Acoustical scale model study of the attenuation of sound by wide barriers

Acoustical scale model study of the attenuation of sound by wide barriers

Elizabeth S. Ivey

Department of Physics, Smith College, Northampton, Massachusetts 01060

G. A. Russell

Department of Mechanical Engineering, University of Massachusetts, Amherst, Massachusetts 01003 (Received 31 March 1976; revised 18 March 1977)

Acoustical scale model experiments carried out with building-size barriers are described. The results of experiments conducted with the barrier in a free field and on a reflecting surface are presented. The free- field measurements are compared to several theoretical models and discrepancies between the theoretical and experimental results are discussed. Also presented is a simple expression which relates the excess attenuation obtained with the barrier situated on the ground to that of the same barrier in the free field. This expression predicts excess attenuations which agree quite closely with those actually measured in the scale model experiments.

PACS numbers: 43.50.Lj, 43.28.Fp, 43.20.Fn, 43.50.Vt.

INTRODUCTION

The attenuation of sound as it propagates over and around building-size barriers has long been recognized by noise control engineers, even though the exact nature of the attenuation process was not completely under- stood. The recent promulgation of government guidelines •-a for acceptable levels of environmental noise has, however, generated a new interest in quantitative prediction methods for such barriers. It is largely in response to these recent governmental guidelines that urban planners and highway designers are now asking for methodologies to predict quickly and accurately the noise attenuation characteristics of buildings and other barriers of finite thickness.

A cursory review of the pertinent acoustical and noise-control literature, however, will convince the reader that the general process of sound attenuation by finite-thickness barriers is not simple, and is not readily modeled in all its important aspects. A fundamental difficulty is that the finite thickness can introduce a double-edge, rather than single-edge, diffraction, although double-edge diffraction is not always the dominant attenuation process. A further complication can be at-. tributed to the interference, absorption, and reflection taking place at the ground surface upon which the barrier is situated. There are also losses occurring along the top surface of the barrier which apparently need to be considered in any realistic model. 4

The problem is evidently one which has conflicting requirements: There is a need for an accurate model

or prediction method, yet the process to be modeled requires the consideration of several relatively complex acoustical phenomena. Our purpose here is to present the results of an acoustical scale model study of a lim- ited class of wide barriers and to compare the experimental results with several theoretical models of the

wide barrier attenuation process. The discrepancies between theory and experiment suggest that the problem has not yet been completely resolved.

I. BACKGROUND

Of the severat thin-screen studies reported in the 'literature, s,0 the most well-known results are those of Maekawa. s Maekawa's experiments dealt with an acoustically opaque thin screen of essentially infinite length. A tone burst point source together with different source and receiver locations was used to measure the excess

attenuation EA as a function of Fresnel number N where

EA = (receiver sound pressure level without barrier in place) minus (receiver sound pressure level with barrier in place), in riB, N= 25/X, in radians, 5 = (path length with barrier in place) minus (path length without barrier in place), and X is the source signal wavelength.

Although Maekawa has suggested a technique s to ex- tend his thin-screen results to wide-barrier situations, a more useful approach to the wide-barrier ease is the analytical model developed by Pierce. ? Pierce has used auxiliary Fresnel functions to derive a point-source double-edge diffraction equation applicable to three- sided wide barriers in a free field:

EA•, = 20 log(L/d)- 10 log{ [f•'(Y>)+g•'(Y>)]

x r<) + r<)]},

where L and d are as defined in Fig. 1, and f and g are the auxiliary functions of Fresnel integrals which can be found in Ref. 8. The barrier width W is character-

ized by the parameter B where

[ W(W+R,+RR) ]•1•' ' (2) The quantities Y> and Y< in Eq. (1) are the larger and smaller, respectively, of the values for Ys and YR where

Ys =[ 2Rs(W + R•)'] • /•' cøs(rr•'/fis) + cøs[(rr/fis)O s] XL (x/•s) sin(•f.//3s ) , (3) and Y• can be found from Eq. (3) with an appropriate substitution of subscripts. The remaining symbols used in Eqs. (2) and (3) are all defined in Fig. 1.

