A computer model for predicting sound attenuation by barrier-buildings

AppliedAcoustics13 (1980) 331-355

A COMPUTER MODEL FOR PREDICTING S O U N D ATTENUATION BY BARRIER-BUILDINGS

SELMA KURRA

Building Research Centre, Faculty of Architecture, lstanbul Technical University, lstanbul (Turkey)

SUMMARY

This paper describes a computer technique involving a procedure f o r finding the performance values within the shadow zone o f a barrier-building of rectangular crosssection used as a point source. Reflections f r o m the ground are also taken into account and a control operation is designed f o r different source and receiver locations related to the building. Consideration is given to the combined effects of wide barriers and finite size screens. The results are confirmed by several experimental measurements carried out in an anechoic room. Some examples o f the application of the technique are given.

INTRODUCTION

In recent years barriers have often been used as a means of noise control. The results of various studies carried out in relation to subjects such as the diffraction of sound waves over screens, wide barriers and wedges and those factors affecting barrier performance such as ground interactions, meteorological events, surface absorption, and so on, reveal that buildings perform as noise barriers more efficiently than roadside screens. Barrier-buildings may involve less sensitive functions or may have specially isolated facades against noise; on the other hand, they may create extensive quiet areas behind them. Some investigators have dealt with the acoustical shielding problems of long buildings against traffic noise, both theoretically and experimentally, mostly in terms of L~o, and some charts have also been recommended as design guides for assessing the shielding effects of buildings. Furthermore, some mathematical predictions and computer techniques have been developed for obtaining the average values of sound propagation in typical urban situations. ~-4 However, before 331 Applied Acoustics 0003-682X/80/0013-0331/$02.25 ~'~ Applied Science Publishers Ltd, England, 1980 Printed in Great Britain

332

SELMA KURRA

reaching general conclusions, the problem of the shielding effect should be examined in terms of diffraction by three sides of the barrier by means of a performance analysis of a single building. This problem calls for consideration of the combined effects of wide barriers of finite length and ground reflections. However, as far as the author knows, the sound attenuation achieved by a three-dimensional rectangular barrier used as a point source has not been studied or reported on previously. This paper describes a procedure for studying the effects of a barrier-building on noise control by combining the three known methods, mentioned below. Since this analysis, having so many effects, is too complicated to deal with algebraically it has been necessary to use a computer technique. Applications of the proposed technique to buildings of various dimensions, have been made and some design charts giving the relationships between various parameters have been obtained. This procedure has been applied to the attenuation of traffic noise 6 and the results are given elsewhere. 5

A BRIEF REVIEW OF THE LITERATURE

The four methods of determining sound attenuation by barriers for different sound sources, some of which have taken environmental factors into account can be classified as follows.

(l)

(2)

(3)

(4)

Classification by type of investigation. (a) Theoretical predictions. (b) Experimental work (field measurements 7 - 10 and model experiments 11 - 17). (c) Practical solutions recommended in design guides. ~8-2° Classification by type of sound source. (a) Point source. 21'22 (b) Line source. 21'22 (c) Traffic noise. 5'14'23-32 Classification by barrier properties: Infinite-length barriers 21'33-35 and finite-length barriers, 36"37 thin screens 3s and thick barriers, 38-43 sharpended screens, 35 wedges, 42'44'45 trapezoids, ~2 rectangular cross-section barriers, parallel barriers 17 and absorptive 43'44 and reflective barriers. Classification by physical environmental factors affecting barrier performance. (a) Ground effect (reflections from the g r o u n d , 28'35'36 ground absorption, 19'47 ground impedance 47 and free-field conditions). (b) Meteorological factors (temperature gradients, winds and turbulenceg.4°). (c) The angle of sound incidence with barrier surface. 36'~6

PREDICTING SOUND ATTENUATION BY BARRIER-BUILDINGS

333

Research studies classified in the previous paragraphs have been summarised in almost all papers on barriers. Before discussing these methods, the goals of the present research can be clarified as follows. (1) (2) (3) (4) (5) (6)

The noise source is a point source. The noise barrier is a three-dimensional and rectangular cross-sectioned building with a smooth roof which has no facade irregularity. The techniques should be applied to different source, receiver and barrier configurations. Ground reflections should be taken into account. The sound attenuation should be obtained in the form of a frequency spectrum. The procedure can be applied to traffic noise control problems and be easily adapted to computer programming.

