio felt that r- re efficient ttr rptlofi ia t,\* cavity and acre c *;l*t# itolatloo and cloiure around ptpet v-.uld provlda a worthwhile lsprovevnt In reliitllity. A* previcuaty note!, radiator* anl their fan* will alvayt be a protlta wit: '.hit tjrpa encloura. Coat c >otIgoratioo* tpprtr to t* Inherently <tu!et, tut at thl* tiae llttla la known about then at t nolle a.urea t.-vl to sutt remain a aatter for Jut.-sent. *zn&rx;ts 1. Kolia Reduction, tiro Bertnek, KcCraw-Kill i960, pp. ??5-301 2. Ibid., 230-361 3. Handbook of Koiie Control, Barrlt, McCraw-Blll IA1, Cb. 22, pp. 7-10 m LIA18594 . i. Q Am:wx i cmis n o miToovTin (*3T rtrirrr, 3 ny-tnt H AITCriX II Pevelopaer.t cf Equation (I) Tha tera decibel, In the field of noise control a* In other f'eld*, 1* 'i*4 V> dcrine the Intensity of a sound In ten* of standard Intensity by tho following re lationship. dbg 10 log (PH/Py) P where P? the power Intensity of * sound being specified, In wstts/r ref*rer._-e intensity, 10 12 watts,/s >r dbg sound Intensity level which night be Indicated by a sound level aster The total power emanating froa a source of ares A, and level dbg la then P^A PXA * 100-1^fc;?^w*tt*. A perfectly attenuating barrier with an area Aq absorbs PjAi PAAxX io- l(llb?) wstts. That power which reaslna to be radiate! Is the difference I\A ^A PjAx Pi * 10 Mdbg)^ , j q ) wstts. The power Intensity resulting froa the redistribution of this power over the origins! area A la !\ - rx iflP*UtfI>2)(i - Ax )/A watta/a* which, when referred to the defined reference level Px Is P^/Pj, * 10`1(<lb?,(A Aa)/A dbk . 10 log (P^/Px) dbg 10 log (1 (Ax/A)) The difference between this resulting sound Intensity level db^ sod the original level dbg Is the attenuation db of equation (1) O db 4\ - dbg . 10 log (1 K) (1) vli'Tt Aj M if O mSk iHiimna r LIA18595 I. AlTiSOlX 111 Development of tqmt\ n (?) tli* developai-nt of ejuetlon 2 fol low* clo**ly tfi* po* r balance aelhod of Af;il* XI. The original aound Intenalty level ti t*It*n ti dbj tnd again rulte In t.ti MUM power of 0G P^A * watte. A perfectly attenuating terrier again eteorte portion determined ty It* srei Aj fjAj PA * 10' watt. Aeou*tle treaenlssloo loo of e terrier 1* ten tine* the loganlth* of the re'.!, of the eourc* tide power Ideality to thet quantity e-uurti on the receiver aide. x* preeled In decibel* it 1* the cunerlcel difference between the sound Intensity level*, Tt dbj - dbj The effect of finite acoustic trnvlIon lo*e cen then be obtained ty repla::.-g thet pert of the origin*! ource repreiented by ere* Ap by new i.urce equal In trr* to A^ and having a strength equal to dbj dbj TL The total power radiated by the barrier la then *3*1 m rl * watt*. By a power balance, the total radiated power la now I^A PpA - P2Ap Fy*l watta. Pj * 10* 1(llb2,(A) - Pp * 100*(db2)(A1) p1 x PO0,1^ * n,(Ap) V - pp s PO0*1*46^! - Ap * ApUff,1(TL))) watta. The power Intenalty resulting free redistribution of thin power over the original area A la % - Pp 10* 1(<,b2,(l - (Ax/A) . (A1/A)(10** 1(TL))) Beferrlng thla to the reference level P|, Vrl P00,1^4b2^(l - (Aj/Ajd - lO*0'^)) db^ 10 log (V*p) db2 10 log (1 - (Aj/A)(l - 10*01!r-))) The difference between the resulting sound Intenalty level, d^, and the orlgiral level, d&2, la the attenuation, db. db db^ dhj m 10 log (1 K (1 10-^ rlh) 12) where Ap KA PW O t ti* W" q O) jo *q -8pj Mp '(2) uoj>*rib jo *uon''to* *-o* *iox oc;[c.uj; ojqnos )jatj 8u;Airq Xq pajiAOS tj i u i wnci *if jo w*J j t usnirjM t*rt j*rn p* -Aajqst *q p t t .c a qr-iq nonf>ui -*. tfov *0(1 fttfAoqt itAjna jo Xij ; i *t{0* *2 Ji i'on *(t) op*nb* jo ucrnTO* qj 'jAjjJkq }pjjd /q p*j a c o *J c a j i io j k h jo vi4 v j{ *ucjnpoos tT{ jipCT rAcjsi. i rtnoA jrrj uc;qnu*n tou *tr JrBjoq AJno ( 'uon*nu*)if Mtcfl 't *$u < 96ser*n |M#I i*W **H vrii^vini we* ( " ------- ----- - - ^ - -- * -rr-"r -- -- Iff - - - --= *** A-j. -- -- - -- -* - - ---- Z.658IVI1