601 J. Acoust. Soc. Am., Vol. 62, No. 3, September 1977 Copyright ¸ 1977 by the Acoustical Society of America 601

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602 E.S. Ivey and G. A. Russell: Attenuation of sound by wide barriers 602

R S

POINT SOURCE =----' d .... --'--'--- R'••ECE VER

FIG. 1. Cross-sectional view ,of bar-

rier configuration pertinent to Eq. (Rs'; 8s, Zs) and (R•, 8R, ZR) are co- ordinates of source and receiver, respectively, where the two top edges of the barrier are parallel to the Z axis. L =[(Rs+ W+R•)2+(Zs-Z_•)2] 1/2. For Zs=Z•e =0, 6=(R s + W+R•) -d.

In his development Pierce has assumed a barrier surface free of any scattering or absorption losses. As with Maekawa's technique, Pierce's model does not provide for ground interactions, thus limiting its ap- plicability in realistic configurations. Pierce's analy- sis does, however, provide a solution to the fundamental problem of double-edge diffraction.

Another approach to the wide barrier case has been proposed by Kurze. 4 Kurze considers double-edge diffraction as the sum of two single-edge diffractions, one for a ray traveling from the source S to a hypothetical receiver R' located in the plane of the barrier top at a distance RB from the far edge and the second for a ray traveling from a hypothetical source S' in the plane of the barrier top at a distance SA from the near edge to the receiver R (see Fig. 2). Assigning two Fresnel numbers N• and N•., one for each of the two single diffractions discussed above, one may then use Maekawa's thin-screen equation for single-edge diffraction (or Maekawa's experimental curve for Fresnel numbers less than 1.0) and sum the resulting excess attenuations. However, since receiver point R' and source point S' have been placed directly on the hypothetical diffracting wedges, a correction is required. Kurze proposes a - 5 dB correction to give

EAtc = EA (Nt) + EA (N•.) - 5 + 201og(L/d) dB , (4)•

where L is the path length with barrier in place, in meters, and d is the path length with barrier removed, in meters.

Like Pierce, Kurze does not include ground effects in his treatment of wide barriers. The complicated nature of ground interactions has caused many investiga- tors to bypass studies of ground effects. However, Fehr 9 developed a theory for calculating the sound attenuation by a thin, infinitely long barrier when both the source and the receiver were on the ground. By placing the source and receiver actually on the ground, sound reflections from the ground become negligible. More recently, Jonasson •ø accounted for ground reflections and diffraction theory simultaneously in his development of a theory to predict the attenuation of sound by barriers on the ground. He used Ingard's • theory on the propagation of spherical waves over a ground surface and then introduced diffraction theory to obtain an approximate solution of the complete problem. Jonasson's theory requires that the acoustic impedance of the ground be known and these calculations become difficult when the sound propagates over more than one kind of ground surface. Irregularities in the surface and sea- sonal variations complicate the situation even further.

J. Acoust. Soc. Am., Vol. 62, No. 3, September 1977

Embleton •' has measured the propagation characteristics of pure tone signals traveling over different ground surfaces at small incidence angles and shows that the propagation losses are strongly dependent on surface type. Embleton, however, did not consider the barrier propagation problem.

In view of the above it appears that no completely satisfactory predictive model for wide barriers on realistic surfaces has yet been developed. Furthermore, the multiplicity of factors which must be considered for realistic situations suggests that an empirical study might yield useful results. For these reasons, a series of acoustical scale model experiments employing various simulated ground surfaces and barrier configurations was carried out. In particular, two effects were investigated: first, how the width of a building-size barrier affects its free-field EA, and secondly, how different ground surfaces change the total EA of barriers whose free-field EA has already been determined. Our purpose here is to report the results of these experiments and to compare the experimental results with analytical predictions where such comparisons are appropriate.

II. SCALE MODEL EXPERIMENTAL STUDY

It is both appropriate and convenient to use scale modeling to investigate sound attenuation by building- size barriers in the free field and on the ground. A significant advantage of scale modeling is that it allows building heights and widths to be readily changed. Free- field measurements are possible with "infinitely" tall buildings and sound diffraction over the building can be isolated by making the buildings "infinitely" long. Also, a variety of ground surfaces can be used, providing even greater flexibility over field experiments. The equipment used in the modeling experiments consisted of a sound source, microphone receiver, processing and display devices, and the physical models. The noise produced by the source was first picked up by the

S]_ A B _ O R' YI/77'71-" V////A

FIG. 2. Cross-sectional view of rectangular wide barrier configuration. ,5 = (SA + W + BR) - SR.


