Scale model experiments on the insertion loss of wide and double barriers

Redistrib

Scale model experiments on the insertion loss of wideand double barriers

Glenn J. Wadsworth and James P. ChambersNational Center for Physical Acoustics, University of Mississippi, University, Misissippi 38677

~Received 23 February 1999; accepted for publication 11 January 2000!

The insertion loss of wide and double barriers is investigated through scale model experiments.Such configurations appear in outdoor sound propagation problems such as highway noise reductionand community noise control. The Biot–Tolstoy–Medwin~BTM! time domain wedge formulationfor multiple diffraction@J. Acoust. Soc. Am.72, 1005–1013~1982!# is used to predict the acousticresponse of an impulsive source. Evaluation of the insertion loss at discrete frequencies isaccomplished via the fast Fourier transform~FFT!. Good agreement has been found between theBTM model and experimental data for all configurations tested. ©2000 Acoustical Society ofAmerica.@S0001-4966~00!03204-5#

PACS numbers: 43.20.Fn, 43.28.Fp, 43.50.Vt@ANN#

ioinahband

ifo

enor

nbyesan

at

itneace

noeiste

naanm

e-o

unoie

ec

arkm-

ults

areyeher

ederelee.is-rein

alu-deral-timeed

dif-e-arethe

pt ofonttime

nedo asese

INTRODUCTION

The purpose of this study was to examine the diffracteffects caused by an acoustical barrier having two diffractedges. The use of barriers to reduce noise near highwrailways, factories, etc. is widespread in large cities. Tmost common measure of the acoustic performance of arier is its insertion loss, which is the difference in soupressure levels with and without the barrier. This quantityused in the present work to describe the acoustic permance of a barrier.

The insertion loss of infinitely long barriers has beextensively studied. Methods of calculating barrier perfmance have been reviewed by Iseiet al.1 and Nicolaset al.2

A thorough collection of references on the theory of soudiffraction can also be found in the more recent workSalomons.3 The majority of the above-mentioned theoriare based in the frequency domain and are utilized by mcurrent computer prediction schemes.

Alternate time domain solutions presented in the l1950’s4,5 have recently been applied in modified forms6–14 tothe wedge diffraction problem and have been validated wscale model experiments. The present work uses Medwietal.’s formulation7,14,15to calculate the insertion loss of widand double barriers in the presence of a rigid ground surf

Wide or three sided barriers were analyzed by Pierc16

but his model is not posed for multiple barriers that areconnected. Salomons3 offers a modification to the Piercmodel to handle multiple arbitrarily placed barriers but hsolution has some singularities that must be negotiaaround. The current model investigated provides an altersolution that may also be ideally suited to investigate trsient phenomena or multiple finite length wedges. Its coputational intensity, however, will probably not favor rplacement of frequency based solutions such as Salomfor many practical noise prediction routines. Typical rtimes for the wide and double barrier problems ranged tfew minutes on a 100 MHz PC while the Pierce wide barrsolution averaged a few seconds.

The extension of the Biot–Tolstoy–Medwin~BTM!model to double-edge diffraction is briefly described in S

2344 J. Acoust. Soc. Am. 107 (5), Pt. 1, May 2000 0001-4966/2000/

ution subject to ASA license or copyright; see http://acousticalsociety.org/c

ngys,er-

sr-

-

d

y

e

h

e.

t

dte--

ns

ar

.

I. The corresponding scale model experiment, using a spas the sound source, is described in Sec. II. Section III copares the theoretical predictions with experimental resand conclusions are made in Sec. IV.

I. THEORY

A. Time domain diffraction

For a point source, the geometry used by Medwin7,15 isfollowed here and is shown in Fig. 1. Source coordinatesgiven byr 0 , u0 , andz50; receiver coordinates are given br, u, andz. The wedge angle,uw , is measured from one facof the wedge through the propagating medium to the otface. For the thin plate, this angle is 2p, and such a barrier isreferred to as a knife-edge barrier.

The diffracted pressure waveform is given in closform by Medwin in Refs. 7 and 15 and is not repeated hfor brevity. The impulse formulation can provide valuabinsight into the relative contributions of each arriving pulsIn addition, ray-tracing techniques allow comparison of dtinct reflected and diffracted components. It is often modesirable, however, to quantify the diffracted sound fieldthe frequency domain. The frequency response of the evated waveform is easily obtained by digital means. In orto represent the diffracted field digitally, instantaneous vues of the pressure are calculated for discrete values ofand the frequency content of the diffracted field is obtainvia the fast Fourier transform~FFT!.

