ACOUSTIC BARRIERS: PERFORMANCE AND EXPERIMENTAL MEASUREMENTS

Transcription

1 ACOUSTIC BARRIERS: PERFORMANCE AND EXPERIMENTAL MEASUREMENTS PACS:.5.Gf G. Alfaro Dgan. Univrsity Roma TRE, Dpt. of Mchanical and Industrial Enginring 79, Via dlla Vasca Naval. Roma. Italia Tl.: Fax : alfdg@hotmail.com ABSTRACT Aim of this work is propos an nginring mthod for calculating th attnuation of sound during propagation outdoor, taking into a particular attntion th attnuation du to barrirs. Th papr outlins th main faturs and th acoustic prformanc of th barrir. INTRODUCTION Th quivalnt continuous downwind octav band sound prssur lvl at a rcivr location shall b calculatd taking into account th sound powr lvl of th sourc, th dirctivity corrction, and th octav bands corrction that occurs during propagation from th point sound sourc to th rcivr. Th most important attnuation trms ar th gomtrical attnuation, atmosphric absorption, ground attnuation ffcts and obviously th prsnc of barrirs and othr miscllanous ffcts (as vgtation or trs). Th forcasting proposd mthod taks into account thos trms laborating a complt procdur.. Barrir s Charactristics W dfin an objct as a scrning obstacl (that mans barrir), if it mts th following charactristics: -Surfac dnsity is at last kg/m -Th objct has a clos surfac without cracks or gaps. -Th horizontal dimnsion of th objct (barrir) normal to th sourc-rcivr lin is largr than th acoustic wavlngth λ at th nominal midband frquncy for th octav band of intrst. In particular, w will study that kind of objct that fulfils ths rquirmnt and w will rprsnt it as a vrtical dg barrir, th top of which is a straight lin that may b sloping. Taking into account th attnuation du to a barrir w will vn considr th rflction, transmission, absorption and obviously th diffraction trms.

2 . OUTDOOR SOUND PROPAGATION Th rfrnc usd to dtrmin th attnuation of sound during propagation outdoors is providd by norm ISO 9 - (99). Th basic quation utilizd in this modl is: L ( f) = L ( f) + D ( f) A( f) [] P W I whr: Lp: th quivalnt continuous downwind octav-band sound prssur lvl at a rcivr location, calculatd for ach point sourc. Lw : th octav-band sound powr lvl, in dcibls, producd by th point sound sourc rlativ to a rfrnc sound powr of on picowatt (pw). D I :dirctivity indx, in dcibls, that dscribs th xtnt by which th quivalnt continuous sound prssur lvl from th point sound sourc dviats in a spcific dirction from th lvl of an omnidirctional point sound sourc producing sound powr lvl Lw. A : th octav -band attnuation, in dcibls, that occurs during propagation from th point sound sourc to th rcivr. Th attnuation trm in quation [], is givn by quation []: A= A + A + A + A + A [] div atm gr bar misc whr: A div : is th attnuation du to gomtrical divrgnc A atm : is th attnuation du to atmosphric absorption A gr : is th attnuation du to ground ffct A bar : is th attnuation du to a barrir A misc : is th attnuation du to miscllanous othr ffcts.. Attnuation du to gomtrical divrgnc and ground ffct. Th attnuation du to gomtrical divrgnc from two distanc points markd d is calculatd by this quation: * d A div,gr = log + 8 [] d whr: d : is th distanc from th sourc and th rcivr in mtrs d : is th rfrnc distanc (d = mtr) Th trm + 8 taks into account th propagation for sphrical sprading in th fr fild ovr rflcting soil from a point sound sourc (this approximation applis to a quarry of ornamntal rocks). Th ISO Standard, suggsts th us of trm + bcaus it indicats a point sound sourc in a fr fild, and introducs a mthod for calculating th ground ffcts sparatly.. Attnuation du to atmosphric absorption. Sound nrgy is dissipatd in th air by viscous losss and molcular rlaxational procss, it dpnds on air molcular composition, mtorogical conditions and sound frquncy. Th first of ths phnomna is du to th friction btwn air molculs rsulting in hat gnration; it dpnds on tmpratur and frquncy. Th rlaxational procss dpnds on momntary nrgy absorption by air molculs that causs thir vibration and rotation. It is th function of tmpratur, rlativ humidity and frquncy. This mchanism is codifid in ANSI Standard S-:995 and ISO 9-; for a standard prssur of on atmosphr, th attnuation du to atmosphric absorption, in dcibls, is calculatd with this quation (par. 7. ISO 9-