603 E.S. Ivey and G. A. Russell' Attenuation of sound by wide barriers 603

microphone, then filtered, processed, and displayed on 50

an oscilloscope as a time history of either the logarithm •= of the total energy or the logarithm of the root-mean- •; o 40

square pressure. The apparatus and basic techniques •- = 30

employed in the experiments were developed by Lyon • and are described in greater detail elsewhere. •3 • • 20

• ]0 When scale modeling, geometric scaling requires the constancy of the ratio of dimensional length to acoustic wave length. A sdale factor of 64:1 was used to con- struct the barrier models (1 m of model length corresponding to a real world length of 64 m) which required a 64: 1 scaling up in frequency (100 Hz in the real world correspondfng to 6400 Hz in the model). 5o

=; 40 The noise source was a high voltage spark having a

high-frequency wide-band spectrum filtered to provide = 30 z

a typical traffic noise spectrum shape. The dominant frequency in the filtered spectrum was 31 500 Hz, cor- • 20 responding to a full scale wavelength of 0 69 m. The '" 10 very short duration of the sound impulse (approximately 25 /•s) allowed noise signals propagating along different 1 noise paths to be isolated from each other so that they could be identified and studied separately.

The barrier models were constructed of cardboard

and were placed on acoustically hard (plywood) or soft (cotton velveteen over Deciban) surfaces. These model materials, i.e., cardboard, plywood, and velveteen over Deciban (a trade name for a soft pressboard mate- rial), have reflection and absorption properties at the modeling frequencies that correspond, respectively, to real world materials of brick, black-top pavement, and newly mown grass. •4 Free-field conditions were modeled by placing both the source and receiver well above the reflecting ground surface. In modeling barriers on a ground surface the source and receiver were both kept at a height of 2.5 cm (1.6 m full scale) above the surface. In addition, the source and receiver were placed in a plane perpendicular to the infinite axis of the barrier and always below the top of the barrier. Variations in Fresnel number for a given barrier width were obtained by locating both source and receiver at varying horizontal distances from the barrier and by changes in the barrier height.

Full scale barrier widths of 3.5, 7.0, and 17.6 m were modeled. For each width, a series of barriers were constructed which were 3.5, 4.8, 8.3, 11.8, and 15.4 m high. An additional set of "infinitely" tall barriers was used in the free-field tests. In all cases the

barrier was rectangular in cross section as indicated in the sketch of Fig. 2. For each barrier width the excess attenuation over a range of Fresnel numbers, typi- cally 1.2-30.0 was measured. The EA was determined by first measuring the received sound pressure with the barrier in place and then repeating the measure- ment with the barrier removed. The difference between

these two measurements is the EA.

. (A) D R : 15.2 m

_ j I

0 10.0 lO0.O

FRESNEL NUMBER, N

III. EXPERIMENTAL RESULTS .

Following Maekawa's example, it is convenient to ex- press the noise attenuation characteristics of the wide- barrier configurations studied in terms of some repre-

50

_ (B) D R: 30.5 m

- •!•O • •

.

0 10.0

FRESNEL NUMBER, N

(C) D R : 61.0 m

I

100.0

30 ß ß ...

' 1o

I I _

1 0 10.0 100.0

FRESNEL NUMBER, N

FIG. 3. Free-field excess attenuation for barrier width oœ 3.5 m and X =0.69 m. Experimental data (filled circle): Pierce solution (open square); and Kurze solution (open triangle).

sentalive Fresnel number. For our purposes here, we have elected to portray the experimental results in terms of excess attenuation versus a single Fresnel number (N=26/X). Here 6 is the total path length difference between source and receiver, as defined in Fig. 2. The wavelength X is that corresponding to a full- scale frequency of 500 Hz (typical of A-weighted traffic noise) as the dominant frequency in the spark source signal used for the experiments was 31 500 Hz.