This discrete, digital representation of the pressurefracted by a barrier follows from a classical Huygen’s wavlet description of the spherical wave. Secondary sourcesdefined at interception points between the wavefront andedge. The first secondary source is located on the intercethe diffracting edge and the least time path. As the wavefrpropagates, secondary sources on both sides of the leastpath contribute to the sound field in pairs. The paths defiby the positions of the secondary sources are referred tpartial least time paths, and pulses propagating along thpaths arrive at intervals ofnDT after the first arrival. Thecomplete time domain waveform is composed ofN points

2344107(5)/2344/7/$17.00 © 2000 Acoustical Society of America

ontent/terms. Download to IP: 130.159.70.209 On: Wed, 03 Dec 2014 10:48:33

is

le

eascdte

peex

idth

-heen-rim-

en-the

gh

aleted.

in-

ngfirstctsbove.ndes;TMar-thew-

er

theus-hegear-, thersttheer-

raat

Redistrib

whose values are written asp(nDT). The desired frequencyrange governs the choice of the discrete time step,DT, andthe total duration,NDT, of the impulse response. In thwork the discrete time step was chosen to be 1ms and thetotal duration was 4.096 ms. The pressure att5t0 , wheret0

is the least time over the barrier, is written asp(0DT). In thesymmetric case where the source-receiver axis is normathe diffracting edge, individual secondary sources makcontribution of 1

2p(nDT) to the total waveform.The model used in this work assumes that all surfac

including the ground, are perfectly reflecting. Under thissumption, ray paths that include one or more ground bounare treated as having originated from an image source anterminating at an image receiver whose locations are demined by Snell’s Law. Once the images are in the prolocation, the ground is removed and the ray path simplytends from image source to edge to image receiver~see, forexample, Ref. 1!.

When a single knife-edge barrier is placed on a rigsurface, four ray paths from the source to a receiver inshadow zone are possible:~1! source-edge-receiver,~2!

FIG. 1. BTM model wedge geometry:~a! side view; ~b! top ~unfolded!view. Dashed lines indicate the least time path.

2345 J. Acoust. Soc. Am., Vol. 107, No. 5, Pt. 1, May 2000 G. J. W


toa

s,-es/orr-r-

e

source-ground-edge-receiver, ~3! source-edge-groundreceiver, and~4! source-ground-edge-ground-receiver. Tdiffracted signal for each ray path is calculated indepdently using the method described above and then supeposed.

B. Double-edge diffraction

Multiple diffraction effects are easily handled by thBTM model in the context of the classical Huygen’s Priciple. These effects must be considered when predictinginsertion losses of thick and/or multiple barriers. Althouthe wide barrier has been addressed by Medwinet al.,15

Pierce16 and Salomons,3 it is reexamined in the presence ofrigid ground surface. In addition, diffraction over doubknife-edge barriers of various separations is investigaThe three types of barriers,~1! single knife-edge,~2! wide,and ~3! double knife-edge, are compared in terms of thesertion loss which will be addressed later.

The double diffraction method treats each diffractiedge independently. Each secondary source along theedge in turn radiates a new, weaker pulse which diffraover the second edge in the same manner as discussed aAlthough similar, the calculations used for the wide adouble knife-edge barriers have a few subtle differenctherefore the two barriers are addressed separately. The Bmodel does not require that the diffracting edges of the briers be parallel, nor does it place any stipulations onrelative heights of the two edges. In this discussion, hoever, the barriers are parallel with constant separation,W,and are the same height,h. Furthermore, the source–receivaxis is normal to thez-axis, or barriers, in all cases.

Cartesian coordinates are used to conveniently givelocations of the source and receiver throughout this discsion. For both the wide and double barrier, the origin of tBTM cylindrical coordinate system depends on which edis being treated in the double diffraction method. In the Ctesian system, used only for measurement convenienceorigin, O, is placed at the point of contact between the fidiffracting edge and the ground surface. The case ofdouble knife-edge barrier is illustrated in Fig. 2. The convsion is the same for the wide barrier.

