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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 acoustic performance 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 2006 Available online 20 October 2006
Abstract The acoustic performance of pairs of diffusive roadside barriers is tested experimentally on a 1:10 scale model, and compared to that of more traditional specularly reflecting barriers. Significant attenuation benefits are detected not only in the shadow zone behind the barriers, but also in the unprotected zone immediately above the barriers, thus proving that diffusive traffic faces of the barriers may effectively help in counteracting multiple reflection effects. In addition, a radiosity-based theoretical model developed for the evaluation of the sound field behind pairs of diffusive noise barriers is described, and its ability to predict the extra SPL attenuation deriving from the replacement of 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 in large conurbations, thus representing, without any doubt, one of the most widespread source of noise nuisance. Reduction in noise exposure may be effectively achieved by the erection of an acoustic barrier which prevents traffic noise reaching the receivers located inside the shadow zone
*
Corresponding author. Tel.: +39 06 44 58 54 43; fax: +39 06 48 80 120. E-mail address: [email protected] (M. Corcione).
0003-682X/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2006.07.018
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by the direct path. In case of residential and other developed areas located on both sides of heavily trafficked roadways, pairs of parallel traffic noise barriers are usually erected, but the multiple reflections occurring between the barriers may result in a significant degradation in the single barrier screening performance [1–3]. In this framework, the improvement of the acoustic efficiency of roadside barriers has been the subject of many studies, both theoretical and experimental, in which new types of barriers have been proposed [4–24]. With respect to traditional roadside barriers, new noise barriers are essentially based on two basic principles. The first principle involves the application of sound absorbing materials to the traffic face of the barriers. The second principle involves the adoption of new barrier shapes which substantially imply the modification of the diffracting-edge of the barrier, i.e., T-shaped barriers, Y-shaped barriers, arrow-shaped barriers, tubular-capped barriers, barriers crowned with phase-interference devices, barriers with quadratic residue diffuser tops, and multiple-edge barriers. In both cases more or less significant noise abatements in the shadow zone behind the barriers are reported. Even more interesting results may be achieved by coupling the two principles, as demonstrated by the high performance obtainable through the installation of soft T-shaped barriers. Actually, whenever pairs of barriers are erected at both sides of a roadway, a third principle may help in further counteracting multiple reflection effects. Such principle involves the use of acoustically rough traffic faces of the barriers, rather than acoustically smooth faces, i.e., traffic faces with a surface roughness between 0.05 m and 0.2 m, so as to obtain a diffusive rather than a geometrical reflection of the incident sound in the main frequency range of the traffic noise spectrum. In fact, owing to the spreading in all directions of the reflected noise, non-negligible abatements with respect to pairs of geometrically reflecting barriers may be achieved, as discussed in details in a first theoretical paper, in which we introduced also a radiosity-based method for the study of the acoustic performance of pairs of diffusive roadside barriers [25]. Indeed, some studies on the effects of the multiple reflections which occur between diffusely reflecting boundary surfaces flanking a roadway are available in the open literature [26–30]. However, as the subject of such papers is the sound field in street canyons, their attention is focused only on what happens between the reflecting surfaces, rather than behind them. In the present paper, after resuming briefly the basic outlines of the aforementioned theoretical/computer model, an experimental verification of its predictions is presented, and the main aspects of the results obtained are discussed. 2. Theoretical model An infinite-length straight roadway sided by flat ground, is considered. Freely flowing traffic is simulated by an infinite incoherent line source placed in the middle of the road at a given height over the road pavement. Atmospheric effects, in terms of wind speed and direction, velocity gradients and temperature stratification, as well as the effects of reflected 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 surrounding ground are assumed to be perfectly smooth and acoustically hard, which implies geometrical reflection. In contrast, both specularly and diffusely reflecting traffic faces of the noise barriers are considered.
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2.1. Acoustic field in the absence of barriers In the absence of noise barriers, the sound field at any location is calculated as the superimposition of the direct and the reflected sound waves, by neglecting any wave effect occurring at the roadway/ground boundary line. Since the road and the adjacent ground are assumed to be smooth, the contribution of the reflected wave is taken into account by the replacement of the surface of the road and the ground by a line source image, as shown in Fig. 1. Under the hypothesis of incoherent sound emission and sound propagation through free progressive waves, the sound field at any receiver location P is calculated by the sum of the sound intensities relevant to each transmission path to the receiver: W 1 1 r 1 IP ¼ þ ð1Þ 0 2p d 10ad=10 d 0 10ad =10 with r ¼ rR r ¼ rG
for a P b for a < b
ð2Þ
where IP is the sound intensity at the receiver location; W is the sound power emitted by the line source; a is the atmospheric absorption in dB/m; rR and rG are the coefficients of reflection of the roadway and the surrounding ground, respectively; d and d 0 are the path lengths of the direct and the reflected waves, respectively; a and b are the angles between the road line and the straight lines which join the virtual line source S 0 to the receiver and to 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 to the multiple image method, the sound field at any location behind the nearside barrier derives 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 compared with the diffraction over the barrier, the contribution of any line source (both real and images) to the total sound field is calculated by summing the sound intensities relevant to the four diffracted paths reported in Fig. 3:
P S
S' Fig. 1. Sound paths in the absence of barriers.
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virtual source
virtual source
S(3)
P
real source
S(2)
S(1)
Fig. 2. Image sources modelling of a pair of specularly reflecting barriers.
1,3 1,2 2,4
P
3,4
S
S'
P'
Fig. 3. Diffracted sound paths.