When the methods cited in the literature were examined with respect to the foregoing principles, it was observed that each is concerned with a special aspect of the whole problem but does not satisfy the above requirements. However, it is possible to utilise the methods related to the sub-problems and to combine the effects contributing to total barrier attenuation. As a result of the present discussion for sound attenuation by thin and infinite screens, Kurze's expression, 2~ which gives satisfactory agreement with the well-known Maekawa chart, has been selected and, in order to calculate the performance of the finite-size barrier for a point source, Maekawa's procedure 35"36 has been applied in the proposed method. The thickness of the barrier has also been calculated by means of a separate process which uses the Fujiwara-Maekawa chart. 3a'4~'43 The possible geometry of the sound source, receiver and barrier may be such that it may be necessary to predict the effect of the wedge angle. In such cases, Maekawa's chart for right-angled wedges 22'45 has been used in obtaining the wedge effect.

PROCESS OF COMPUTATION OF THE SOUND ATTENUATION BY A BARRIER-BUILDING

The procedure for predicting the excess attenuation of a thick and finite-length barrier primarily involves the control of the validity of the diffraction theory. As is well known, the acoustical shadow region behind a barrier occurs when the wavelength of the sound is smaller than the barrier dimensions. Since no one dimension of a functional building can be less than 3 m, it can be said that this condition always obtains, however, for this purpose there is a control operation at the start of the procedure (Fig. 1). By considering the determination of the values of parameters related to the direct and diffracted waves as an analytical problem, a three-dimensional co-ordinate system has been established and the origin has been assumed to be at the meeting

SELMA KURRA

334

_ldot ermiret ~onof the 1 to total b;lrrler

/ ~ toat,,~, I the ;t'~''~co'di"g varl(~Js

[ x$.ya,zs

i coordinates L xr, y r , z r

ioufc e _r eoever geometries ~

j

JI '

frocluencies

,

det er ruination of $our~l attenuation by buitSng barrier

PROCESS B

~

1

PROCESS A

sound velocity ! c l b e apl

'

4Catzutati,an~.

•

CII. C 'Jr I t il~'l $ O~

the ~L'Jes of ~t ~ e n u a t l o ~

t

'

matrix of coordinate rltat;ons

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of-

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b

t

,

~

i

,

i

" I- i

~ [

£ '~

•

~L_:

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:

, .

Fig. 1. Process for calculating the sound attenuation by a barrier-building for a point source. point of the vertical symmetry axis of the receiver-side of the barrier with the ground. Every point whose position it is necessary to know has been expressed with its coordinates in this system and prepared in tabular form (Fig. 2). In the process the abscissa of the receiver whose height is lower than the height of the barrier can be changed between + I/2 ( / = length of the building) behind the barrier. The location of the source can also be changed within the angles of view of the receiver. In order to apply this method for numerous point sources on a line in one photograph for traffic noise calculations using the Galloway-Clark method, it is thought to be more simple to scrutinise the possibility of locating the source separately in either of the two regions shown in Figs 2 and 3. Input of the program includes the co-ordinates of source (xs, ys, zs) and receiver

PREDICTING SOUND ATTENUATION BY BARRIER-BUILDINGS

~. ........

OlK~'minotion of the source position

335

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s,

ISa

S

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I q K S U t . T : Varlati~ of attenu=tlqm IN b a r r i e ' - b u l t = ~ retated to ttte ~,equettcies.

effect

Fig. l--contd.

(xr, yr, zr) and the dimensions of the barrier-building (b, l, h). In addition the sound velocity and sound frequencies should also be given as data. Lastly, the effect of wind has been neglected and the climate has been assumed to be an homogeneous, loss-frec medium. As the changes in ambient temperature would influence sound, sound velocity can be changed within the data according to the relative humidity and temperature. Atmospheric absorption, which is very small in the frequency range associated with traffic noise, and other environmental factors, can easily be added to the process when they are treated as excess attenuations. The procedure for estimating the attenuation of sound by a barrier-building consists of two steps. (1) The determination of the attenuation values. (2) Controlling the process for different geometries.

