Experimental verification of the acoustic performance of diffusive roadside noise barriers

Applied Acoustics 68 (2007) 1357–1372

www.elsevier.com/locate/apacoust

Experimental verification of the acousticperformance of diffusive roadside noise barriers

Claudio Cianfrini, Massimo Corcione *, Lucia Fontana

Dipartimento di Fisica Tecnica, University of Rome ‘‘La Sapienza’’, via Eudossiana, 18, 00184 Rome, Italy

Received 24 March 2006; received in revised form 26 July 2006; accepted 26 July 2006Available online 20 October 2006

Abstract

The acoustic performance of pairs of diffusive roadside barriers is tested experimentally on a 1:10scale model, and compared to that of more traditional specularly reflecting barriers. Significantattenuation benefits are detected not only in the shadow zone behind the barriers, but also in theunprotected zone immediately above the barriers, thus proving that diffusive traffic faces of the bar-riers may effectively help in counteracting multiple reflection effects. In addition, a radiosity-basedtheoretical model developed for the evaluation of the sound field behind pairs of diffusive noise bar-riers is described, and its ability to predict the extra SPL attenuation deriving from the replacementof geometrically reflecting barriers with diffusely reflecting barriers is verified.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Traffic noise barriers; Diffusive sound reflection; Experimental analysis; Theoretical/computer model

1. Introduction

In recent years road traffic has rapidly increased, particularly in towns and even more inlarge conurbations, thus representing, without any doubt, one of the most widespreadsource of noise nuisance.

Reduction in noise exposure may be effectively achieved by the erection of an acousticbarrier which prevents traffic noise reaching the receivers located inside the shadow zone

0003-682X/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.apacoust.2006.07.018

* Corresponding author. Tel.: +39 06 44 58 54 43; fax: +39 06 48 80 120.E-mail address: [email protected] (M. Corcione).

mailto:[email protected]

1358 C. Cianfrini et al. / Applied Acoustics 68 (2007) 1357–1372

by the direct path. In case of residential and other developed areas located on both sidesof heavily trafficked roadways, pairs of parallel traffic noise barriers are usually erected,but the multiple reflections occurring between the barriers may result in a significantdegradation in the single barrier screening performance [1–3]. In this framework, theimprovement of the acoustic efficiency of roadside barriers has been the subject of manystudies, both theoretical and experimental, in which new types of barriers have been pro-posed [4–24].

With respect to traditional roadside barriers, new noise barriers are essentially basedon two basic principles. The first principle involves the application of sound absorbingmaterials to the traffic face of the barriers. The second principle involves the adoptionof new barrier shapes which substantially imply the modification of the diffracting-edgeof the barrier, i.e., T-shaped barriers, Y-shaped barriers, arrow-shaped barriers, tubu-lar-capped barriers, barriers crowned with phase-interference devices, barriers with qua-dratic residue diffuser tops, and multiple-edge barriers. In both cases more or lesssignificant noise abatements in the shadow zone behind the barriers are reported. Evenmore interesting results may be achieved by coupling the two principles, as demon-strated by the high performance obtainable through the installation of soft T-shapedbarriers.

Actually, whenever pairs of barriers are erected at both sides of a roadway, a third prin-ciple may help in further counteracting multiple reflection effects. Such principle involvesthe use of acoustically rough traffic faces of the barriers, rather than acoustically smoothfaces, i.e., traffic faces with a surface roughness between 0.05 m and 0.2 m, so as to obtaina diffusive rather than a geometrical reflection of the incident sound in the main frequencyrange of the traffic noise spectrum. In fact, owing to the spreading in all directions of thereflected noise, non-negligible abatements with respect to pairs of geometrically reflectingbarriers may be achieved, as discussed in details in a first theoretical paper, in which weintroduced also a radiosity-based method for the study of the acoustic performance ofpairs of diffusive roadside barriers [25]. Indeed, some studies on the effects of the multiplereflections which occur between diffusely reflecting boundary surfaces flanking a roadwayare available in the open literature [26–30]. However, as the subject of such papers is thesound field in street canyons, their attention is focused only on what happens between thereflecting surfaces, rather than behind them.