IP ¼
W 2p
1 X
rBn1
n¼1
1 rG rR rR r G Að1; nÞ þ 0 Að2; nÞ þ 0 Að3; nÞ þ Að4; nÞ dðnÞ d ðnÞ d ðnÞ dðnÞ
ð3Þ
with Aðk; nÞ ¼
1 10
ð4Þ
½ILðk;nÞþaDðk;nÞ=10
where d(n) and d 0 (n) are the lengths of the straight lines which join the receiver to the nth line source S(n) and its image S 0 (n) reflected by the road, respectively; IL(k, n) is the barrier insertion loss relevant to the kth diffracted path (k = 1, 2, 3, 4) from the nth line source to the receiver; D(k, n) is the length of the kth diffracted path from the nth line source to the receiver. Under the assumption of thin-walled barrier, IL(k, n) may be calculated in terms of the Fresnel number N(k, n), as widely reported in the literature (see, e.g., [31]): 2 N ðk; nÞ ¼ dðk; nÞ k pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2pN ðk; nÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 5 dB ILðk; nÞ ¼ 15 log tanh 2pN ðk; nÞ for N ðk; nÞ ¼ 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2pjN ðk; nÞj pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 5 dB ILðk; nÞ ¼ 20 log tan 2pjN ðk; nÞj
ð5Þ for N ðk; nÞ > 0
ILðk; nÞ ¼ 5 dB
ILðk; nÞ ¼ 0 dB
for N ðk; nÞ 6 0:2
ð6Þ ð7Þ
for 0:2 < N ðk; nÞ < 0
ð8Þ ð9Þ
where k is the wavelength and d(k, n) is the difference between the diffracted and the direct path lengths: dðk; nÞ ¼ Dðk; nÞ dðnÞ 0
dðk; nÞ ¼ Dðk; nÞ d ðnÞ
for k ¼ 1; 4
ð10Þ
for k ¼ 2; 3
ð11Þ
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Since IL(k, n) = 0 dB means that the wave relevant to the kth sound path reaches the receiver location directly, without intervening any diffraction effect at the top edge of the nearside barrier, in such case Eq. (4) must be calculated by the replacement of D(k, n) with the length of the straight line which joins the nth line source S(n) or its image S 0 (n) to the receiver. Currently, the calculation of the summation in Eq. (3) may be stopped at a large but finite number of source images beyond which any further contribution is less than a prescribed per-cent value of the previous total, i.e., 103. A typical number of source images required to achieve such result with a pair of barriers with coefficient of absorption of about 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 of the roadway, their acoustic behaviour is modelled by assuming that the sound power reflected by any infinitesimal element of each barrier is radiated according to a directional distribution which follows the Lambert’s cosine law, whichever is the direction of the incident sound power. As is well-known, diffusive sound reflection may be obtained through wells/protrusions or surface roughness of the same order of the wavelengths of the incident sound. The total sound field at any receiver location derives from the contributions of the traffic line primary source and the secondary sound sources represented by the infinitesimal surface elements of the farside barrier. The calculation of the sound power emerging from each surface element is carried out through a procedure derived from a theoretical/computer model developed for the study of non-uniform sound fields inside spaces bounded by diffusive surfaces [32], appropriately modified in order to take into account the geometrical reflection occurring at the road pavement [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 by the ith infinitesimal surface element of the farside barrier is calculated as the sum of the incident sound power due to irradiation by the traffic line source S and by its image S 0 ,
1,2
dh(i)
1,3 1,2 3,4
2,4
S
S'
P
3,4
P'
dh(i')
Fig. 4. Diffracted sound paths for a pair of diffusive barriers.
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and the incident sound power which, due to multiple reflections, emerges by any jth infinitesimal surface element of the nearside barrier B and by any j 0 th mirror-image element of the virtual nearside barrier B 0 , multiplied by the coefficient of reflection of the barrier: dW out ðiÞ ¼ rB ½W dF SdhðiÞ þ rR W dF S0 dhðiÞ Z Z dW out ðjÞ dF dhðjÞdhðiÞ þ dW out ðj0 Þ dF dhðj0 ÞdhðiÞ þ rB
ð12Þ
B0
B
with dW out ðj0 Þ ¼ rR dW out ðjÞ
ð13Þ
where dFSdh(i) (or dF S0 dhðiÞ ) is the view factor between the line source S (or the line source image S 0 ) and the ith element of the farside barrier, and dFdh(j)dh(i) (or dFdh(j )dh(i)) is the view factor between the jth element (or the j 0 th element image) of the nearside barrier B (or the nearside barrier image B 0 ) and the ith element of the farside barrier. The view factor FAB between two generic surfaces A and B, either finite or infinitesimal, is defined as WA–B/WA, i.e., the fraction of the power emerging from A directly intercepted by B. Same concept applies to view factor FS–B between a line source S and a surface B. Full details on view factors and on the methods for their calculation may be found in textbooks on radiative heat transfer (see, e.g., [33]). For each sound source, either primary or secondary, the four diffracted paths shown in Fig. 3 must be considered, thus obtaining: Z W 1 rG rR rR rG Að1Þ þ 0 Að2Þ þ 0 Að3Þ þ IP ¼ Að4Þ þ dW u ðiÞAð1; iÞ 2p d d d d B Z Z Z þ rG dW u ðiÞAð2; iÞ þ rR dW u ðiÞAð3; iÞ þ rR rG dW u ðiÞAð4; iÞ ð14Þ 0
B
B
B
where dWu(i) is the sound power radiated by the ith surface element of the farside barrier along the direction of the top edge of the nearside barrier, which forms an angle u(i) with the normal to the surface element. According to the Lambert’s cosine law for 2D geometry, the following expression holds: dW u ðiÞ ¼
dW out ðiÞ cos uðiÞ 2
ð15Þ
As concerns A(k) and A(k, i) of Eq. (14), which are relevant to the kth diffracted path from the primary line source to the receiver, and to the kth diffracted path from the ith secondary infinitesimal surface source to the receiver, respectively, their value may be directly derived 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 the unknown dependent variable appears inside an integral, in practice it is convenient to break 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 uniform. This corresponds to split the integral equations (12) and (14) in two different systems of M discretized equations. As concerns the evaluation of the finite view factors, the crossed-string method for 2D geometry, developed for the solution of radiant heat transfer problems, 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,
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which means that rG = 0 must be replaced in the above equations. Moreover, for receivers located relatively close to the roadway, atmospheric absorption may be neglected, which corresponds 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 m wide flanked by two noise barriers 3 m high; (2) the electronic equipment necessary to simulate a line of freely flowing traffic; and (3) the instrumentation for the measurement of the sound pressure level (SPL) at several receiving points. In particular, the use of a 1:10 scale for the roadway model implied that the test frequencies were 10 times those typical for the traffic noise. The experiments were performed in a 3.5 m · 3 m · 2.5 m test chamber whose boundary walls were covered with wedge-shaped absorbing material 100 mm thick, so as to reproduce the free-field situation, at least for the high frequencies. The roadway was made of flat wooden chipboard panels 25 mm thick, whose surface was subjected to a fine smoothing treatment in order to obtain a geometrical reflection of the incident sound waves. The barriers were made of flat wooden chipboard panels 18 mm thick. As for the roadway, one side of such panels was finely smoothed, for geometrical reflection behaviour. The reverse side of the barriers was covered by a layer of crushed 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 range between nearly 8 kHz and more than 16 kHz. The diffracting edge of the barriers consisted of a removable hardwood list with a triangular section. The length of the entire test section, i.e., of the roadway model, was 2.8 m. Two specularly reflecting float glasses 20 mm thick with reflection coefficient of nearly unity in the experimental bandwidth were mounted at both ends of the model, perpendicular to the roadway and the barriers, so as to reproduce an infinite-length configuration. The coefficient of absorption of the roadway and the barriers were obtained from onethird octave band measurements of the decrease in reverberation time inside a reverberant room, which for both types of panels gave values of 0.15 ± 0.05 for frequencies between 8 kHz and 20 kHz. The traffic line source was simulated by 14 independent sound sources, each of which consisted 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 facing one of the two barriers. The fourteen pairs of loudspeakers were aligned in the middle of the road at a 20 cm distance from each other, facing the noise barriers with a 15 tilting angle, embedded in a trapezoidal mounting assembly, which may somehow resemble a line of vehicles. The spectrum of the signal produced by the handmade pink noise generators is reported in Fig. 5, while a schematic of a normal hemi-section of the experimental set-up, as well as a 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 simulated an absorbing ground. A Bruel & Kjaer precision sound level meter model 2231 equipped with a 1/400 microphone model 4939 was used as receiver system.
