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Barriers' efficiency dependence on types of environments
Applied Acowfics 44 (1995) B-324 0 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0003-682X/95/59.50 ELSEVIER
0003-682X(94)00028-X
Barriers’ Efficiency Dependence on Types of Environments* E. Walerian, M. Czechowicz$ & R. Janczur Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland (Received 5 January 1994; revised version received 18 June 1994; accepted 8 July 1994)
ABSTRACT Real, thin barriers are limited in length and have a finite isolation. Thus, it is hard to treat them as ideal half-planes for which the insertion loss in the free space is defined, The real features of barriers and interactions with the environment cause their efjiciencies (the barrier shielding efficiencies) to be drastically lower than the insertion loss. In this paper, simple means for allowing one to avoid the influence of the real barrier features, i.e. its length and isolation, are given. Also, simple expressions for the barrier shielding eficiency in dtflerent environments are presented. The experimental results for a barrier in the pseudo-free field: on the ground and under the roof, are shown. Further investigation in a more densely occupied space, such as an industrial hall, is also represented.
NOTATION a b
zl
Distance from source to barrier edge (Fig. 1) Distance from observation point to barrier edge (Fig. 1) Sound speed Distance between source and observation point (Fig. 1) Distance between barrier and observation point (Fig. 3) Coefficient describing the geometrical shielding of observation point P by barrier
*Sponsored by PZWK (Poznan Factory of Cork Products), Poland. STo whom correspondence should be addressed. 291
ul. Ksiazeca
1, Poznan,
292
E. Walerian, M. Czechowicz,
R. Janczur
Center frequency of ith octave band Insertion loss of ideal barrier in free space A-weighted acoustical energy flux at point P,in industrial hall Sound (pressure) level at point P,in free space L”, (P) Sound (pressure) level at point P,behind barrier, in free space L2 (P) Sound (pressure) level at point P,in real system with reflecting 4 (P> panels Sound (pressure) level at point P,behind barrier, in real system 4 (P) with reflecting panels Barrier shielding efficiency in real system AL N Fresnel number Acoustical pressure in ith octave band Pw p x p(O) Observation point located at worker’s head position, 1.5 m above floor p’, p(i=I) First-order image observation point Q = Q(O) Noise source @, Q@=‘) First-order image noise source A-weighted power of Ah source expressed in mW (A) Q (0 Effective room constant R Room constant measured for ith octave band R (4
f(i)
IL
a!
a (4 Ql (32
P s
Barrier effective absorption coefficient Barrier absorption coefficient for ith octave band Coefficient describing decrease of direct wave energy from In-th shielded source Coefficient describing change of reverberant field after barrier application Barrier effective reflection coefficient Difference between wave path through edge and direct distance from source to observation point
1 INTRODUCTION Barriers are frequently applied as protectors against noise, where the so-called shadow area is used. The barrier efficiency as a noise control measure depends on the barrier itself and its interactions with the environment. All these factors cause degradation of the barrier efficiency. In the free space the barrier efficiency is determined by barrier acoustical features and the source-barrier-observation point geometry, and is defined as the insertion loss:
Barriers’ esciency
dependence on types
of environments
IL = Li (P) - L2 (P)
293
(1)
In the case of the ideal half-plane in the shadow area there is only the wave diffracted at the half-plane edge. As a real barrier is never the ideal half-plane it is less efficient than the ideal one. For the real barrier some special means have to be undertaken to prevent a decreasing of its efficiency caused chiefly by its limited length and finite isolation. In a real system, containing obstacles of reflecting surfaces, an inserted barrier acts not only as a screen, but also as an additional reflecting panel. This causes further degradation of a barrier efficiency. To distinguish between the insertion loss (eqn (1)) defined in the free space, and the barrier efficiency in the real system, the notion of shielding efficiency is introduced: AL = L; (P) - L; (P)
(2)
In this paper, it is shown how the barrier efficiency decreases with a growing number of obstacles in a space. A prediction of the barrier shielding efficiency needs the assumption of a barrier model and a model of the acoustical field in the system. The accuracy of prediction depends on the applied models’ accuracy and accuracy of the model parameters’ estimation. Here, simple expressions, accurate enough for technical purposes, are given for calculation of the barrier shielding efficiency in different environments.