In the present paper, after resuming briefly the basic outlines of the aforementioned the-oretical/computer model, an experimental verification of its predictions is presented, andthe main aspects of the results obtained are discussed.

2. Theoretical model

An infinite-length straight roadway sided by flat ground, is considered. Freely flowingtraffic is simulated by an infinite incoherent line source placed in the middle of the road ata given height over the road pavement. Atmospheric effects, in terms of wind speed anddirection, velocity gradients and temperature stratification, as well as the effects ofreflected noise scattering by both vehicles and associated air turbulence, are neglected.Air absorption may be assumed equal to 0.008 dB/m [17]. The road pavement and the sur-rounding ground are assumed to be perfectly smooth and acoustically hard, which impliesgeometrical reflection. In contrast, both specularly and diffusely reflecting traffic faces ofthe noise barriers are considered.

C. Cianfrini et al. / Applied Acoustics 68 (2007) 1357–1372 1359

2.1. Acoustic field in the absence of barriers

In the absence of noise barriers, the sound field at any location is calculated as thesuperimposition of the direct and the reflected sound waves, by neglecting any wave effectoccurring at the roadway/ground boundary line. Since the road and the adjacent groundare assumed to be smooth, the contribution of the reflected wave is taken into account bythe replacement of the surface of the road and the ground by a line source image, as shownin Fig. 1.

Under the hypothesis of incoherent sound emission and sound propagation throughfree progressive waves, the sound field at any receiver location P is calculated by thesum of the sound intensities relevant to each transmission path to the receiver:

IP ¼W2p

1

d� 1

10ad=10þ r

d 0� 1

10ad 0=10

� �ð1Þ

with

r ¼ rR for a P b

r ¼ rG for a < bð2Þ

where IP is the sound intensity at the receiver location; W is the sound power emitted bythe line source; a is the atmospheric absorption in dB/m; rR and rG are the coefficients ofreflection of the roadway and the surrounding ground, respectively; d and d 0 are the pathlengths of the direct and the reflected waves, respectively; a and b are the angles betweenthe road line and the straight lines which join the virtual line source S 0 to the receiver andto the roadway/ground boundary line, respectively.

2.2. Acoustic field with a pair of specularly reflecting barriers

When two parallel, specularly reflecting noise barriers with coefficient of reflection rB

are erected at both sides of the roadway, multiple reflections occur and, according tothe multiple image method, the sound field at any location behind the nearside barrierderives from the contributions of an infinite number of line sources, as shown in Fig. 2.If the sound transmission through the nearside barrier is assumed as negligible comparedwith the diffraction over the barrier, the contribution of any line source (both real andimages) to the total sound field is calculated by summing the sound intensities relevantto the four diffracted paths reported in Fig. 3:

S

S'

P

Fig. 1. Sound paths in the absence of barriers.

S(1)S(2)S(3)

Preal sourcevirtual sourcevirtual source

Fig. 2. Image sources modelling of a pair of specularly reflecting barriers.

S

S'

P

P'

1,2

3,4

1,3

2,4

Fig. 3. Diffracted sound paths.


IP ¼W2p

X1n¼1

rn�1B

1

dðnÞAð1; nÞ þrG

d 0ðnÞAð2; nÞ þrR

d 0ðnÞAð3; nÞ þrRrG

dðnÞ Að4; nÞ� �

ð3Þ

with

Aðk; nÞ ¼ 1

10½ILðk;nÞþaDðk;nÞ�=10ð4Þ

where d(n) and d 0(n) are the lengths of the straight lines which join the receiver to the nthline source S(n) and its image S 0(n) reflected by the road, respectively; IL(k, n) is the barrierinsertion loss relevant to the kth diffracted path (k = 1, 2, 3, 4) from the nth line source tothe receiver; D(k, n) is the length of the kth diffracted path from the nth line source to thereceiver.