3 d Aatm = α [] whr: d : is th propagation distanc, in mtrs, from sound sourc and rcivrs α : is th atmosphric attnuation cofficint, in dcibl pr mtr, for ach octav band at th midband frquncy and on atmosphr. It is givn by th following xprssion: / 5/ T T.75.8 α = 8,89 f T T F f F F f F 9./ T 5/ T ro, + / ro, rn, + / rn, [5] Th function (5) is a function of two rlaxation frquncis, F r,o and F r,n, which ar rspctivly th oxygn and nitrogn rlaxation frquncis; thir valus in hrtz shall b calculatd from F ro,.+ h = +. h.9 + h and / / T.7 ( T/ T ) FrN, = 9+ 8h T [] T : ambint atmosphric tmpratur, in Klvin T : rfrnc air tmpratur: T = 9,5 K h : molar concntration of watr vapour (%).. Rflction Rflctions ar considrd in trms of imag sourc. Ths rflctions ar from outdoor cilings and vrtical surfacs, such as rock walls which can incras th sound prssur lvl at th rcivr. Onc th gomtry of th sit is known, w idntify th imag sound sourc and its charactristics (sound powr lvls and dirctivity), thus applying th algorithm without considring th ground ffct on obtains: L ( f) = L ( f) + D ( f) A( f) [7] P W I. Th Huygns-Frsnl Principl Th attnuation du th barrir will b studid using th classical approach to th diffraction problm. According to th Huygns construction vry point of a wav-front may b considrd as a cntr of a scondary disturbanc which givs ris to a sphrical wavlts, and th wav-front at any latr instant may b rgardd as th nvlop of ths wavlts. Lt S b th instantanous position of a sphrical monochromatic wav-front of radius r which procds from a point sourc P and lt P b a point at which th disturbanc is to b dtrmind. It is possibl to obtain for th lmntary contribution du(p) du to th lmnt ds at Q th xprssion: du A r ikr s iks ( P) K( χ ) ds = [8] whr s=qp and K(χ) is an inclination factor which dscribs th variation with dirction of th amplitud of th scondary wavs. Hnc th total disturbanc at P is givn by U A r ikr s ( P) = K ( χ )ds S iks [9]

4 Th basic ida of th Huygns-Frsnl thory was put in a mathmatical basis by Kirchhoff who considrd first a strictly monochromatic scalar wav: iωt V ( x, y, z) = U ( x, y, z) in vacuum th spac dpndnt part thn satisfis th tim-indpndnt wav quation (Hlmotz Equation): ( + k ) U = whr k is th wav numbr k=ω/c. Lt now V b a volum boundd by a closd surfac S, and lt P b any point within it; w assum that U posssss continuous first and scond ordr partial drivativs within and on th surfac. If U is any othr function that satisfis th sam continuity rquirmnts as U, w hav th Grn s thorm: U' U ( U U' U ' U) dv = ( U U' ) ds v S [] n n whr dnots diffrntiation along th inward normal to S. n Aftr som approximation and applying th thory to a straight dg barrir, w obt ain: whr ν = H + λ a b = log C( ν ) + S( ) [.] ν Att [], is proportional to th Frsnl numbr Solving with numrical mthod th Frsnl s intgrals on can obtain th attnuation du to a smifinit barrir. Th Frsnl intgrals ar calculatd using th Nwton intgral mthod that is a simpl numrical solution. According to Makawa s thory [5] it is possibl to add togthr mor attnuation (i.. ground attnuation), paying attntion that w ar now looking for an xprssion for th attnuation du to diffraction trough a window whras Makawa spok about diffraction ovr a smi-infinit barrir. According vn to th Babint s [] principl, w obtain th total attnuation lik a sum of contributions du to th four attnuation trms of ach window dg. C(v) S(v) Figur. Makawa attnuation graphic mthod (lft) and Frsnl s intgrals C(v) and S(v) (right) Figur shows th wll-known Makawa graphic which allows calculating th attnuation trm du to a barrir only using th Frsnl numbr that is a simpl function of th wavlngth.