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spectrum (dB)
-10 -20 -30 -40 -50 -60 10 2
10 3
10 4
frequency (Hz)
symmetry midplane
20
Fig. 5. Spectrum of the signal produced by the pink noise generators.
hardwood list
barrier chipboard panel
30 traffic line assembly
15˚
25
roadway chipboard panel
40
tweeter diffuser 40
280
crushed stone layer
18
500
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 be expected inside the test chamber, measurements of reverberation time were conducted. A Bruel & Kjaer white noise generator model 1405 was used as exciting source, whose signal was fed via a power amplifier LEM model PPA702 to a tweeter Audax type TWXAMT8. Reverberation time was measured for one-third octave band at different locations, 10 times at any location so as to calculate an average thereof, thus deriving the local value of the coefficient of absorption ac of the test chamber. The contribution of the reverberant sound field at the several measurement points was then calculated in terms of sound energy density ratio:
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roadside barrier traffic line float glass
roadway
Fig. 7. Schematic 3D view of one of the two ends of the model.
DR ð4=RÞ ¼ Dtot ðQ=4pr2 Þ þ ð4=RÞ
ð16Þ
with R¼S
ac 1 ac
ð17Þ
where DR is the sound energy density of the reverberant sound field at a given point, Dtot is the total sound energy density at same location, S is the area of the boundary surface of the 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 previously defined through one-third octave band measurements performed inside an anechoic room. According to the results obtained, the contribution of reverberation in the experimental bandwidth was at most the 4.9% of the total sound field, which occurred at 8 kHz in a measurement 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 to the 1 kHz peak frequency in the A-weighted spectrum of typical highway traffic noise, the maximum per-cent contribution of the reverberant field decreased to 3.4%, thus proving that 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 emissions of the 14 pairs of loudspeakers, which the traffic line consisted of, were the same. For this reason, the bottom-open casing depicted in Fig. 8 was built by hardwood panels 15 mm
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250
calibrated hole
200 400 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 with absorbing material 20 mm thick. The two frontwalls were profiled so as to match perfectly the mounting assembly of the traffic line source. A calibrated hole of the same diameter of the 1/400 microphone Bruel & Kjaer model 4939, was drilled at the centre of the top endwall. Before any experimental session were started, the casing was placed across any pair of loudspeakers, and the volume of the respective hi-fi amplifier was regulated to obtain a prescribed value of SPL. The same casing was used also to carry out tests of temporal stability of the sound sources through continuous measurements of SPL, which remained constant 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 executed in the absence of barriers (SPL0), with the barrier panels mounted with the specularly reflecting face opposite the traffic (SPLspec), and with the barrier panels reversed such that the diffusive face was facing the traffic line (SPLdiff). Measurement points were located in the midplane normal to the roadway and the barriers, and arranged according to two different grids: (a) a Cartesian grid, whose points were located 20 cm apart along the horizontal coordinate x, and 10 cm apart along the vertical coordinate y, as sketched in Fig. 9; and (b) a cylindrical polar grid, whose points were located 20 cm apart along the radial coordinate r, and 5 apart along the angular coordinate h, as sketched in Fig. 10. The tolerances of the microphone positioning were ±2 mm and ±0.5, for the linear and the angular displacements, respectively. At any measurement location the attenuations due to the erection of specularly and diffusely reflecting barriers, Aspec = (SPL0 SPLspec) and Adiff = (SPL0 SPLdiff), as well as their difference, i.e., the so-called extra attenuation, EA = Adiff Aspec = SPLspec SPLdiff, were calculated.
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0.3 m
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traffic line source 0.1 m 1.0 m
0.2 m
0 .2 m
Fig. 9. Cartesian grid of measurement points.
0.3 m
traffic line source
1.0 m
0--
5˚ 0 .2 m
0.2 m
Fig. 10. Cylindrical polar grid of measurement points.
5. Experimental results and discussion Typical distributions of the extra attenuation EA vs. the angular position of the receiving point h in the range between 0 and 90, at frequencies 5 kHz, 10 kHz, 12.5 kHz, and 16 kHz, are reported in Figs. 11–13, for distances of the receiver from the traffic line source r = 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 were obtained at receiving points located in the shadow zone behind the barriers, viz., at an angular coordinate h up to little more than 30. Non-negligible values of the extra attenuation were also detected at receiving points located in the unscreened zone immediately above the barriers, viz., at an angular
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5.0 kHz
+5
extra attenuation EA (dB)
10.0 kHz +4
12.5 kHz
+3
16.0 kHz
+2 +1 0 -1 -2
r = 0.7 m
-3 0
10
20
30
40
50
60
70
80
90
angular coordinate (degrees) Fig. 11. Distributions of extra attenuation EA vs. h at r = 0.7 m.