Under the assumption of thin-walled barrier, IL(k, n) may be calculated in terms of theFresnel number N(k, n), as widely reported in the literature (see, e.g., [31]):

Nðk; nÞ ¼ 2

kdðk; nÞ ð5Þ

ILðk; nÞ ¼ 15 log

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2pNðk; nÞ

ptanh

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2pNðk; nÞ

p þ 5 dB for Nðk; nÞ > 0 ð6Þ

ILðk; nÞ ¼ 5 dB for Nðk; nÞ ¼ 0 ð7Þ

ILðk; nÞ ¼ 20 log

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2pjNðk; nÞj

ptan

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2pjNðk; nÞj

p þ 5 dB for � 0:2 < Nðk; nÞ < 0 ð8Þ

ILðk; nÞ ¼ 0 dB for Nðk; nÞ 6 �0:2 ð9Þ

where k is the wavelength and d(k, n) is the difference between the diffracted and the directpath lengths:

dðk; nÞ ¼ Dðk; nÞ � dðnÞ for k ¼ 1; 4 ð10Þdðk; nÞ ¼ Dðk; nÞ � d 0ðnÞ for k ¼ 2; 3 ð11Þ


Since IL(k, n) = 0 dB means that the wave relevant to the kth sound path reaches the re-ceiver location directly, without intervening any diffraction effect at the top edge of thenearside barrier, in such case Eq. (4) must be calculated by the replacement of D(k, n) withthe length of the straight line which joins the nth line source S(n) or its image S 0(n) to thereceiver.

Currently, the calculation of the summation in Eq. (3) may be stopped at a large butfinite number of source images beyond which any further contribution is less than a pre-scribed per-cent value of the previous total, i.e., 10�3. A typical number of source imagesrequired to achieve such result with a pair of barriers with coefficient of absorption ofabout 0.1 is of the order of one thousand.

2.3. Acoustic field with a pair of diffusive barriers

When two diffusive barriers with coefficient of reflection rB are erected at both sides ofthe roadway, their acoustic behaviour is modelled by assuming that the sound powerreflected by any infinitesimal element of each barrier is radiated according to a directionaldistribution which follows the Lambert’s cosine law, whichever is the direction of the inci-dent sound power. As is well-known, diffusive sound reflection may be obtained throughwells/protrusions or surface roughness of the same order of the wavelengths of the inci-dent sound.

The total sound field at any receiver location derives from the contributions of the traf-fic line primary source and the secondary sound sources represented by the infinitesimalsurface elements of the farside barrier.

The calculation of the sound power emerging from each surface element is carried outthrough a procedure derived from a theoretical/computer model developed for the studyof non-uniform sound fields inside spaces bounded by diffusive surfaces [32], appropriatelymodified in order to take into account the geometrical reflection occurring at the roadpavement [25], whose basic outlines are briefly recalled below.

Once the road surface is replaced by a virtual line source and a pair of virtual barriers,mirror-images of the real ones, as shown in Fig. 4, the sound power dWout(i) radiated bythe ith infinitesimal surface element of the farside barrier is calculated as the sum of theincident sound power due to irradiation by the traffic line source S and by its image S 0,

S

S'

P

P'

1,2

3,4

1,3

2,4

1,2

3,4

dh(i)

dh(i')

Fig. 4. Diffracted sound paths for a pair of diffusive barriers.


and the incident sound power which, due to multiple reflections, emerges by any jth infin-itesimal surface element of the nearside barrier B and by any j 0th mirror-image element ofthe virtual nearside barrier B 0, multiplied by the coefficient of reflection of the barrier:

dW outðiÞ ¼ rB½W dF S�dhðiÞ þ rRW dF S0�dhðiÞ�

þ rB

ZB

dW outðjÞdF dhðjÞ�dhðiÞ þZ

B0dW outðj0ÞdF dhðj0Þ�dhðiÞ

� �ð12Þ

with

dW outðj0Þ ¼ rR dW outðjÞ ð13Þwhere dFS�dh(i) (or dF S0�dhðiÞ) is the view factor between the line source S (or the line sourceimage S 0) and the ith element of the farside barrier, and dFdh(j)�dh(i) (or dFdh(j0)�dh(i)) is theview factor between the jth element (or the j 0th element image) of the nearside barrier B (orthe nearside barrier image B 0) and the ith element of the farside barrier. The view factorFA�B between two generic surfaces A and B, either finite or infinitesimal, is defined asWA–B/WA, i.e., the fraction of the power emerging from A directly intercepted by B. Sameconcept applies to view factor FS–B between a line source S and a surface B. Full details onview factors and on the methods for their calculation may be found in textbooks on radi-ative heat transfer (see, e.g., [33]).