336

SELMA KURRA

'

/~.:

,,-

~B N

~

~~ .

o(~ ~ -~ \ ~

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i/

..i

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0

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,,.2

0

..-,

°~ L

o

U.I I'OU% tY

I,LI 0,..

r,i d~

337

PREDICTING SOUND ATTENUATION BY BARRIER-BUILDINGS

t/2~ xs:"'l/2

IIl. z o n e

c~

S

~.,

o

II. z o n e

,o2

(~

® SS

R

@

o '

"".

?

R Fig. 3.

?Y 3/o2

-l~

R GETBB

,,.

"

.o

R

Different source-barrier-receiver geometries and the functions which will be calculated in the program.

Parameters related to attenuation by thin barriers In order to estimate the attenuation achieved by a barrier larger than half a wavelength thick by means of the Fujiwara-Maekawa procedure, the total attenuation has been assumed to be composed of the effect of a virtual thin barrier and the effect of thickness. As shown in the barrier geometry in Fig. 2, for the calculations for a thin barrier, sound waves are supposed to be coming from the virtual sources, S', to the virtual barrier. In the sub-process, parameters affecting the calculation of the attenuation achieved by a thin, infinite barrier are the wavelength of the sound to be analysed and the path difference (6) between a direct sound ray from the source to the receiver and a diffracted sound ray in the shortest path.

338

SELMA K U R R A

The length of the direct wave is denoted by: d = S'IR = x/(xs'l

-

xr) 2 + (ys' 1 -

yr) 2 +

(zs' 1 -

zr) 2

(1)

When a barrier is inserted between the source and the receiver, the length of the diffracted ray is: A + B = S'lO 1 + 01R

= x/(xsl

_ xo)2

+ x/(x01

+ ( y s , l _ y 0 1 ) 2 , + ( z s , 1 _ z o 1)2

- - x r ) 2 + ( y o I -- y r ) 2 + ( z o I - - z r ) 2

(2)

The points S'~ and O~, whose co-ordinates are required for the above equations, are on the same plane ( D a ) which involves both the source and the receiver and is perpendicular to the ground. If the length of the barrier is finite on both sides, two more diffraction zones occur in addition to the diffraction at the top of the barrier and it is necessary to integrate all the contributions of total excess attenuation from all three sides. 36"37 The shortest paths of the side diffractions can be calculated by means of the co-ordinates of points S 2, 0 2 and S 3, 0 3, as explained above. These points are on the same plane (defined as D b in Fig. 2) whose intersections with the vertical surfaces of the barrier; facing either source or receiver, are horizontal lines. If the heights of the source and the receiver are not equal, this is a sloping plane with reference to the ground. The coordinates of S'l , S~, S~ and O1, O 2, 0 3 have been expressed in terms of input data by using the equations of projection-lines of sound paths in the planes of X O Y and ZOY. To make them convenient for use in calculations, these co-ordinates have been collected as a matrix of co-ordinate relationships called subroutine A K O R in the program (Table 1). For a reflective ground, four possible sound paths for the real and the imaginary source and receiver can be considered 34 as shown in Fig. 4. In the computer program, the whole process is repeated by taking z s = - z s or z r = - z r according to the situation, and the resultant attenuation is obtained by superposing the individual contributions, as in Maekawa's proposal. 36"37 After the path differences (6) are calculated, the attenuation of a thin, infinite barrier can be obtained by the following process 21'33 with the aid of function S A T T O in the main program: N (Fresnel number) = -

[Att]o = 5 + 20log

~ d B tanh x/2n N

26 2

for N > 0 (shadow zone)

[Att]o = 5 + 201°gtan -,,/2nlNb -'==~=-- dS for 0 > N > - 0 . 2 (transition zone)

(3)

(4)

(5)

PREDICTING SOUND ATTENUATION BY BARRIER-BUILDINGS

[Att]o=5dB

forN=0

[Att]o = 0 d B

for N < - 0 . 2 (bright zone)