5 By applying th Kirchhoff diffraction thory which mbodis th basic ida of th Huyghns thory to a smi-infinit barrir th sound attnuation by scrns, aftr som approximation is givn by a formula that dpnds on th Frsnl s intgrals and th v paramtr, function of th H numbr oftn calld ffctiv hight. Th figur blow (figur ) shows th valus assumd by th attnuation trm dpnding on th point of obsrvation lis in an illuminatd rgion (v<) or in th gomtrical shadow zon (v>). Attnuazion v Figur. Attnuation in function of th v paramtr. MEASUREMENTS AN EXPERIMENTS W mad two sts of masurmnts; at th bgin w usd a continuous signal. Th sourc is a known sound rproducd by a digital compact disc with a pink nois, and th figur shows th spctral charactrization. Th sound lvl mtr usd is a Larson & Davis 8. 9 db 85 sound prssur lvl (sourc) - TH Spctrum - Lq - Linar 9 Hz 8. db Hz K K K 8K K Figur : Sourc charactrization In figur it is shown how th forcasting mthod works. Going from lft to right you can s th acoustics fild for th frquncy of,5 hz, 5 hz, hz and hz.

6 5,5 Hz 5 5 Hz Hz 5 Hz Figur : Diffraction of sound around th barrir. A First conclusion Th comparison btwn th forcasts and th masurmnts shows good rsults at th mdium frquncis. Low frquncis suffr from th havy prsnc of th nois floor, in particular w may say that: - hz: th nois floor causs mistaks mainly bcaus th low frquncy sounds propagation is not obstructd by th barrir and by atmosphric attnuation. -5hz: good rsults, th masurd and th forcast valus ar quit clos. -hz: rsults ar good till valus about 7 db. Going lowr nois floor (ambint nois) bcoms th main caus of nois. In ordr to ras ths mistaks w introducd nw masurmnts using impulsiv signals and two diffrnt analyzrs: th first (L&D 8) is situatd nar th sound sourc, th scond dscribs a rticular grid ( masurmnts) ovr th barrir (L&D 9).

7 db 9 8 impulsiv masurmnts - Tim History - Liv (A Fast) impulsiv masurmnts - Tim History - Lq (A) - Running Lq Sc. 8. db 9. db dcibl 7 5 s 8 tim Figur 5. Th impulsiv signal usd in th scond masurmnt. Rpating th calculus and, abov all, introducing a nw fictitious sourc givn by th nois floor as masurd bfor th impulsiv signal, w obtain nw valus quit closr to th masurmnts thn th prvious ons. That bcaus th nois floor is quit prpondrant, as said bfor, at th low bands. CONCLUSION In th prsnt papr an asy mthod in forcasting th sound barrir charactristics was prsntd. Good rsults wr found for th middl-high bands frquncy vn without considring th nois floor. Anyway w could forss that bhaviour, bing th Kirchhoff s thory good for high frquncy. Nvrthlss good rsults was found vn at low frquncy whn w addd a fictitious nois sourc that taks into account th nois floor. Comparison btwn forcast and masurmnts in this scond st of xprimnts shows a diffrnc not highr thn db(a). REFERENCES. ISO 99-:98 Acoustics - Dscription and masurmnt of nvironmntal nois - Part : Basic quantitis and procdurs. ISO 9-:99: Acoustics - Attnuation of sound during propagation outdoors - Gnral mthod of calculation.. ISO 9-:99 Acoustics-Attnuation of sound during propagation outdoors- Part : Calculation of th absorption of sound by th atmosphr.. M. Born and E. Wolf, principls of optics, Prgamon, Oxford, Z. Makawa, Nois rduction by scrns, Kob, Japan, 98.. U.J. Kurz, Nois rduction by barrirs, J. Acoust. Soc. Am. 97, Frankfurt, Grmany, A.D. Pirc, Diffraction of sound around cornrs and ovr wid barrirs, Acoustics and Vibration Laboratory, Massachustts Institut of tchnology, Cambrig, U.S.A., J.B. Kllr, Gomtrical Thory of Diffraction, Journal of th Optical Socity of Amrica, Nw York Univrsity, U.S.A K.D. Milnz, Computation of Frsnl Intgrals. II, Journal of Rsarch of th National Institut of Standards and Tchnology. Volum 5 Numbr July August.. U.J. Kurz, G.A. Andrson, Sound attnuation by barrirs, Appl. Acoust., 5-5, (97).