For each sound source, either primary or secondary, the four diffracted paths shown inFig. 3 must be considered, thus obtaining:

IP ¼W2p

1

dAð1Þ þ rG

d 0Að2Þ þ rR

d 0Að3Þ þ rRrG

dAð4Þ

� �þZ

BdW uðiÞAð1; iÞ

þ rG

ZB

dW uðiÞAð2; iÞ þ rR

ZB

dW uðiÞAð3; iÞ þ rRrG

ZB

dW uðiÞAð4; iÞ ð14Þ

where dWu(i) is the sound power radiated by the ith surface element of the farside barrieralong the direction of the top edge of the nearside barrier, which forms an angle u(i) withthe normal to the surface element. According to the Lambert’s cosine law for 2D geome-try, the following expression holds:

dW uðiÞ ¼dW outðiÞ

2cos uðiÞ ð15Þ

As concerns A(k) and A(k, i) of Eq. (14), which are relevant to the kth diffracted path fromthe primary line source to the receiver, and to the kth diffracted path from the ith second-ary infinitesimal surface source to the receiver, respectively, their value may be directly de-rived from Eq. (4) by the replacement of indexes (k, n) with (k) and (k, i), respectively.

However, since the solution of Eq. (12) is considerably difficult due to the fact that theunknown dependent variable appears inside an integral, in practice it is convenient tobreak up the barrier continuous surface into a finite number M of sub-surfaces (viz., strips,in 2D geometry), over each of which the incident sound power may be assumed as uni-form. This corresponds to split the integral equations (12) and (14) in two different systemsof M discretized equations. As concerns the evaluation of the finite view factors, thecrossed-string method for 2D geometry, developed for the solution of radiant heat transferproblems, may be used [33]. Of course, if the surrounding ground is perfectly absorbing,the model remains valid provided that the 2nd and 4th diffracted sound paths are erased,


which means that rG = 0 must be replaced in the above equations. Moreover, for receiverslocated relatively close to the roadway, atmospheric absorption may be neglected, whichcorresponds to assume a = 0 in Eqs. (1) and (4).

3. Experimental set-up

The experimental set-up consisted basically of: (1) a 1:10 scale model of a roadway 10 mwide flanked by two noise barriers 3 m high; (2) the electronic equipment necessary to sim-ulate a line of freely flowing traffic; and (3) the instrumentation for the measurement of thesound pressure level (SPL) at several receiving points. In particular, the use of a 1:10 scalefor the roadway model implied that the test frequencies were 10 times those typical for thetraffic noise.

The experiments were performed in a 3.5 m · 3 m · 2.5 m test chamber whose bound-ary walls were covered with wedge-shaped absorbing material 100 mm thick, so as toreproduce the free-field situation, at least for the high frequencies.

The roadway was made of flat wooden chipboard panels 25 mm thick, whose surfacewas subjected to a fine smoothing treatment in order to obtain a geometrical reflectionof the incident sound waves. The barriers were made of flat wooden chipboard panels18 mm thick. As for the roadway, one side of such panels was finely smoothed, for geo-metrical reflection behaviour. The reverse side of the barriers was covered by a layer ofcrushed stones distributed at random with sizes in the range between 5 mm and 15 mm,which correspond to a diffusive reflection of the incident sound in the frequency rangebetween nearly 8 kHz and more than 16 kHz. The diffracting edge of the barriers consistedof a removable hardwood list with a triangular section. The length of the entire test sec-tion, i.e., of the roadway model, was 2.8 m. Two specularly reflecting float glasses 20 mmthick with reflection coefficient of nearly unity in the experimental bandwidth weremounted at both ends of the model, perpendicular to the roadway and the barriers, soas to reproduce an infinite-length configuration.