+6
5.0 kH z
+5
extra attenuation EA (dB)
10.0 kHz +4
12.5 kHz
+3
16.0 kHz
+2 +1 0 -1 -2
r = 0.9 m 0
10
20
30
40
50
60
70
80
90
angular coordinate (degrees) Fig. 12. Distributions of extra attenuation EA vs. h at r = 0.9 m.
coordinate h in the range between 30–35 and nearly 55. Of course, such significant values for EA were achieved only for those frequencies at which the reflection of sound waves by the stone layer covering the traffic side of the barriers was actually diffusive, i.e., above 8 kHz, the larger was the sound frequency, the higher was the extra attenuation. In contrast, negative values of the extra attenuation were observed at receiving points located in the 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 all directions 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 behind them in the shadow zone. As a consequence, on account of the energy conservation law, an increased amount of sound energy is re-directed towards the unscreened zone. On the
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+6
5.0 kH z
+5
extra attenuation EA (dB)
10.0 kH z +4
12.5 kH z
+3
16.0 kH z
+2 +1 0 -1 -2
r = 1.1 m
-3 0
10
20
30
40
50
60
70
80
90
angular coordinate (degrees) Fig. 13. Distributions of extra attenuation EA vs. h at r = 1.1 m.
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, of the unscreened zone. Furthermore, it is worth noticing that the values of the extra attenuation increase with increasing 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 distance from the roadway, which obviously leads to increases in EA. Many more details on the comparative performance of pairs of specularly and diffusely reflecting 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 sound field in the shadow zone behind pairs of both specularly and diffusely reflecting traffic noise barriers, for the same geometry and sound absorption characteristics of the experimental test section. Theoretical values of the extra attenuation were then calculated at a wide variety of locations, in order to assess what accuracy could be expected in evaluating the performance of pairs of diffusive barriers relative to that of more traditional specularly reflecting barriers. The comparison between theoretical and experimental values of EA at frequencies 5 kHz, 10 kHz, 12.5 kHz, and 16 kHz, reported in Fig. 14, shows that the computer model developed is able to predict the relative acoustic performance of pairs of diffusive noise barriers with error ranges of ±1.5 dB, ±1.0 dB, and ±0.5 dB, with levels of confidence of 100%, 87%, and 68%, respectively. Discrepancies between theoretical and experimental data may be ascribed to the fact that the assumptions of: (a) totally diffusive reflection at the barrier surface, i.e., according to the Lambert’s cosine law; (b) thin-walled barriers; and (c) two-dimensional cylindrical sound emission by the traffic line, do not apply perfectly well to the experimental arrangement. In addition, the theoretical model developed does not take into account any wave
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f = 10.0 kHz
theoretical values of EA (dB)
theoretical values of EA (dB)
8 7 6 5 4 3 2 1 0
0
1
2
3
4
5
6
7
6 5 4 3 2 1 0
8
f = 12.5 kHz
7
0
experimental values of EA (dB) 8
f = 16.0 kHz
7 6 5 4 3 2 1 0 0
1
2
3
4
5
6
experimental values of EA (dB)
3
4
5
6
7
8
8
f = 20.0 kHz
7 6 5 4 3 2 1 0
7
2
experimental values of EA (dB)
theoretical values of EA (dB)
theoretical values of EA (dB)
8
1
0
1
2
3
4
5
6
7
8
experimental values of EA (dB)
Fig. 14. Comparison between theoretical and experimental values of EA.
effect occurring at the intersections between the barriers and the roadway, as well as any scattering effect produced by vehicles, which, in contrast, is somehow reproduced in experiments 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 lowest sound frequencies investigated. 7. Conclusions An experimental study on the performance of pairs of parallel diffusive roadside barriers relative to that of more traditional specularly reflecting barriers, was conducted on a 1:10 scale model. According to the results obtained, significant values of the extra SPL attenuation may be achieved in the shadow zone behind the barriers, as well as in the unscreened area immediately above the barriers, which proves that the use of diffusive barriers may represent an effective help in counteracting multiple reflection effects. In addition, the extra attenuation increases with increasing the distance from the roadway. Finally, the acoustic performance of pairs of diffusive noise barriers relative to geometrically reflecting barriers may be well evaluated through the theoretical computer model proposed and discussed.
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References [1] Bowlby W, Cohn LF. Insertion loss degradation for parallel traffic noise barriers. In: Proc. internoise ’94, Honolulu, USA. [2] Slutsky S, Bertoni HL. Analysis and programs for assessment of absorptive and tilted parallel barriers. Transportation Research Record, vol. 1176. Washington (DC): National Research Council; 1988. [3] Watts GR. Acoustic performance of a parallel traffic noise barriers. Appl Acoust 1996;47:95–119. [4] Fujiwara K, Ando Y, Maekawa Z. Noise control by barriers – Part 2. Noise reduction by an absorptive barrier. Appl Acoust 1977;10:167–79. [5] May DN, Osman MN. Highway noise barriers: new shapes. J Sound Vibr 1980;71:73–101. [6] Iida K, Kondoh Y, Okado Y. Research on a device for reducing noise. Transportation Research Record, vol. 983. Washington (DC): National Research Council; 1984. [7] Mizuno K, Sekiguchi H, Iida K. Research on a noise control device-first report, fundamental principles of the device. Jpn Soc Mech Eng 1984;27:1499–505. [8] Mizuno K, Sekiguchi H, Iida K. Research on a noise control device-second report, fundamental design of the device. Jpn Soc Mech Eng 1985;28:2737–43. [9] Hayek SI. Mathematical modelling of absorbent highway noise barriers. Appl Acoust 1990;31:77–100. [10] Fujiwara K, Furuta N. Sound shielding efficiency of a barrier with a cylinder at the edge. Noise Control Eng J 1991;37:5–11. [11] Hothersall DC, Crombie DH, Chandler-Wilde SN. The performance of T-profile and assorted noise barriers. Appl Acoust 1991;32:269–87. [12] Watts GR. Acoustic performance of new designs of traffic noise barriers. In: Proc. noise ’93, St. Petersburg, Russia. [13] Watts GR, Crombie DH, Hothersall DC. Acoustic performance of new designs of traffic noise barriers: full scale tests. J Sound Vibr 1994;177:289–305. [14] Crombie DH, Hothersall DC, Chandler-Wilde SN. Multiple-edge noise barriers. Appl Acoust 1995;44:353–67. [15] Fujiwara K, Ohkubu T, Omoto A. A note on the noise shielding efficiency of a barrier with absorbing obstacle at the edge. In: Proc. internoise ’95, Newport Beach, USA. [16] Yamamoto K, Shono Y, Ochiai H, Yoshihiro H. Measurements of noise reduction by absorptive devices mounted at the top of highway noise barriers. In: Proc. internoise ’95, Newport Beach, USA. [17] Watts GR. Acoustic performance of a multiple edge noise barrier profile at motorway sites. Appl Acoust 1996;42:47–66. [18] Shima H, Watanabe T, Mizuno K, Iida K, Matsumoto K, Nakasaki K. Noise reduction of a multiple