The double diffraction method is illustrated in Fig. 3 fothe wide barrier. The wide barrier is extended to formsingle right-angle wedge, and a virtual receiver is placed

r
FIG. 2. Conversion from cylindrical toCartesian coordinates for the wide odouble knife-edge barrier. The originof the Cartesian system is at pointO.
2345adsworth and J. P. Chambers: Insertion loss of wide barriers


g.

em

eue

ou-urce

frac-

ig.(s

areper-nse

pliedof

inttionn ofythen a

nofleleve

arythe

ife-

re-ide

hs,

Redistrib

coordinates (r 8,u8,0! where r 85W1r and u85uw53p/2.Using the single diffraction formulation,N values ofp(nDT)are calculated at the virtual receiver. The fractional strenof the zeroth secondary source,Sss,0 , is then determinedThis source strength is simplySss,05F0S, where

F05p~0DT!

pd,0. ~1!

The value of pd,0 gives what the pressure ‘‘would havbeen’’ at the virtual receiver had the pulse originated frothe zeroth secondary source location, and is given by

pd,05Sr

2pR0DT, ~2!

FIG. 3. Wide barrier double diffraction method.~a! Typical wide barriergeometry.~b! Placement of virtual receiver.~c! Diffraction over the secondedge from thenth secondary source.~d! The nth partial least time path, topview.



th

where R05W1r ,r is the density and S is the sourcstrength of the original point source, typically having a valof 1. The factor of 2 in the denominator of Eq.~2! replacesthe usual factor of 4 for a point source due to pressure dbling at the face of the wedge. Subsequent secondary sostrengths are calculated in pairs asSss,n5FnS, where

Fn51

2

p~nDT!

pd,n~3!

and

pd,n5Sr

2pRnDT~4!

for Rn5@(W1r )21zn2#1/2. Contributions from secondary

sources accumulate until the cutoff criteria

Fn5Sss,n

S,0.5% ~5!

is met. This cutoff criteria~also used by Medwin in Ref. 15!definesNss, the value ofn when Eq.~5! is satisfied. Oncethese secondary source strengths have been found, diftion over the second edge can be treated.

A second right-angle wedge is formed as shown in F3~c! such that each secondary source has coordinatesr 08 ,u08 , zn) wherer 085W andu0850. TheNss secondary sourceare used to calculateNss diffracted waveforms which arecombined at the appropriate delay times ofnDT to give thefinal pressure signal due to that ray path. These stepsrepeated for each of the four possible ray paths. The suposition of these four signals gives the total impulse respofor diffraction over the original wide barrier.

The same basic technique as described above is apto the double knife-edge barrier to calculate the effectsdouble diffraction. That is, the impulse response of a posource diffracted over this double barrier is the superposiof separate ray paths, each of which is the superpositioNss individual waveforms originating from secondarsources along the first diffracting edge. However, sincedouble knife-edge barrier consists of two plates rather thasolid object, several distinct differences arise.

For both diffracting edges, the wedge angle,uw , is 2prather than 3p/2. An additional ground bounce in betweethe two plates is introduced to each of the four ray pathsthe wide barrier, effectively doubling the number of possibray paths to eight. Multiple diffraction effects beyond doubdiffraction, e.g., multiple scatter between the barriers, habeen neglected.

The coordinates of the virtual receiver and secondsources depend on the path taken. Paths that includeground bounce between the two plates of the double knedge barrier use a virtual receiver at coordinates (r 8, u8, 0!where r 85@W21(2h)2#1/21r and u852p2arctan(W/2h)and secondary sources at (r 08 ,u08 ,zn) where r 085@W2

1(2h)2#1/2 andu085arctan(W/2h). Paths that do not includethe ground bounce have secondary source and virtualceiver coordinates that are the same as those of the wbarrier with the exception ofu08 , which isp/2. In using Eq.~2! and Eq.~4! to calculate the secondary source strengt



nthfo

orrieousttanfoinrunoenici

feeln

ith

di

glcmowcet.lsat

th

n

eny

s

nn

-

-

a

Redistrib

the effect of pressure doubling at the virtual receiver islonger applicable. In both expressions, the factor of 2 indenominators is replaced with the usual factor of 4spherical spreading.