The coefficient of absorption of the roadway and the barriers were obtained from one-third octave band measurements of the decrease in reverberation time inside a reverberantroom, which for both types of panels gave values of 0.15 ± 0.05 for frequencies between8 kHz and 20 kHz.

The traffic line source was simulated by 14 independent sound sources, each of whichconsisted of: (1) a handmade generator of pink noise; (2) a hi-fi power amplifier; and(3) a pair of tweeters Philips type CT140 with a diameter of about 30 mm, each one facingone of the two barriers. The fourteen pairs of loudspeakers were aligned in the middle ofthe road at a 20 cm distance from each other, facing the noise barriers with a 15� tiltingangle, embedded in a trapezoidal mounting assembly, which may somehow resemble a lineof vehicles.

The spectrum of the signal produced by the handmade pink noise generators is reportedin Fig. 5, while a schematic of a normal hemi-section of the experimental set-up, as well asa 3D view of one of the two ends of the model, are depicted in Figs. 6 and 7, respectively.

The surrounding ground was represented by the floor of the test chamber, which sim-ulated an absorbing ground.

A Bruel & Kjaer precision sound level meter model 2231 equipped with a 1/400 micro-phone model 4939 was used as receiver system.

-50

-40

-30

-20

-10

0

-60102 103 104

spec

trum

(dB

)

frequency (Hz)

Fig. 5. Spectrum of the signal produced by the pink noise generators.

25

18

barr

ier

chip

boar

d pa

nel

280

20

roadway chipboard panel

500

tweeter diffuser

traffic line assembly

crushed stone layer

15˚

hardwood list

4040

30

sym

met

ry m

idpl

ane

Fig. 6. Schematic of a normal hemi-section of the experimental set-up (dimensions are in mm).


4. Measurements

4.1. Acoustic performance of the test chamber

In order to verify what free-field accuracy within the experimental bandwidth could beexpected inside the test chamber, measurements of reverberation time were conducted.

A Bruel & Kjaer white noise generator model 1405 was used as exciting source, whosesignal was fed via a power amplifier LEM model PPA702 to a tweeter Audax typeTWXAMT8. Reverberation time was measured for one-third octave band at differentlocations, 10 times at any location so as to calculate an average thereof, thus derivingthe local value of the coefficient of absorption ac of the test chamber. The contributionof the reverberant sound field at the several measurement points was then calculated interms of sound energy density ratio:

float glass roadway

roadside barrier

traffic line

Fig. 7. Schematic 3D view of one of the two ends of the model.


DR

Dtot

¼ ð4=RÞðQ=4pr2Þ þ ð4=RÞ ð16Þ

with

R ¼ Sac

1� ac

ð17Þ

where DR is the sound energy density of the reverberant sound field at a given point, Dtot isthe total sound energy density at same location, S is the area of the boundary surface ofthe test chamber, r is the distance of the measurement point from the sound source, and Q

is the directivity factor of the loudspeaker, whose polar distributions had been previouslydefined through one-third octave band measurements performed inside an anechoic room.

According to the results obtained, the contribution of reverberation in the experimentalbandwidth was at most the 4.9% of the total sound field, which occurred at 8 kHz in ameasurement point located close to one of the boundary walls of the chamber. Moreover,at 10 kHz, which, taking into account the 1:10 scale of the roadway model, corresponds tothe 1 kHz peak frequency in the A-weighted spectrum of typical highway traffic noise, themaximum per-cent contribution of the reverberant field decreased to 3.4%, thus provingthat the assumption of free-field is well applicable.

4.2. Setting of the traffic line source

The approximation of a 2D, infinite-length roadway required that the sound emissionsof the 14 pairs of loudspeakers, which the traffic line consisted of, were the same. For thisreason, the bottom-open casing depicted in Fig. 8 was built by hardwood panels 15 mm

400200

250

calibrated hole

Fig. 8. Sketch of the bottom-open casing used for the line source setting (dimensions are in mm).


thick. Its dimensions were 40 cm · 20 cm · 25 cm, and its interior was covered withabsorbing material 20 mm thick. The two frontwalls were profiled so as to match perfectlythe mounting assembly of the traffic line source. A calibrated hole of the same diameter ofthe 1/400 microphone Bruel & Kjaer model 4939, was drilled at the centre of the top end-wall. Before any experimental session were started, the casing was placed across any pairof loudspeakers, and the volume of the respective hi-fi amplifier was regulated to obtain aprescribed value of SPL. The same casing was used also to carry out tests of temporal sta-bility of the sound sources through continuous measurements of SPL, which remainedconstant with a margin of error of ±0.1 dB across time intervals of the order of 2 h.