edge noise barrier. In: Proc. internoise ’96, Liverpool, UK. [19] Fujiwara K, Hothersall DC, Kim C. Noise barriers with reactive surfaces. Appl Acoust 1998;53:255–72. [20] Okubo T, Fujiwara K. Efficiency of a noise barrier on the ground with an acoustically soft cylindrical edge. J Sound Vibr 1998;215:771–90. [21] Watts GR, Godfrey NS. Effects on roadside noise levels of sound absorptive materials in noise barriers. Appl Acoust 1999;58:385–402. [22] Arenas JP, Monsalve AM. Modification of the diffracted sound field by some noise barrier edge designs. Int J Acoust Vibr 2001;6:76–82. [23] Ishizuka T, Fujiwara K. Performance of noise barriers with various edge shapes and acoustical conditions. Appl Acoust 2004;65:125–41. [24] Monazzam MR, Lam YW. Performance of profiled single noise barriers covered with quadratic residue diffusers. Appl Acoust 2005;66:709–30. [25] Cianfrini C, Corcione M, Fontana DM. Theoretical analysis of the acoustical behaviour of roadside barriers with diffusive internal surfaces. Appl Acoust 1996;48:323–38. [26] Kang J. Sound propagation in street canyons: comparison between diffusely and geometrically reflecting boundaries. J Acoust Soc Am 2000;107:1394–404. [27] Kang J. Sound fields in urban streets with diffusely reflecting boundaries. Proc Inst Acoust 2000;22:163–70. [28] Kang J. Numerical modelling of the sound fields in urban streets with diffusely reflecting boundaries. J Sound Vibr 2002;258:793–813. [29] Le Polle`s T, Picaut J, Be´rengier M. Sound field modeling in a street canyon with partially diffusely reflecting boundaries by a transport theory. J Acoust Soc Am 2004;116:2969–83.
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[30] Ismail MR, Oldham DJ. A scale model investigation of sound reflection from building facades. Appl Acoust 2005;66:123–47. [31] Beranek LL, Ver IL. Noise and vibration control engineering: principles and applications. New York: Wiley; 1992. [32] Cianfrini C, Corcione M, Fontana DM. A method for predicting non-uniform steady sound fields within spaces bounded by diffusive surfaces. Appl Acoust 1998;54:305–21. [33] Hottel HC. Radiant heat transmission. In: McAdams WH, editor. Heat transmission. New York: McGrawHill; 1954.
Experimental verification of the acoustic performance 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 2006 Available online 20 October 2006
Abstract The acoustic performance of pairs of diffusive roadside barriers is tested experimentally on a 1:10 scale model, and compared to that of more traditional specularly reflecting barriers. Significant attenuation benefits are detected not only in the shadow zone behind the barriers, but also in the unprotected zone immediately above the barriers, thus proving that diffusive traffic faces of the barriers may effectively help in counteracting multiple reflection effects. In addition, a radiosity-based theoretical model developed for the evaluation of the sound field behind pairs of diffusive noise barriers is described, and its ability to predict the extra SPL attenuation deriving from the replacement of 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 in large conurbations, thus representing, without any doubt, one of the most widespread source of noise nuisance. Reduction in noise exposure may be effectively achieved by the erection of an acoustic barrier which prevents traffic noise reaching the receivers located inside the shadow zone
*
Corresponding author. Tel.: +39 06 44 58 54 43; fax: +39 06 48 80 120. E-mail address: [email protected] (M. Corcione).
0003-682X/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2006.07.018
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by the direct path. In case of residential and other developed areas located on both sides of heavily trafficked roadways, pairs of parallel traffic noise barriers are usually erected, but the multiple reflections occurring between the barriers may result in a significant degradation in the single barrier screening performance [1–3]. In this framework, the improvement of the acoustic efficiency of roadside barriers has been the subject of many studies, both theoretical and experimental, in which new types of barriers have been proposed [4–24]. With respect to traditional roadside barriers, new noise barriers are essentially based on two basic principles. The first principle involves the application of sound absorbing materials to the traffic face of the barriers. The second principle involves the adoption of new barrier shapes which substantially imply the modification of the diffracting-edge of the barrier, i.e., T-shaped barriers, Y-shaped barriers, arrow-shaped barriers, tubular-capped barriers, barriers crowned with phase-interference devices, barriers with quadratic residue diffuser tops, and multiple-edge barriers. In both cases more or less significant noise abatements in the shadow zone behind the barriers are reported. Even more interesting results may be achieved by coupling the two principles, as demonstrated by the high performance obtainable through the installation of soft T-shaped barriers. Actually, whenever pairs of barriers are erected at both sides of a roadway, a third principle may help in further counteracting multiple reflection effects. Such principle involves the use of acoustically rough traffic faces of the barriers, rather than acoustically smooth faces, i.e., traffic faces with a surface roughness between 0.05 m and 0.2 m, so as to obtain a diffusive rather than a geometrical reflection of the incident sound in the main frequency range of the traffic noise spectrum. In fact, owing to the spreading in all directions of the reflected noise, non-negligible abatements with respect to pairs of geometrically reflecting barriers may be achieved, as discussed in details in a first theoretical paper, in which we introduced also a radiosity-based method for the study of the acoustic performance of pairs of diffusive roadside barriers [25]. Indeed, some studies on the effects of the multiple reflections which occur between diffusely reflecting boundary surfaces flanking a roadway are available in the open literature [26–30]. However, as the subject of such papers is the sound field in street canyons, their attention is focused only on what happens between the reflecting surfaces, rather than behind them. In the present paper, after resuming briefly the basic outlines of the aforementioned theoretical/computer model, an experimental verification of its predictions is presented, and the main aspects of the results obtained are discussed. 2. Theoretical model An infinite-length straight roadway sided by flat ground, is considered. Freely flowing traffic is simulated by an infinite incoherent line source placed in the middle of the road at a given height over the road pavement. Atmospheric effects, in terms of wind speed and direction, velocity gradients and temperature stratification, as well as the effects of reflected 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 surrounding ground are assumed to be perfectly smooth and acoustically hard, which implies geometrical reflection. In contrast, both specularly and diffusely reflecting traffic faces of the noise barriers are considered.