The metric of interest in this work is the insertion losschange in sound pressure level with and without a barpresent. Many authors investigate diffraction effects withincorporating ground reflections in either the pre- or pobarrier data sets. Such a measurement does provide a dawith minimal structure and allows for a more conveniecomparison between diffraction models but is less idealanalyzing actual barrier effectiveness. The present workvestigates the sound pressure level present at the receivethe actual source–receiver geometry used, including grosurfaces both when the barrier is present and when it isThis normalization, with ground reflections included, is oftreferred to as the total field as opposed to the free field whrefers to the direct signal only. Including ground bouncesthe analysis provides a direct measure of a barrier’s eftiveness including the possibility of increasing sound levby removing the destructive interference of the groubounce.17 Furthermore a ‘‘2’’ sign to force the loss to be apositive quantity was not included in order to compare wMedwin’s data in the initial calculations~data not shown!.Thus a negative value for the insertion loss indicates acreased sound level and a positive value indicates ancreased sound level.

Pierce’s three sided barrier model16 was selected forcomparison to the BTM model for the wide barrier. Usinthe Pierce model, values for the insertion loss were calated every 100 Hz, while values for the insertion loss frothe BTM model are determined from a digital transformthe sound field calculated in the time domain. Figure 4 shothe insertion loss of a wide barrier on a rigid ground surfaThe agreement between these two models is excellenshould be noted, however, that while the Pierce modewell suited to predict multiple diffraction effects, it requireadjacent diffracting edges to have a common side planetherefore cannot be utilized as presented to examinedouble knife-edge barrier. A comparison to extensions of

FIG. 4. Insertion loss, normalized to the total field, of a wide barrierpredicted by the BTM~solid line! and Pierce~dashed line! models. For thisgeometry,W520 cm,xs540 cm,ys515 cm,xr570 cm,yr520 cm, andh530 cm.



oer

rt-set

tr-for

ndt.

hnc-sd

e-n-

u-

fs.It

is

ndhee

Pierce model for multiple barriers3 will be left to futurework.

II. EXPERIMENT

Experiments were conducted to determine the insertioloss of three types of barriers:~1! the single knife-edge,~2!the wide, and~3! the double knife-edge. Since one of thegoals of the work was to have an application to highwaynoise barriers, source and receiver coordinates were chosto roughly correspond to typical test configurations used bthe Federal Highway Administration.18 Barrier heights werechosen to correspond to the national mean barrier height areported by Armstrong.19 These dimensions were scaled at1:10 in order to be able to perform the experiments in awell-controlled indoor environment.

The sound source was produced by the discharge of aelectric spark which generated a transient pulse of duratiot5 100 ms. At 1.2 m, the signal-to-noise ratio was 40 dB62 dB in the range of 2 kHz to 20 kHz. Given the scalingfactor, the experiments corresponeded to a real world problem of 12 m propagation over a 3 mbarrier in the frequencyrange of 200 Hz to 2 kHz. Since the spark source was non

FIG. 5. Single knife-edge barrier insertion loss forxs559.5 cm,ys515 cm,xr560.5 cm,yr520 cm, andh531.7 cm. The solid line is the BTM modelprediction and the open circles are experimental data.

FIG. 6. Wide barrier insertion loss forW518.9 cm,xs550 cm,ys515 cm,xr570 cm,yr520 cm, andh531.7 cm. The solid line is the BTM modelprediction and the open circles are experimental data.

s



raire

eegeo

ick-sl toef-ndheerey.

ntsthese,andeldf theosi-

ndon-ightgle

rieride

dir

R,

direct

Redistrib

repeatable, a reference microphone was used to calibeach measurement. The source was found to be omnidtional within 61.7 dB in angles of650° in both the hori-zontal and vertical planes. The direct sound pressure fiwas observed to decay as 1/r and nonlinear effects wernegligible. All surfaces, with the exception of the knife-edbarriers, were constructed with smoothed, varnished wo

FIG. 7. Double knife-edge barrier insertion loss forW518.9 cm,xs550cm,ys515 cm,xr570 cm,yr520 cm, andh531.7 cm. The solid line is theBTM model prediction and the open circles are experimental data.

FIG. 8. Single knife-edge barrier~a! time domain data and~b! calculatedimpulse response forxs559.5 cm,ys515 cm,xr560.5 cm,yr520 cm, andh531.7 cm. The impulse response has been normalized such that thesignal impulse response~not present due to barrier shielding! has an ampli-tude of 1. The four arrivals are from pathsSER, SGER, SEGR, SGEGwhereS is the source,G is the ground,E is the barrier edge andR is thereceiver.



tec-

ld

d.