4.3. Acoustic performance of the roadside barriers

One-third octave band measurements of SPL at a wide number of locations were exe-cuted in the absence of barriers (SPL0), with the barrier panels mounted with the specu-larly reflecting face opposite the traffic (SPLspec), and with the barrier panels reversedsuch that the diffusive face was facing the traffic line (SPLdiff).

Measurement points were located in the midplane normal to the roadway and the bar-riers, and arranged according to two different grids: (a) a Cartesian grid, whose pointswere located 20 cm apart along the horizontal coordinate x, and 10 cm apart along thevertical coordinate y, as sketched in Fig. 9; and (b) a cylindrical polar grid, whose pointswere located 20 cm apart along the radial coordinate r, and 5� apart along the angularcoordinate h, as sketched in Fig. 10.

The tolerances of the microphone positioning were ±2 mm and ±0.5�, for the linearand the angular displacements, respectively.

At any measurement location the attenuations due to the erection of specularly and dif-fusely reflecting barriers, Aspec = (SPL0 � SPLspec) and Adiff = (SPL0 � SPLdiff), as well astheir difference, i.e., the so-called extra attenuation, EA = Adiff � Aspec = SPLspec � SPLdiff,were calculated.

traffic line source

0.2 m

5˚

0.3 m

1.0 m 0.2 m

0--

Fig. 10. Cylindrical polar grid of measurement points.

traffic line source

0.2 m

0.1 m

0.3 m

1.0 m 0.2 m

Fig. 9. Cartesian grid of measurement points.


5. Experimental results and discussion

Typical distributions of the extra attenuation EA vs. the angular position of the receiv-ing point h in the range between 0� and 90�, at frequencies 5 kHz, 10 kHz, 12.5 kHz, and16 kHz, are reported in Figs. 11–13, for distances of the receiver from the traffic line sourcer = 0.7 m, r = 0.9 m, and r = 1.1 m, respectively.

It may be seen that values of the extra attenuation within the range 0–5 dB wereobtained at receiving points located in the shadow zone behind the barriers, viz., at anangular coordinate h up to little more than 30�.

Non-negligible values of the extra attenuation were also detected at receiving pointslocated in the unscreened zone immediately above the barriers, viz., at an angular

angular coordinate (degrees)40

+ 1

extr

a at

tenu

atio

n E

A (

dB)

-3

-2

-1

30100 20

r = 0.7 m

0

+ 4

+ 6

+ 5

+ 2

+ 3

80706050 90

10.0 kHz

16.0 kHz

12.5 kHz

5.0 kHz

Fig. 11. Distributions of extra attenuation EA vs. h at r = 0.7 m.

5.0 kH z

angular coordinate (degrees)

+3

+2

+5

+4

-1

-2

+1

extr

a at

tenu

atio

n E

A (

dB)

r = 0.9 m

0

12.5 kHz

16.0 kHz

10.0 kHz

+6

4030100 20 80706050 90



coordinate h in the range between 30–35� and nearly 55�. Of course, such significant valuesfor EA were achieved only for those frequencies at which the reflection of sound waves bythe stone layer covering the traffic side of the barriers was actually diffusive, i.e., above8 kHz, the larger was the sound frequency, the higher was the extra attenuation. In con-trast, negative values of the extra attenuation were observed at receiving points located inthe unscreened zone well above the barriers, viz., for angular coordinates h > 55�.