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2.1. Acoustic field in the absence of barriers In the absence of noise barriers, the sound field at any location is calculated as the superimposition of the direct and the reflected sound waves, by neglecting any wave effect occurring at the roadway/ground boundary line. Since the road and the adjacent ground are assumed to be smooth, the contribution of the reflected wave is taken into account by the replacement of the surface of the road and the ground by a line source image, as shown in Fig. 1. Under the hypothesis of incoherent sound emission and sound propagation through free progressive waves, the sound field at any receiver location P is calculated by the sum of the sound intensities relevant to each transmission path to the receiver: W 1 1 r 1 IP ¼ þ ð1Þ 0 2p d 10ad=10 d 0 10ad =10 with r ¼ rR r ¼ rG
for a P b for a < b
ð2Þ
where IP is the sound intensity at the receiver location; W is the sound power emitted by the line source; a is the atmospheric absorption in dB/m; rR and rG are the coefficients of reflection of the roadway and the surrounding ground, respectively; d and d 0 are the path lengths of the direct and the reflected waves, respectively; a and b are the angles between the road line and the straight lines which join the virtual line source S 0 to the receiver and to 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 to the multiple image method, the sound field at any location behind the nearside barrier derives 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 compared with the diffraction over the barrier, the contribution of any line source (both real and images) to the total sound field is calculated by summing the sound intensities relevant to the four diffracted paths reported in Fig. 3:
P S
S' Fig. 1. Sound paths in the absence of barriers.
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virtual source
virtual source
S(3)
P
real source
S(2)
S(1)
Fig. 2. Image sources modelling of a pair of specularly reflecting barriers.
1,3 1,2 2,4
P
3,4
S
S'
P'
Fig. 3. Diffracted sound paths.
IP ¼
W 2p
1 X
rBn1
n¼1
1 rG rR rR r G Að1; nÞ þ 0 Að2; nÞ þ 0 Að3; nÞ þ Að4; nÞ dðnÞ d ðnÞ d ðnÞ dðnÞ
ð3Þ
with Aðk; nÞ ¼
1 10
ð4Þ
½ILðk;nÞþaDðk;nÞ=10
where d(n) and d 0 (n) are the lengths of the straight lines which join the receiver to the nth line source S(n) and its image S 0 (n) reflected by the road, respectively; IL(k, n) is the barrier insertion loss relevant to the kth diffracted path (k = 1, 2, 3, 4) from the nth line source to the receiver; D(k, n) is the length of the kth diffracted path from the nth line source to the receiver. Under the assumption of thin-walled barrier, IL(k, n) may be calculated in terms of the Fresnel number N(k, n), as widely reported in the literature (see, e.g., [31]): 2 N ðk; nÞ ¼ dðk; nÞ k pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2pN ðk; nÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 5 dB ILðk; nÞ ¼ 15 log tanh 2pN ðk; nÞ for N ðk; nÞ ¼ 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2pjN ðk; nÞj pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 5 dB ILðk; nÞ ¼ 20 log tan 2pjN ðk; nÞj
ð5Þ for N ðk; nÞ > 0
ILðk; nÞ ¼ 5 dB
ILðk; nÞ ¼ 0 dB
for N ðk; nÞ 6 0:2
ð6Þ ð7Þ
for 0:2 < N ðk; nÞ < 0
ð8Þ ð9Þ
where k is the wavelength and d(k, n) is the difference between the diffracted and the direct path lengths: dðk; nÞ ¼ Dðk; nÞ dðnÞ 0
dðk; nÞ ¼ Dðk; nÞ d ðnÞ
for k ¼ 1; 4
ð10Þ
for k ¼ 2; 3
ð11Þ
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Since IL(k, n) = 0 dB means that the wave relevant to the kth sound path reaches the receiver location directly, without intervening any diffraction effect at the top edge of the nearside barrier, in such case Eq. (4) must be calculated by the replacement of D(k, n) with the length of the straight line which joins the nth line source S(n) or its image S 0 (n) to the receiver. Currently, the calculation of the summation in Eq. (3) may be stopped at a large but finite number of source images beyond which any further contribution is less than a prescribed per-cent value of the previous total, i.e., 103. A typical number of source images required to achieve such result with a pair of barriers with coefficient of absorption of about 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 of the roadway, their acoustic behaviour is modelled by assuming that the sound power reflected by any infinitesimal element of each barrier is radiated according to a directional distribution which follows the Lambert’s cosine law, whichever is the direction of the incident sound power. As is well-known, diffusive sound reflection may be obtained through wells/protrusions or surface roughness of the same order of the wavelengths of the incident sound. The total sound field at any receiver location derives from the contributions of the traffic line primary source and the secondary sound sources represented by the infinitesimal surface elements of the farside barrier. The calculation of the sound power emerging from each surface element is carried out through a procedure derived from a theoretical/computer model developed for the study of non-uniform sound fields inside spaces bounded by diffusive surfaces [32], appropriately modified in order to take into account the geometrical reflection occurring at the road pavement [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 by the ith infinitesimal surface element of the farside barrier is calculated as the sum of the incident sound power due to irradiation by the traffic line source S and by its image S 0 ,
1,2
dh(i)
1,3 1,2 3,4
2,4
S
S'
P
3,4
P'
dh(i')
Fig. 4. Diffracted sound paths for a pair of diffusive barriers.