The knife-edge barriers were made from steel plates of thness 3 mm. The receivers were1

4 in. condenser microphonewith their diaphragms always oriented in a plane parallethe least time propagation path in order to minimize thefects of directivity. The time domain signal was captured atransformed via FFT by an HP 35665A signal analyzer. Ttime domain signals and the frequency transforms wtransferred to a PC for analysis and comparison to theor

III. RESULTS AND COMPARISONS

The insertion loss data from the series of experimewere compared to the BTM predicted insertion loss forthree types of barriers investigated in this work. In each cathe receivers were in the shadow zones of the barriersthe diffracted sound field was normalized to the sound fifor the same source–receiver geometry in the absence obarriers. Several configurations of source and receiver ptions relative to the barrier were tested.20 Figures 5–7 showinsertion loss curves for the single knife-edge, wide adouble knife-edge barriers, respectively, for one such cfiguration. Each barrier was 31.7 cm high; the source hewas 15 cm and the receiver height was 20 cm. For the sinknife-edge barrier, the source was 59.5 cm from the barand the receiver was 60.5 cm from the barrier. For the wand double knife-edge barriers, from Fig. 2,xs550 cm, ys

ect

FIG. 9. Wide barrier~a! time domain data and~b! calculated impulse re-sponse forW518.9 cm,xs550 cm,ys515 cm,xr570 cm,yr520 cm, andh531.7 cm. The impulse response has been normalized such that thesignal impulse response~not present due to barrier shielding! has an ampli-tude of 1. The four arrivals are from pathsSE1E2R, SGE1E2R, SE1E2GR,SGE1E2GR, whereS is the source,G is the ground,E1 is the first barrieredge,E2 is the second barrier edge andR is the receiver.



sdohaine.caanthth

edor

,ithd

ineb

thtwteo

ip

theataaynot

ey

ar-

umford-edofeing

mtwogli-thendge

3–5is

med.

d-

ers

ure-e of

ithdif-

ses

u

Redistrib

570 cm, andW518.9 cm. The solid lines in the figurerepresent the BTM predicted insertion losses, and therepresent the average of five firings of the spark for tconfiguration. The three prominent peaks in each of thesertion loss curves indicate the removal of the destructivinterfering bounce path from the preinsertion sound field

Figures 8–10 show the time domain data traces andculated impulse responses for the knife-edge, widedouble knife-edge barriers respectively. Figure 11 showsacoustic signal with no barrier present which is used asreference signal. The acoustic data have been presentunits of pressure~Pa!. The impulse response has been nmalized such that the direct signal impulse response~notpresent due to barrier shielding! has an amplitude of 1. Thusthe free field signal from the spark could be convolved wthe impulse response presented to reproduce the barrieracquired~figure not shown!.

The first four dominant arrivals are clearly identifiablethe data as the model impulse response aligns with theperimental data. Some late acoustic arrivals are evidentanalysis indicated that they were weak reflections fromspark support system which can be seen in Fig. 11 whereweak signals follow the dominant direct and ground reflecsignals. While these signals could have been windowedof the reference signal they are embedded in the mult

FIG. 10. Double knife-edge barrier~a! time domain data and~b! calculatedimpulse response forW518.9 cm,xs550 cm, ys515 cm,xr570 cm, yr

520 cm, andh531.7 cm. The impulse response has been normalized sthat the direct signal impulse response~not present due to barrier shielding!has an amplitude of 1. The eight arrivals are from pathsSE1E2R,SGE1E2R, SE1E2GR, SGE1E2GR, SE1GE2R, SGE1GE2R,SE1GE2GR, SGE1GE2GR, whereS is the source,G is the ground,E1 isthe first barrier edge,E2 is the second barrier edge andR is the receiver.



tst-

ly

l-deein

-

ata

x-uteo

dutle

diffraction data and were consequently retained as part ofreference signal. For the double knife-edge barrier dshown in Fig. 10, the last four arrivals, corresponding to rpaths that include a ground bounce between barriers, areat all discernible in the data. Later calculations in which thwere removed~data not shown! indicated that they had anegligible influence on the insertion loss. For shallower briers or wider separations this observation may not hold.

IV. CONCLUSIONS

Excellent agreement is found in the audible spectrbetween the BTM predictions and the experimental dataall three types of barriers included in this study. These finings should provide a good benchmark for the continudevelopment of frequency domain or empirical modelsmultiple diffraction which may be incorporated into noisprediction models. The model is also capable of analyztransient phenomena and finite length barriers.