The results obtained may be explained by taking into due account the spreading in alldirections of the sound reflected by the diffusive barriers. In fact, owing to such spreading,a smaller amount of sound energy reaches the top of the barriers and is diffracted behindthem in the shadow zone. As a consequence, on account of the energy conservation law, anincreased amount of sound energy is re-directed towards the unscreened zone. On the

0

+1

extr

a at

tenu

atio

n E

A (

dB)

-3

-2

0

-1

+5

+3

+2

+4

+6

angular coordinate (degrees)40302010

r = 1.1 m

90806050 70

5.0 kH z

12.5 kH z

10.0 kH z

16.0 kH z



other hand, as the specularly reflecting roadway pavement acts as a concentrator mirror,such re-directed sound energy is radiated mostly towards the top, rather than the sides, ofthe unscreened zone.

Furthermore, it is worth noticing that the values of the extra attenuation increase withincreasing the distance from the sound source. In fact, as already found theoretically in[25], Adiff tends to keep constant, while Aspec tends to decrease with increasing the distancefrom the roadway, which obviously leads to increases in EA.

Many more details on the comparative performance of pairs of specularly and diffuselyreflecting roadside barriers are available in Ref. [25].

6. Theoretical analysis and comparison with experimental data

The model previously described was used to perform a theoretical study of the soundfield in the shadow zone behind pairs of both specularly and diffusely reflecting trafficnoise barriers, for the same geometry and sound absorption characteristics of the experi-mental test section. Theoretical values of the extra attenuation were then calculated at awide variety of locations, in order to assess what accuracy could be expected in evaluatingthe performance of pairs of diffusive barriers relative to that of more traditional specularlyreflecting barriers.

The comparison between theoretical and experimental values of EA at frequencies5 kHz, 10 kHz, 12.5 kHz, and 16 kHz, reported in Fig. 14, shows that the computer modeldeveloped is able to predict the relative acoustic performance of pairs of diffusive noisebarriers with error ranges of ±1.5 dB, ±1.0 dB, and ±0.5 dB, with levels of confidenceof 100%, 87%, and 68%, respectively.

Discrepancies between theoretical and experimental data may be ascribed to the factthat the assumptions of: (a) totally diffusive reflection at the barrier surface, i.e., accordingto the Lambert’s cosine law; (b) thin-walled barriers; and (c) two-dimensional cylindricalsound emission by the traffic line, do not apply perfectly well to the experimental arrange-ment. In addition, the theoretical model developed does not take into account any wave

3

theo

retic

al v

alue

s of

EA

(dB

)th

eore

tical

val

ues

of E

A (

dB)

theo

retic

al v

alue

s of

EA

(dB

)th

eore

tical

val

ues

of E

A (

dB)

experimental values of EA (dB) experimental values of EA (dB)

1

00 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8

2

f = 10.0 kHz8

6

4

5

7

3

1

0

0 1 2 3 4 5 6 7 80 1 2 3 4 5 6 7 80

2

8

6

4

5

7

f = 12.5 kHz

3

experimental values of EA (dB)

1

0

2

f = 16.0 kHz8

6

4

5

7

3

experimental values of EA (dB)

1

2

8

6

4

5

7

f = 20.0 kHz

Fig. 14. Comparison between theoretical and experimental values of EA.


effect occurring at the intersections between the barriers and the roadway, as well as anyscattering effect produced by vehicles, which, in contrast, is somehow reproduced in exper-iments owing to the presence of the tweeters’ mounting assembly in the middle of the road.Finally, the assumption of geometrical reflection may be not well approximated at the low-est sound frequencies investigated.

7. Conclusions

An experimental study on the performance of pairs of parallel diffusive roadside barri-ers relative to that of more traditional specularly reflecting barriers, was conducted on a1:10 scale model.

According to the results obtained, significant values of the extra SPL attenuation maybe achieved in the shadow zone behind the barriers, as well as in the unscreened areaimmediately above the barriers, which proves that the use of diffusive barriers may repre-sent an effective help in counteracting multiple reflection effects. In addition, the extraattenuation increases with increasing the distance from the roadway.

Finally, the acoustic performance of pairs of diffusive noise barriers relative to geomet-rically reflecting barriers may be well evaluated through the theoretical computer modelproposed and discussed.


References

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Documents

Experimental verification of the acoustic performance of diffusive roadside noise barriers