339

Parameters related to the calculation o f the thickness effect

Parameters in the second sub-process affecting the calculation of the effect of thickness according to reference 41 are the K factor related to profile angle, wave number (k) and effective barrier length. Profile angles which exist on the Da plane in Zone I and the Db plane in Zone II can be denoted here after the calculation of the required co-ordinates and lengths of the pieces of the diffracted rays. These angles are shown in Table 2 as a matrix whose terms are functions of the known values. The terms of the matrix are computed with the aid of subroutine VERI in the program. When the line between the source and the receiver is not perpendicular to the barrier, it is necessary to suggest an effective barrier length which can be calculated by means of the O~, O'~, 0 2, 0'2 and 0 3, O~ points. The co-ordinates of 0'~, 0'2 and O~ have been obtained as mentioned above and are shown in Table 1. For the purpose of calculating the thickness effect, Fujiwara et al. 38'41'43 have presented a simple chart to be used for arbitrary combinations of profile angles instead of an impractical calculation of the complex split functions to derive the total diffracted sound waves. Since, in this study, the aim has been to write a computer program and as the calculation used by the above-mentioned investigators is also inconvenient for simple programming, an empirical equation has been derived from the curves of the original chart, as denoted by:

y=-

.4+'4 ~

(6)

`4 = a o + a 1K + a2K 2 + a3K 3 + a4K 4

(7)

B = b o + b l K + b z K 2 + b3 K3 + b4K 4

(8)

The a o, a I , a 2, a3, a 4 and b o, b 1, b 2, b 3 and b4coefficients have been obtained a s t h e following values after the solution o f t h e e q u a t i o n s with four unknowns: a o = 64-6715 a~ = 2.7239 a2 = 0.0276 a 3 = -0.0275 a4 = 0-0045

bo = 7.395129 bI = 4"9345049 b z = -2"677782 b3 = 0"9082329 b, = -0"0624841

In eq. (6), y and x correspond to the profile angles (0 and ®). In the program, one of the profile angles (say ®) can be taken as 'x' and then 'y' can be calculated assuming K = I initially; the other angle (0) and y, calculated by iteration, are then compared. The K value which gives 0.1 difference after comparisons is used in eqn. (9)

I

+

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t ~ it

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If

~

-II

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I A

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il

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II

II

II

,m

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+

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c-.

342

SELMA KURRA

0

I , |

~

/ ~/

I

\ x

I

~J 0 Fig. 4.

~JR'

R"

b

Propagation paths of direct and reflected sound waves from the ground (a) without and (b) with a barrier.

TABLE 2 MATRIX FOR C A L C U L A T I O N OF PROFILE A N G L E S

(.[ETk)

O_ TETA

0_ T I T A

Zone I GETBA

f ~ / s o i ~ - (z~ - h) ~]

arctan L

arctan [ x / R O ~ ( _ z ~

J+n

zs-h

1+~

ye < - b

Zone II GETBB

arctan~x/SO'22-(-v°'2-xs)2]+ I_ xo'2 - xs

n

arctan[x/RO~-(x°2-xr)2]+ L xo 2 - xr •

n

Zone I!I GETBC

F,/so;

arctan [

~- ~

- ~o'~)2 q

x ~ _ xo3

J+n

arctan [ x / R O ~ - ( x r - x°3)2 ] + n L xr - xo 3 3

Zone I GETBE

[ ~ / S O ' ; 2 - ( z s - h )2 7

arctan L

zs--h

J+n

I-~/go~- ~z~-h)~] +

arctan [

zr- h

ye > - b

source in region A Zone l GETBG

F , / s o ' ; '2 - ( z s - h) 2q

arctan [

~s--h

J+ n

ye > - b

source in region B 1

2

J

343

P R E D I C T I N G S O U N D A T T E N U A T I O N BY B A R R I E R - B U I L D I N G S

,[ET]b = K l o g (kb) dB

(9)

This process, used to obtain the value o f , l E T ] b, is carried out in the program with the G E T B function. Figure 5 shows the original curve and that calculated using the above approximate procedure. The standard error is 0.12 in the K = 0-9 region and 0.16 for K = 9-10. Consequently, sound attenuation of a barrier, b thick, due to diffractions from either the top or the sides of the barrier can be expressed as: 41"46 [Att]b = [Att]o + .[ET]b

(10)

]

]

t~ v

O ~u O~ r" ill

]

°~

oL . t3t.