Typical experimental results for the free-field situation are shown in Figs. 3-5 for barrier widths of 3.5, 7.0, and 17.6 m, respectively. To show the experimental results in greater detail, each figure shows three graphs with each graph representing data taken at a single receiver horizontal distance (DR in Fig. 2) be- hind the barrier. The variation in Fresnel number was

obtained by changing the source/receiver vertical distance below the top surface of the barrier and by changing the horizontal distance (D s in Fig. 2) from the source to the barrier.

Individual experimental points shown in these figures represent a particular free-field barrier, source, and




50

=• 40

,r 30

• 20

"' 10 x

1 0

(A) D R : 15.2 m

_ ß •l 0 •

I , I 10.0 100.0

FRESNEL NUMBER, N

50

• 40 o

-r 30

•- 20

"' 10 x

(B) D R = 30.5 m -

I

lO.O

FRESNEL NUMBER, N

i

100.0

50

• 40

,• 2o

(C) D R = 61.0 m

FRESNEL NUMBER, N

I

100.0

FIG. 4. Free-field excess attenuation for barrier width of

7.0 m and X = 0.69 m. Experimental data (closed circle); Pierce solution (open square); and Kurze solution (open triangle).

receiver configuration. For all particular configurations the excess attenuation predicted by both the Pierce and Kurze theoretical models has been calculated and

plotted on the graphs. The solid line shown represents the approximate trend of the Kurze theoretical predictions and the dashed line shows the approximate trend of the Pierce model on each of these graphs.

The results shown in Figs. 3-5 indicate t'hat the free- field experimental data follow the general shape of Pierce's predicted values. The experimental data points are however, displaced upwards by a noticeable amount, indicating higher excess attenuations. This displacement is more pronounced at the large barrier widths which implies a greater increase in excess attenuation with increasing barrier width than predicted by Pierce. This discrepancy between experiment and theory could be due to scattering and absorption losses taking place along the top surface of the scale model barrier, such losses not being included in the Pierce equations. A second possible cause for the discrepancy could be frequency effects. In evaluating the Pierce and Kurze equations for the curves of Figs. 3-5 only the single dominant frequency of 500 Hzwas used.

The Kurze equations also give generally lower EA values than those found experimentally. The overall trend of the Kurze theory does not, however, follow the experimental EA versus N characteristic as well as the Pierce solution.

When the barriers were placed on ground surfaces, less excess attenuation was measured than with the bar-

riers in the free field. Test results for three barrier

widths are shown in the three curves of Fig. 6. Each of the graphs shows three lines representing experimental data corresponding to: (1) free field, (2) plywood ground surface, and (3) a ground surface of cotton velveteen over Deciban. For a given Fresnel number and barrier width the free-field configuration generally yields the greatest EA, the plywood ground surface, gives approximately 8 rib less EA than the free-field case, and the velveteen over Deciban surface gives about 10 dB less EA than the free-field configuration. This trend holds for the range of Fresnel numbers tested.

Placing the barrier on a reflecting ground surface necessarily changes the EA characteristic of the barri-

• 50 • .o

,• 2o

50

:• 40

• 30

'1'-- • 20

x

(A) D R: 15.2 m ß

..

lo

1.o

I

lO.O

FRESNEL NUMBER, N

(B) D R : 30.5 m -

i

10.0

FRESNEL NUMBER, N

I ,

190.0

I

100.0

50

• 40

• 20

lO x

(C) D R = 61.0 m --

! i

1.0 10.0 100.0

FRESNEL NUMBER, N

FIG. 5. Free-field excess attenuation for barrier width of

17.6 rn and 2,=0.69 m. Experimental. data (filled circle); Pierce solution (open square); and Kurze solution (open triangle).



605 E. S. Ivey and G. A. Russell' Attenuation of sound by wide barriers 605

5O

• 4O

• 30

• 2o

(A) BARRIER WIDTH = 3.5 m .