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and the incident sound power which, due to multiple reflections, emerges by any jth infinitesimal surface element of the nearside barrier B and by any j 0 th mirror-image element of the virtual nearside barrier B 0 , multiplied by the coefficient of reflection of the barrier: dW out ðiÞ ¼ rB ½W dF SdhðiÞ þ rR W dF S0 dhðiÞ Z Z dW out ðjÞ dF dhðjÞdhðiÞ þ dW out ðj0 Þ dF dhðj0 ÞdhðiÞ þ rB
ð12Þ
B0
B
with dW out ðj0 Þ ¼ rR dW out ðjÞ
ð13Þ
where dFSdh(i) (or dF S0 dhðiÞ ) is the view factor between the line source S (or the line source image S 0 ) and the ith element of the farside barrier, and dFdh(j)dh(i) (or dFdh(j )dh(i)) is the view factor between the jth element (or the j 0 th element image) of the nearside barrier B (or the nearside barrier image B 0 ) and the ith element of the farside barrier. The view factor FAB between two generic surfaces A and B, either finite or infinitesimal, is defined as WA–B/WA, i.e., the fraction of the power emerging from A directly intercepted by B. Same concept applies to view factor FS–B between a line source S and a surface B. Full details on view factors and on the methods for their calculation may be found in textbooks on radiative heat transfer (see, e.g., [33]). For each sound source, either primary or secondary, the four diffracted paths shown in Fig. 3 must be considered, thus obtaining: Z W 1 rG rR rR rG Að1Þ þ 0 Að2Þ þ 0 Að3Þ þ IP ¼ Að4Þ þ dW u ðiÞAð1; iÞ 2p d d d d B Z Z Z þ rG dW u ðiÞAð2; iÞ þ rR dW u ðiÞAð3; iÞ þ rR rG dW u ðiÞAð4; iÞ ð14Þ 0
B
B
B
where dWu(i) is the sound power radiated by the ith surface element of the farside barrier along the direction of the top edge of the nearside barrier, which forms an angle u(i) with the normal to the surface element. According to the Lambert’s cosine law for 2D geometry, the following expression holds: dW u ðiÞ ¼
dW out ðiÞ cos uðiÞ 2
ð15Þ
As concerns A(k) and A(k, i) of Eq. (14), which are relevant to the kth diffracted path from the primary line source to the receiver, and to the kth diffracted path from the ith secondary infinitesimal surface source to the receiver, respectively, their value may be directly derived 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 the unknown dependent variable appears inside an integral, in practice it is convenient to break 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 uniform. This corresponds to split the integral equations (12) and (14) in two different systems of M discretized equations. As concerns the evaluation of the finite view factors, the crossed-string method for 2D geometry, developed for the solution of radiant heat transfer problems, 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,
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which means that rG = 0 must be replaced in the above equations. Moreover, for receivers located relatively close to the roadway, atmospheric absorption may be neglected, which corresponds 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 m wide flanked by two noise barriers 3 m high; (2) the electronic equipment necessary to simulate a line of freely flowing traffic; and (3) the instrumentation for the measurement of the sound pressure level (SPL) at several receiving points. In particular, the use of a 1:10 scale for the roadway model implied that the test frequencies were 10 times those typical for the traffic noise. The experiments were performed in a 3.5 m · 3 m · 2.5 m test chamber whose boundary walls were covered with wedge-shaped absorbing material 100 mm thick, so as to reproduce the free-field situation, at least for the high frequencies. The roadway was made of flat wooden chipboard panels 25 mm thick, whose surface was subjected to a fine smoothing treatment in order to obtain a geometrical reflection of the incident sound waves. The barriers were made of flat wooden chipboard panels 18 mm thick. As for the roadway, one side of such panels was finely smoothed, for geometrical reflection behaviour. The reverse side of the barriers was covered by a layer of crushed 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 range between nearly 8 kHz and more than 16 kHz. The diffracting edge of the barriers consisted of a removable hardwood list with a triangular section. The length of the entire test section, i.e., of the roadway model, was 2.8 m. Two specularly reflecting float glasses 20 mm thick with reflection coefficient of nearly unity in the experimental bandwidth were mounted at both ends of the model, perpendicular to the roadway and the barriers, so as to reproduce an infinite-length configuration. The coefficient of absorption of the roadway and the barriers were obtained from onethird octave band measurements of the decrease in reverberation time inside a reverberant room, which for both types of panels gave values of 0.15 ± 0.05 for frequencies between 8 kHz and 20 kHz. The traffic line source was simulated by 14 independent sound sources, each of which consisted 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 facing one of the two barriers. The fourteen pairs of loudspeakers were aligned in the middle of the road at a 20 cm distance from each other, facing the noise barriers with a 15 tilting angle, embedded in a trapezoidal mounting assembly, which may somehow resemble a line of vehicles. The spectrum of the signal produced by the handmade pink noise generators is reported in Fig. 5, while a schematic of a normal hemi-section of the experimental set-up, as well as a 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 simulated an absorbing ground. A Bruel & Kjaer precision sound level meter model 2231 equipped with a 1/400 microphone model 4939 was used as receiver system.
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spectrum (dB)
-10 -20 -30 -40 -50 -60 10 2
10 3
10 4
frequency (Hz)
symmetry midplane
20
Fig. 5. Spectrum of the signal produced by the pink noise generators.
hardwood list
barrier chipboard panel
30 traffic line assembly
15˚
25
roadway chipboard panel
40
tweeter diffuser 40
280
crushed stone layer
18
500
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 be expected inside the test chamber, measurements of reverberation time were conducted. A Bruel & Kjaer white noise generator model 1405 was used as exciting source, whose signal was fed via a power amplifier LEM model PPA702 to a tweeter Audax type TWXAMT8. Reverberation time was measured for one-third octave band at different locations, 10 times at any location so as to calculate an average thereof, thus deriving the local value of the coefficient of absorption ac of the test chamber. The contribution of the reverberant sound field at the several measurement points was then calculated in terms of sound energy density ratio:
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roadside barrier traffic line float glass
roadway
Fig. 7. Schematic 3D view of one of the two ends of the model.
DR ð4=RÞ ¼ Dtot ðQ=4pr2 Þ þ ð4=RÞ
ð16Þ
with R¼S
ac 1 ac
ð17Þ
where DR is the sound energy density of the reverberant sound field at a given point, Dtot is the total sound energy density at same location, S is the area of the boundary surface of the 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 previously defined through one-third octave band measurements performed inside an anechoic room. According to the results obtained, the contribution of reverberation in the experimental bandwidth was at most the 4.9% of the total sound field, which occurred at 8 kHz in a measurement 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 to the 1 kHz peak frequency in the A-weighted spectrum of typical highway traffic noise, the maximum per-cent contribution of the reverberant field decreased to 3.4%, thus proving that 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 emissions of the 14 pairs of loudspeakers, which the traffic line consisted of, were the same. For this reason, the bottom-open casing depicted in Fig. 8 was built by hardwood panels 15 mm
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250
calibrated hole
200 400 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 with absorbing material 20 mm thick. The two frontwalls were profiled so as to match perfectly the mounting assembly of the traffic line source. A calibrated hole of the same diameter of the 1/400 microphone Bruel & Kjaer model 4939, was drilled at the centre of the top endwall. Before any experimental session were started, the casing was placed across any pair of loudspeakers, and the volume of the respective hi-fi amplifier was regulated to obtain a prescribed value of SPL. The same casing was used also to carry out tests of temporal stability of the sound sources through continuous measurements of SPL, which remained constant 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 executed in the absence of barriers (SPL0), with the barrier panels mounted with the specularly reflecting face opposite the traffic (SPLspec), and with the barrier panels reversed such that the diffusive face was facing the traffic line (SPLdiff). Measurement points were located in the midplane normal to the roadway and the barriers, and arranged according to two different grids: (a) a Cartesian grid, whose points were located 20 cm apart along the horizontal coordinate x, and 10 cm apart along the vertical coordinate y, as sketched in Fig. 9; and (b) a cylindrical polar grid, whose points were located 20 cm apart along the radial coordinate r, and 5 apart along the angular coordinate h, as sketched in Fig. 10. The tolerances of the microphone positioning were ±2 mm and ±0.5, for the linear and the angular displacements, respectively. At any measurement location the attenuations due to the erection of specularly and diffusely reflecting barriers, Aspec = (SPL0 SPLspec) and Adiff = (SPL0 SPLdiff), as well as their difference, i.e., the so-called extra attenuation, EA = Adiff Aspec = SPLspec SPLdiff, were calculated.