90 °

120"

150"

180"

wofRe angle 0 (0) Fig. 5.

C h a r t for effect of t h i c k n e s s ; c o m p a r i s o n of o r i g i n a l a n d c a l c u l a t e d curves, 43; . . . . . . e q u a t i o n 6.

after reference

Parameters related to the calculation of the wedge effect In the specific case of the very oblique incidence of sound waves on the barrier which can be met in traffic noise calculations, the effect of the wedge angle should be determined. Maekawa 22 and Fujiwara et al. 46 have presented a chart for obtaining the right-angle wedge effect which will be subtracted from the attenuation of the thin

344

SELMA KURRA

barrier after calculations similar to the method used for obtaining the effect of thickness. The parameters are the angle of incidence and the angle of diffraction (Fig. 6). In the procedure, since the wedge effect cannot be mentioned for diffractions at the top of the barrier because of the prior assumption that the receiver and source heights are below the barrier height, for side diffractions the angles of incidence (0') and diffraction (¢) can be denoted by the equations shown in Table 3. These have been obtained by means of the analytical expression for an angle between a given line and a plane within the space and it is possible to calculate them by calling the subroutine VERII in the main program. In order to be able to use it in computations, a simple expression (eqn. (10)), has been derived from Maekawa's chart for determining the effect of a right-angle wedge with a standard error of estimation of 0-25. This sub-process is executed in the program by the WET function.

III. zone

Fig. 6.

II. z o n e

Scheme of incidence a n d diffraction angles. TABLE 3

MATRIX FOR C A L C U L A T I O N

(n[ET])

OF I N C I D E N C E A N D DIFFRACTION ANGLES

$-PSI

0'- T E T A 1 a 2 = XS

- -

XO 2

b 2 =ys--yo

a I =xr--xo

C 3 = ZS -- ZO 2 2

WETD

--0

arctan . . . .

2

v/b~ + c~

arctan

btx/bi

a4

I

2

+c~-alx/a~

+c~

0 3 ~ zr -- ZO 3 2

arctan - ~/b42 + c,,2

2

a 3 = x r -- x o 3 b3 = y r - y 0 3

3

C4 = ZS -- 203

WETF

2

x/al +ct ~/b 2 +c z +bta 2

a 4 = X.S -- XO 3 b 4 =ys--yo

2

b t =yr-yo 2 c I =____zr- z o 2

2

arctan

2'

2

2

~ / a , + c 3 x / b 4 + c 4 -- b a a ,

2

345

PREDICTING SOUND ATTENUATION BY BARRIER-BUILDINGS

[EW]n= -(0"0311+0-083.tg10')(~d/-3)

(11)

Figure 7 shows the original curve and that calculated using the above equation. wed9e angLe = 90°

-1

-2

o

•'~

\

-3

"\

U

tD

\

lIP

0 incidence an~e

-~-~,,- ~, ~

\

.... ~6 0Q

10"

20"

30"

/.0 °

50 °

60"

equation

(1.1)

I

I

70 °

80 °

90*

diffraction an~e

Fig. 7.

Chart for effect of wedge angle: comparison of original and calculated curves. Photograph shows experiments in the anaechoic room.

346

SELMA K U R R A

When a wedge effect is considered the thin barrier attenuation can be obtained for the S 0 2 R and S03R diffraction paths and the required parameters are easily calculable. The resultant attenuation is: [Att]n = [Att] o + [ET] n

(12)