-

!

lO.O

FRESNEL NUMBER, N

I

lO0.O

50

• 40 o

< 30

•- 20

,., 10 x

1 0

(B) BARRIER WIDTH = 7.0 m

10.0

FRESNEL NUMBER, N

100.0

(C) BARRIER WIDTH = 17.6 m

• •o

• lO I i

lO0.O 1.0 10.0

FRESNEL NUMBER, N

FIG. 6. Excess 'attenuation for barriers of three widths in the free field and on two ground surfaces. Lines shown represent best fit to experimental data points. Free field (solid line); over plywoo. d (short-dashed line); over cotton velveteen on Deciban (long- and short-dashed line).

er. While not immediately obvious that this change should produce the results shown in Fig. 6, the experimental trend can be rationalized in terms of two significant effects which can be identified when the barrier is

situated on a reflecting surface.

The first of these significant effects is that due to scattering and absorption losses along the ground surface, this effect being particularly noticeable when both the source and receiver are near the ground. 9 The scattering and absorption losses show up as a geometric spreading (from a point source) greater than 6 dB per doubling of distance when the sound is propagating close to the ground surface. When the sound propagates up and over the barrier to the receiver, free-field spreading of 6 dB per doubling of distance can be ex- pected. Since excess attenuation has been defined as a

difference in received sound pressure (SPL without the barrier minus SPL with the barrier), the change in spreading characteristic induced by the ground surface necessitates a compensating correction factor. This correction should only be applied to the "without barri-

er" term and hence reduces the EA from that measured

in the free-field configuration. The magnitude of the correction can be found from the distance between the

source and receiver together with a knowledge of the geometric spreading law for the particular ground surface involved. Typical spreading characteristics were measured for the two ground surfaces employed and are shown in Fig. 7. The spreading characteristics for both ground surfaces shown in Fig. 7 were taken with the source and receiver 1.6 m (full scale) above the ground surface. This source and receiver height was also used for all the ground surface EA measurements shown in Fig. 6. The experimentally determined spreading characteristics of Fig. 7 indicate that, at a source-to-receiver distance of 64 m, this correction term may be as much as 6 dB.

The second important ground effect is that of reflected signals, on both the source and receiver sides of the barrier. As has been suggested by Jonas son, •0 a convenient approach to use with ground reflections is possible if the source and receiver are restricted to being relatively close (within one or two wavelengths) to the ground. With this restriction, the point source acts as a hemispherical rather than a spherical radiator, and becomes 3-dB stronger than the same source in a free- field situation. This doubling of source strength due to reflections on the source side of the barrier results in

a 3-dB increase in received signal and a corresponding decrease of 3-dB from the free-field excess attenua-

tion. On the receiver side of the barrier similar re-

flections are occurring causing a further 3-dB increase in received signal. Combining the source side and receiver side increases in received signal gives a maxi- mum reduction of 6-dB from the free-field excess at-

tenuation due to ground reflections.

Applying this 6-dB correction for ground reflections to the free-field equation, together with the nonspherical spreading correction discussed earlier gives

EA =EAff- 6- (extra geometrical spreading loss) . (5)

Equation (5) provides a convenient methodology for mod- ifying free-field results to account for ground effects.

•, 80

•_ 70 -

j 60 -

,,,50 • D

'" 40

• 30 < 100 _2 ß

I

lO0.O

FREE FIELD

6 dB/dd) PLYWOOD

(7.5 dB/dd) VELVETEEN ON DECIBAN (10 dB/dd)

i

1000.0

DIRECT MODELING DISTANCE BETWEEN SOURCE AND RECEIVER, CM.

FIG. 7. Geometric spreading characteristic in the free field, over plywood, and over cotton velveteen on Deciban. Both the source and receiver were at an actual height of 2.5 cm for the latter two curves.




5O

;• 40-

• :30 - z

I--- - •: 20

• lO x

D R = 30.5 m

rl rl

ß

I i,

1.0 10.0 100.0

FRESNEL NUMBER, N, RADIANS

FIG. 8. lqxperimental data points (filled circle) and corresponding predicted values (open square) using Eq. (5) for a barrier of width 3.5 monaplywood surface. X=0.69 m.