An interesting observation is that the contributions frothe ray paths containing the ground bounce between theplates of the double knife-edge barrier appear to be negible for the geometry examined. This can be seen fromsimilarities between the insertion losses of the wide adouble knife-edge barriers. However, the double knife-edbarrier is seen to reduce the sound level by an additionaldB over a wide barrier of the same dimensions, whichattributed to the change in wall angle from 3p/2 to 2p. Thisobservation could lead to improvements in computation tiby discarding negligible contributions to the diffracted fiel

ACKNOWLEDGMENT

This work was supported by the Federal Highway Aministration~FHWA!.

1T. Isei, T. F. W. Embleton, and J. E. Piercy, ‘‘Noise reduction by barrion finite impedance ground,’’ J. Acoust. Soc. Am.67, 46–58~1980!.

2J. Nicolas, T. F. W. Embleton, and J. E. Piercy, ‘‘Precise model measments versus theoretical prediction of barrier insertion loss in presencthe ground,’’ J. Acoust. Soc. Am.73, 44–54~1983!.

3E. M. Salomons, ‘‘Sound propagation in complex outdoor situations wa non-refracting atmosphere: model based on analytical solutions forfraction and reflection,’’ Acustica83, 436–454~1997!.

4F. Oberhettinger, ‘‘On the diffraction and reflection of waves and pulby wedges and corners,’’ J. Res. Natl. Bur. Stand.61, 343–365~1958!.

ch

FIG. 11. Time domain data without a barrier present forxs559.5 cm,ys

515 cm,xr560.5 cm, andyr520 cm.



eJ.

an

.

th

by

oo

in

iv

nsble

y

ble

ri-

und

ll

ide

Redistrib

5M. A. Biot and I. Tolstoy, ‘‘Formulation of wave propagation in infinitmedia by normal coordinates with an Application to diffraction,’’Acoust. Soc. Am.29, 381–391~1957!.

6R. Raspet, J. Ezell, and S. Coggeshall, ‘‘Diffraction of an explosive trsient,’’ J. Acoust. Soc. Am.79, 1326–1334~1986!.

7H. Medwin, ‘‘Shadowing by finite noise barriers,’’ J. Acoust. Soc. Am69, 1060–1064~1981!.

8J. P. Chambers and Y. H. Berthelot, ‘‘Time-domain experiments ondiffraction of sound by a step discontinuity,’’ J. Acoust. Soc. Am.96,1887–1892~1994!.

9A. I. Papadopoulos and C. G. Don, ‘‘A study of barrier attenuationusing acoustic impulses,’’ J. Acoust. Soc. Am.90, 1011–1018~1991!.

10D. Chu, ‘‘Impulse response of density contrast wedge using normal cdinates,’’ J. Acoust. Soc. Am.86, 1883–1896~1989!.

11D. Chu, ‘‘Exact solution for a density contrast shallow-water wedge usnormal coordinates,’’ J. Acoust. Soc. Am.87, 2442–2450~1990!.

12S. Li and C. S. Clay, ‘‘Sound transmission experiments from an impulssource near rigid wedges,’’ J. Acoust. Soc. Am.84, 2135–2143~1988!.



-

e

r-

g

e

13S. Li, D. Chu, and C. S. Clay, ‘‘Time domain reflections and diffractiofrom facet-wedge constructions: Acoustic experiments including doudiffractions,’’ J. Acoust. Soc. Am.96, 3715–3720~1994!.

14H. Medwin and C. S. Clay,Fundamentals of Acoustical Oceanograph~Academic, New York, 1997!, p. 712.

15H. Medwin, E. Childs, and G. M. Jebsen, ‘‘Impulse studies of doudiffraction: A discrete Huygens interpretation,’’ J. Acoust. Soc. Am.72,1005–1013~1982!.

16A. D. Pierce, ‘‘Diffraction of sound around corners and over wide barers,’’ J. Acoust. Soc. Am.55, 941–955~1974!.

17H. G. Jonasson, ‘‘Sound reduction by barriers on the ground,’’ J. SoVib. 22, 113–126~1972!.

18C. Menge, C. Rossano, G. Anderson, and C. Bajdek,FHWA Traffic NoiseModel Version 1.0 Technical Manual~1995!, p. 24.

19R. Armstrong, ‘‘Highway traffic noise barrier construction trends,’’ WaJournal26, 12–19~1996!.

20G. J. Wadsworth, ‘‘Scale model experiments on the insertion loss of wand double barriers,’’ M.S. Thesis, University of Mississippi~1998!.



Documents

Scale model experiments on the insertion loss of wide and double barriers