Combination of the contributions to the total attenuation The attenuations for diffraction at three sides of the barrier-building should be superposed by considering them to be negative values. 36"37 This procedure can be carried out by taking only one reference level instead of using three reference points, as explained in references 36 and 37, and neglecting the term [ - N ~ ] or [AL_ a] since its value is always 0 under the conditions of zr < h, -1/2 < xr < + l/2 and the source only is within the angles of view. These assumptions result in the superposition of the three attenuation values by means of the D B T O P function in the program and to this is added the effect of the excess attenuation by distance without a barrier in order to obtain the total attenuation. Control operation of the process in different geometries This step involves the selection of the sub-programs in order to determine the effects which will be contributed to the total barrier attenuation and to choose the parameters which will be used in the sub-processes, depending upon the diffractions occurring in various configurations. The locations of the source and the receiver relative to the barrier, which are determined by their co-ordinates, can be at three alternative positions. As has already been explained, to facilitate the computations in the application to linearly placed multi-numbered point sources, five alternative geometries can be considered in two regions separated by a perpendicular line from the receiver to the barrier. These regions are in the projection plane within two angles of view from the receiver. The program FSATT repeats the computations for whole sound frequencies and for the image source and image receiver. Scale model experimental study In order to establish the validity of the procedure described in this paper as a computer technique, it is both appropriate and convenient to use scale modelling. ~2.14.15.48.49 A significant advantage of scale modelling is that it allows barrier heights, lengths and widths to be readily changed and enables free field conditions to be simulated. The anechoic chamber, 2.85m high and with a 3-00 x 4.80m 2 floor area, belonging to the Electricity Faculty of ITU was available for carrying out the measurements. The model scale was chosen as 1/20 based on source and room characteristics. The barrier-building models were constructed from half-inch thick fibre board as box shaped rectangular prisms and filled in with sand pack pieces to

PREDICTING

SOUND

ATTENUATION

347

BY B A R R I E R - B U I L D I N G S

E o

t--

O

tO o~

t.,.

..=

o e.

e,

U

.2

t:

C

q

o

¢,0

._.q "0 at~

t'~ .,O

~t

o t-, r~

,=

-r-

°' #

t...

•

a:

•

r

348

SELMA KURRA.

prevent sound transmission through them. To enhance the relevance of the surfaces of model barriers to external walls, they were varnished so that reflection coefficients corresponded to painted plaster. The sound source employed for the experiment was an omnidirectional miniature air-jet similar to that developed by Delany et al.14 This source had a reproducible broad band noise which gave a similar spectrum and directivity characteristics to those mentioned in references 14 and 49. The measurement procedure was carried out by taking values at frequencies of 2.5, 5, 10 and 20kHz, corresponding to 125, 250, 500 and 1000Hz, respectively, with a reference microphone positioned 20cm from the source and the receiver microphone before and after the barrier models were in position. The experimental set-up is shown in Fig. 8. The dimensions of the model barriers were changed as follows: length 15, 30, 60, 90, 150, 180, 210, 240 and 270cm for a 15cm height and a 15 cm width, and heights, 15, 30, 45, 60, 75 and 90 cm (corresponding to a building of between one and six floors)for 15 cm width and 270 cm length. The source height is taken at about 3 cm, corresponding to the source height of vehicle noise. The height of the receiver microphone was varied between 5 and 75 cm. Due to the possible effect of ground reflections, it was decided to obtain the results in the free-field and to compare them with the calculated results by modifying the program. The walking floor of the anaechoic room is a metal grid positioned at the 1 m height of the wedge elements. It was first covered with thick hardboard and then with hard glass wool panels. After the measurement of room performance in this situation, it was seen that the free-field conditions were divergent due to the absorbent floor-covering, therefore some correction factors obtained from the charts 5 have been applied to the results, especially for low receiver heights. Distance from the source to the barrier was fixed at 60cm (12.00m in the full scale). Figure 9 shows that calculated and measured attenuations agree quite well.

APPLICATION OF THE COMPUTER PROCESS

The model has been applied to different building dimensions and receiver distances from the barrier in order to determine the effect of different parameters on sound attenuation. The results are plotted in Figs 10, 11, 12 and 13. After interpretation of these graphs, the results can be summarised as follows. The curves for separate variations in the height and length of the barrier-building rise more or less parallel for a building with a constant width and for a constant distance between the source and the receiver, although the variation in height is more crucial to barrier performance. Both effects increase the sound attenuation until certain values are reached when the results change in small increments. The effect of varying the width by fixing other parameters is a very steep increase in attenuation. This is due to the fact that widening the barrier results in smaller distances from source to barrier and so the barrier's performance improves.

349

PREDICTING SOUND ATTENUATION BY BARRIER-BUILDINGS 1.0

3[

**

30

** •

•

ee

*o

$"

•

e/:

25~

20

15

10

*

I

5

Fig. 9.

*

I

10

6.~

I

15

I

20

I

25

CAL!U~ATED 30

35

4O

Comparison of calculated and measured attenuations by barrier-buildings for a point source.