It should be noted that both ground effects identified, i.e.', reflections and nonspherical spreading, act to decrease the excess attenuation found in the free-field situation. This trend is consistent with full scale field

data which have indicated that theoretically predicted attenuations (based solely on free-field theories) usually exceed those actually measured, particularly over ab- sorptive ground surfaces. t5

To check the validity of Eqo (5), it was used to predict the EA that would result from a barrier 3.5-m wide

placed on a black-top pavement (plywood) surface. The free-field EA characteristic for a barrier of this width

was assumed to be given by the series of experimental points shown in Fig. 3. Each of these measured free- field EA values was reduced by 6-dB to account for the first and second terms of the right hand side of Eq. (5). The extra geometrical spreading loss term was obtained from Fig. 7 (the difference in decibels between the spherical spreading line and the over-plywood spreading line) for the horizontal separation between source and receiver associated with each of the experimental points shown in Fig. 3. The extra spreadin• loss term was incorporated to give the net result shown in Fig. 8. Also shown in Fig. 8 are the EA values actually measured with a 3.5 barrier placed on the plywood model surface. The agreement between the two sets of points is very good, showing a correlation coefficient of 0.92.

The close agreement between the measured EA values and those calculated from Eq. (5) is an encouraging and perhaps significant result. Subject to the limitations in- herent to scale model studies, it seems to suggest that the simple computation of Eq. (5) provides an accurate methodology for predicting the EA of wide barriers situated on actual ground surfaces. It is also interesting to note that the arguments leading to Eq. (5) are appropriate to the thin-screen situation and could therefore be applied to the highway noise barrier problem as well.

IV. CONCLUSIONS

A series of acoustical scale model experiments have been carried out on various wide-barrier configurations. The experimental results indicate that the free-field excess attenuation of wide, rectangular cross section, barriers is slightly greater l{han that predicted by Pierce. This discrepancy can probably be attributed to losses taking place along the top surface of the model barriers, such losses not being considered in the for- mulation of Pierce.

Model studies carried out with wide barriers situated

on various ground surfaces indicate excess attenuations less than those obtained with the same barrier in a free

field. Two ground effects, nonspherical spreading, and additional reflection paths, appear to contribute to the decrease in EA when the barrier is placed on a ground surface.

A simple analytical expression relating the EA obtained when the barrier is on a ground surface to the free-field EA and the spreading characteristic of the particular ground surface has also been given. Excess attenuations predicted by this analytical expression agree quite closely with those actually measured for model barriers on the ground.

iNoise Abatement and Control: Department Policy, Imple- mentation Responsibilities and Standards, C itc ular 1390.2, U.S. Department of Housing and Urban Development (August 1971).

•'Noise Standards and Procedures, PPM 90-2, Federal Highway Administration, U. S. Department of Transportation(February

Sinformations on Levels of Environmental Noise Requisite to Protect Public Health and Welfare with an Adequate Margin of Safety, U.S. Environmental Protection Agency, 550-9-74-004 (March 1974).

4U. J. Kurze, J. Acoust. Soc. Am. $$, 504-518 (1974). OZ. Maekawa, "Noise Reduction by Screens," Appl. Acoust.

1, 157-173 (1968). SU. J. Kurze and G. Anderson, "Sound Attenuation byBarriers,"

Appl. Acoust. 4, 35-53 (1971). 7A. D. Pierce, J. Acoust. Soc. Am. $$, 941-955 (1974). 8M. Abramowitz and I. Stegun, NBS Handbook of Mathematical

Functions (Dover, New York, 1965), pp. 323-324. sR. Fehr, "The Reduction of Industrial Machine Noise," Proc.

2nd Ann. Nat. Noise Abatement Symposium, 93-103 (1951). •øH. Jonasson, "Sound Reduction by Barriers on the Ground,"

J. Sound Vib. 22, 113-126 (1972). llK. U. Ingard, J. Acoust. Soc. Am. 23, 329-335 (1951). l•'T. F. W. Embleton, J. E. Piercy, and N. Olson, J. Acoust.

Soc. Am. 59, 267-227 (1976). 13R. H. Lyon, R. DeJong, R. Cann, and F. Schlaffer, J.

Acoust. Soc. Am. 55, 521-524 (1975). •4H. Davies, "Modeling Materials for Acoustic Scale Models,"

MIT Dept. Mech. Eng. Report (March 1974). l•U. Kurze and L. L. Beranek, "Sound Propagation Outdoors,"

in Noise an Vibrational Control, edited by L. L. Beranek (McGraw-Hill, New York, 1971), p. 180.



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Acoustical scale model study of the attenuation of sound by wide barriers