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0.3 m
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traffic line source 0.1 m 1.0 m
0.2 m
0 .2 m
Fig. 9. Cartesian grid of measurement points.
0.3 m
traffic line source
1.0 m
0--
5˚ 0 .2 m
0.2 m
Fig. 10. Cylindrical polar grid of measurement points.
5. Experimental results and discussion Typical distributions of the extra attenuation EA vs. the angular position of the receiving point h in the range between 0 and 90, at frequencies 5 kHz, 10 kHz, 12.5 kHz, and 16 kHz, are reported in Figs. 11–13, for distances of the receiver from the traffic line source r = 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 were obtained at receiving points located in the shadow zone behind the barriers, viz., at an angular coordinate h up to little more than 30. Non-negligible values of the extra attenuation were also detected at receiving points located in the unscreened zone immediately above the barriers, viz., at an angular
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5.0 kHz
+5
extra attenuation EA (dB)
10.0 kHz +4
12.5 kHz
+3
16.0 kHz
+2 +1 0 -1 -2
r = 0.7 m
-3 0
10
20
30
40
50
60
70
80
90
angular coordinate (degrees) Fig. 11. Distributions of extra attenuation EA vs. h at r = 0.7 m.
+6
5.0 kH z
+5
extra attenuation EA (dB)
10.0 kHz +4
12.5 kHz
+3
16.0 kHz
+2 +1 0 -1 -2
r = 0.9 m 0
10
20
30
40
50
60
70
80
90
angular coordinate (degrees) Fig. 12. Distributions of extra attenuation EA vs. h at r = 0.9 m.
coordinate h in the range between 30–35 and nearly 55. Of course, such significant values for EA were achieved only for those frequencies at which the reflection of sound waves by the stone layer covering the traffic side of the barriers was actually diffusive, i.e., above 8 kHz, the larger was the sound frequency, the higher was the extra attenuation. In contrast, negative values of the extra attenuation were observed at receiving points located in the 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 all directions 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 behind them in the shadow zone. As a consequence, on account of the energy conservation law, an increased amount of sound energy is re-directed towards the unscreened zone. On the
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+6
5.0 kH z
+5
extra attenuation EA (dB)
10.0 kH z +4
12.5 kH z
+3
16.0 kH z
+2 +1 0 -1 -2
r = 1.1 m
-3 0
10
20
30
40
50
60
70
80
90
angular coordinate (degrees) Fig. 13. Distributions of extra attenuation EA vs. h at r = 1.1 m.
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, of the unscreened zone. Furthermore, it is worth noticing that the values of the extra attenuation increase with increasing 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 distance from the roadway, which obviously leads to increases in EA. Many more details on the comparative performance of pairs of specularly and diffusely reflecting 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 sound field in the shadow zone behind pairs of both specularly and diffusely reflecting traffic noise barriers, for the same geometry and sound absorption characteristics of the experimental test section. Theoretical values of the extra attenuation were then calculated at a wide variety of locations, in order to assess what accuracy could be expected in evaluating the performance of pairs of diffusive barriers relative to that of more traditional specularly reflecting barriers. The comparison between theoretical and experimental values of EA at frequencies 5 kHz, 10 kHz, 12.5 kHz, and 16 kHz, reported in Fig. 14, shows that the computer model developed is able to predict the relative acoustic performance of pairs of diffusive noise barriers with error ranges of ±1.5 dB, ±1.0 dB, and ±0.5 dB, with levels of confidence of 100%, 87%, and 68%, respectively. Discrepancies between theoretical and experimental data may be ascribed to the fact that the assumptions of: (a) totally diffusive reflection at the barrier surface, i.e., according to the Lambert’s cosine law; (b) thin-walled barriers; and (c) two-dimensional cylindrical sound emission by the traffic line, do not apply perfectly well to the experimental arrangement. In addition, the theoretical model developed does not take into account any wave
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f = 10.0 kHz
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theoretical values of EA (dB)
8 7 6 5 4 3 2 1 0
0
1
2
3
4
5
6
7
6 5 4 3 2 1 0
8
f = 12.5 kHz
7
0
experimental values of EA (dB) 8
f = 16.0 kHz
7 6 5 4 3 2 1 0 0
1
2
3
4
5
6
experimental values of EA (dB)
3
4
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6
7
8
8
f = 20.0 kHz
7 6 5 4 3 2 1 0
7
2
experimental values of EA (dB)
theoretical values of EA (dB)
theoretical values of EA (dB)
8
1
0
1
2
3
4
5
6
7
8
experimental values of EA (dB)
Fig. 14. Comparison between theoretical and experimental values of EA.
effect occurring at the intersections between the barriers and the roadway, as well as any scattering effect produced by vehicles, which, in contrast, is somehow reproduced in experiments 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 lowest sound frequencies investigated. 7. Conclusions An experimental study on the performance of pairs of parallel diffusive roadside barriers relative to that of more traditional specularly reflecting barriers, was conducted on a 1:10 scale model. According to the results obtained, significant values of the extra SPL attenuation may be achieved in the shadow zone behind the barriers, as well as in the unscreened area immediately above the barriers, which proves that the use of diffusive barriers may represent an effective help in counteracting multiple reflection effects. In addition, the extra attenuation increases with increasing the distance from the roadway. Finally, the acoustic performance of pairs of diffusive noise barriers relative to geometrically reflecting barriers may be well evaluated through the theoretical computer model proposed and discussed.
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