CONCLUSIONS

(1) (2)

(3) (4)

(5)

By means of supplementary work on existing models it is possible to calculate noise levels in terms of the frequency spectrum behind a given building used as a barrier against noise and located in a reflective ground. The technique described can be used to establish meaningful relationships between various parameters related to sound diffraction of thick and finite length barriers and their sound attenuation and also to produce simple graphs from the results of the calculations for use by planners. Other environmental factors, so long as their effects are expressed as independent excess attenuations, can be added to the program to achieve a real simulation of the environmental conditions. By applying this computer model to different linear point sources and integrating the results using Kurze and Anderson's line source equation,21 it is possible to determine the barrier performance for an infinite line source. The procedure can be used to assess the cumulative distribution of traffic

350

SELMA KURRA i

15

d

125 Hz.

i

H,,IZ,iL. ;nL

i/ii; 13

/

12

i

:

:

1

'

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]

BxLxH

i

1~3, L;6m. hlJ:3, L=3m.

,.--'-'r--i-- i

10

I

9

,

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(

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I

I

I

I I

I

8

2,.50 Hz

16 nn

distance from recieverto barrier: 12 m.

I

r

11

distance from source to borrier: 10 m.

/I'H,3,J

L,6 m.

15

'I0

~ 6 , B.~3m.

z o

lt.

:3 zhi

13

/

.....

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In the free-field the effect of the variations in barrier dimensions on barrier performance . . . . . . variation of L; . . . . . . variation of H; variation of B.

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353

PREDICTING SOUND ATTENUATION BY BARRIER-BUILDINGS

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Fig. 13--contd.

(6)

noise behind the buildings s considering the traffic stream to be a sequence of moving point sources, by means of the Galloway-Clark technique. 6'24 The main purpose is to control noise at the site planning stage. This procedure can be used as a sub-program in different investigations, written as computer programs related to sound propagation and noise control in an urban environment. The model can also be supplemented with mathematical models of other problems such as sound reflections from vertical surfaces of other buildings, 2'3°'51 effects of the gaps between the buildings, sound diffusion by corners, 5° etc.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

K. W. YEOW, Journal of Sound and Vibration, 57(2) (1978), pp. 203-24. A. D. CLAYDEN,R. W. D. CULLEYand P. S. MARCH, Applied Acoustics, 8(1) (1975), pp. 1-12. VON H. GOYDKE, W. KALLENBACHand H. J. SCHROEDER, Acustica, 20 (1968), pp. 276-88. M. E. DELA~qV,W. C. COPELArqDand R. C. RAVNE, NPL Acoustics Report, AC 54 (1971). S. KURRA,A Method for Predicting the Criteria Units Relevant to the Areas Behind Buildings Which Are To Be Used as Barriers Against Traffic Noise, Istanbul: 1TU Faculty of Arch. Pub., Thesis, 1977. J. W. GALLOWAY, W. E. CLARK and J. S. KEVRlCK, National Cooperative Highway Research Programme Report 78, 1969, Appendix C. W. E. SCHDES,A. M. MACKIE,G. H. VULKANand D. G. HARLAND,BRECurrent Paper, 50(1974). G. REINI~OLD, Strassenbau und Strassenverkehrstechnik, 119 (1971). W. E. SCHOLES,A. A. SALWDGEand J. W. SAgGENT, Journal of Sound and Vibration, 16(4) (1971). pp. 627-42. E. F. STACY, P. J. ARNOLDand S. J. LEACH, BRE Current Paper, 48 (1974). E. A. MOHSEN,Department of Building Science, University of Sheffield Report, No. BS16, 1975. M. RIrqGHEIM, LBA 335 Akustiks Laboratorium, Trondheim-Norway (1971). M. Y^MASmTAand M. KOYASU,Applied Acoustics, 6(3) (1973), pp. 233~42. M. E. DELANY,A. J. RENrqIEand K. M. COLLINS, Report AC 58, NPL, 1972. M. RINGrlEIM, LBA 461 Akustiks Laboratorium, Trondheim, Norway, 1972. J. STRVJENSIq, D. COURTILLATand T. DUBOULOZ,B&K Technical Review (2) (1973), pp. 39-50.

PREDICTING SOUND ATTENUATION BY BARRIER-BUILDINGS 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51.

355

W. PORADA,Applied .Acoustics, 8(4) (1975), pp. 271-80. S. LJUNGGREN,DI0, National Swedish Building Research, Stockholm, 1973. J. DXCmNSON,Design Bulletin No. 26, Dept. of the Environment, London, 1972. ANON., Dept. of the Environment, Welsh Office, 1975. U. KURZE and G. S. ANUE~ON, Applied Acoustics, 4(1) (1971), pp. 35-53. Z. MAEKAWA,Proc. Eighth International Congress on Acoustics, London, 1974. B. LUNOQUlST,Report 3, Byggjforskningen, Stockholm, 1969. E. A. MOHSEN, BS31, Department of Building Science, Fac. of Arch. Studies, Univ. of Sheffield, 1976. W. E. SCHOLES,A. SALVlDGEand J. W. SARGENT, Applied Acoustics, 5 (1972), pp. 205-22. W. E. SCHOLESand J. W. SARGENT, BRE Current Paper No. 20, 1971. W. E. SC.OLES, BRE Current Paper, No. 26, 1974. H. G. JONASSON, Journal of Sound and Vibration, 30(3) (1973), pp. 289-304, W. E. SCHOLES,A. C. SALVIDGE,J. W. SARGENTand D. J. FIsK, BRE Current Paper No. 35, 1975. B. FAVRE,Centre D'evaluation et de Recherche des Nuisences lnstitut de Recherche des Transports (IRT) Lyon, No. 657-41 (1974). B. FAVRE,Centre D'evaluation et de Recherche des Nuisences Institut de Recherche des Transports (IRT) Lyon (1975). E. A. MOHSEN, Applied Acoustics, 10(4) (1977), pp. 243-57. L. L. BERANEK,Noise and Vibration Control, McGraw-Hill, 1971, p. 175. Z. MAEKAWA,Memoirs of the Fae. ofEng, Kobe Univ., No. ll (1965), pp. 29-53. Z. MAEKAWA,Applied Acoustics, I (1968), pp. 157-73. Z. MAEKAWA,Memoirs of the Fac. ofEng, Kobe Univ., No. 12 (1966), pp. 1-12. R. J. ALFREDSONand B. C. SEOW, Applied Acoustics, 9(1) (1976), pp. 45-55. K. FUJIWARA,Y. ANDO and Z. MAEKAWA,Applied Acoustics, 10(2) (1977), pp. 147-59. E. S. lvEY and G. A. RUSSELL,Journal of Acoustical Society of America, 62(3) (1977), pp. 601-6. U. J. KURZE, Journal of Acoustical Society of America, 55(3) (1974), pp. 504-18. K. FUJlWARA,Y. ANDO and Z. MAEKAWA,Acuslica, 28 (1973), pp. 341-7. A. D. PIERCE, J. Acoust. Soc. Am., 55(5) (1974), pp. 941-55. K. FUJIWARA,Y. ANDO and Z. MAEKAWA, Proc. Eighth International Congress on Acoustics, London, 1974. H. G. JONASSON, Journal of'Sound and Vibration, 25(4) (1972), pp. 577 85. Z. MAEKAWA,N. NAPANOand Y. ANDO, Faculty of Engineering, Kobe University Report of Meeting o/Society of Japan, 1972, pp. 461 2. K. FUJIWARA,Y. ANDO and Z. MAEKAWA,Applied Acoustics, 10(3) (1977), pp. 167-79. H. G. JONASSON, Journal of Sound and Vibration, 22(1)(1972), pp. 113-26. E. A. MOHSE~, BS20, Dept. of Build. Science, Fac. of Arch. Studies, Univ. of Sheffield, 1975. E. A. MO.SEN, BS21, Dept. of Build. Science, Fac. of Arch. Studies, Univ. of Sheffield, 1975. R. BULLENand F. R. FRICKE, J. Soundand Vibration, 46(1) (1976), pp. 33-42. M. E. DELANY,A. J. RENNIEand K. M. COLHNS, J. Soundand Vibration, 56(3) (1978), pp. 325-40.