2 THE EFFECT
OF THE BARRIER
APPLICATION
2.1 The efficiency of ideal barrier in free space Treating the Kirchhoff diffraction theory, which assumes a nonreflective, opaque half-plane screen, as a good approximation,i4 Maekawa gives the expression for reduction of the sound pressure level of frequency fat the point P in the shadow area (Fig. l), where only the wave diffracted at the upper edge exists:’ ILM (f, P) = LI (f, P) - L2 (f, P) = 10 log (20N + 3) (dB) N=; 2f (a+b-d)
=O.O058fS
(3)
(4)
294
E. Walerian, M. Czechowicz. R. Janczur
\
Q,,l-
\
\ P’ .
(b)
Fig. 1. The barrier applied in the system containing only the ground, Q-a real source; Q’-an image source; P-an observation point; P’-an image observation point. (a) Situation without a barrier; (b) situation with a barrier.
Thus, the sound pressure level reduction ILM (1; P) gives the insertion loss (eqn (1)) of a barrier in the free space. 2.1 .I Eficiency of barrier for signal of defined spectrum ]It is possible to calculate the barrier insertion loss for a signal of the defined A-weighted, relative power spectrum: V(i) =
P’ (i) a(i) T p2 (i) a (i)
(5)
where the A-weighting coefficient a (i) is related to the A-weighting curve ALA (i) as below: a
(i)
=
100”
“A
(i) (6)
When the barrier insertion loss for the ith octave band is known IL [f(i)] = IL (i)
(7)
then the barrier overall insertion loss is given by
IL [dB (A)] = -10 log
10Po” iLCi)V(i)
c i
(8)
295
Barriers’ efficiency dependence on types of environments
By use of the Maekawa formula (eqn (3)) for the barrier insertion loss IL (i) calculation, the barrier overall insertion loss can be expressed as
ILM [dB(A)l =-l”log
7
o_ll$;a+3
1
which gives the sound level reduction. 2.1.2 Eficiency of jinite size barrier The real barrier is always sited on the ground. When there is no gap between a barrier lower edge and the ground (floor), then there is no diffraction at the lower barrier edge. The diffraction effect caused by the junction of the ground and a screen, in the first approximation, can be omitted.’ Thus, when the barrier is thin and opaque, it can be treated as a half-plane screen, for which diffraction occurs only at its upper edge. For barriers being screens of limited length, and for screens with edges of more complicated shape, the theories can be applied independently to each straight line segment of the edge.“’ In the case of a barrier of limited length the diffraction at side-edges makes the barrier efficiency lower. To avoid this the barrier ends can be folded in the direction of a source or an observation point. Then, the side diffraction waves have negligible amplitudes as their Fresnel numbers N (eqn (4)) are large. In the case of a barrier applied in a room the side diffraction can be eliminated by a barrier extension up to the room wall. For the wall-screen junction the same assumption is valid as for the groundscreen one. 2.1.3 Eficiency offinite isolation barrier When a barrier has a finite isolation, then a portion of the acoustical energy is transmitted into the shadow area through a barrier. In effect, the insertion loss ILr of a barrier of a finite isolation may be diminished’ and in this case is given by ILr = -10 log [10-O” IL + 10-O”rr]
(10)
where IL is the insertion loss of an opaque barrier, and TL is the transmission loss of the real barrier. Equation (10) can be used for a pure tone or for a signal of defined spectrum. For some typical values of IL and TL, the barrier insertion loss ILr is calculated in Table 1.
E. Walerian, M. Czechowicz,
296
The Insertion
R. Janczur
TABLE 1 Loss of a Barrier of Finite Isolation
IL
TL
TL - IL
IL-r
30 25 20
20 20 20
-10 -5 0
19.59 18.81 17.00
Light barriers of about 3 m height, when applied in industry, have the insertion loss for high frequency of about 20 dB. For this range of frequencies one should assume that the isolation of barriers should not be smaller than 25 dB. 2.2 The shielding efficiency of barrier in pseudo-free field The simplest real systems in which a barrier can be applied are the systems containing the ground, or a floor and ceiling. The shielding efficiency of a barrier is affected by reflections from the ground and reflections between a floor and a ceiling. When the influence is small then the conditions under which the barrier acts can be called the pseudo-free field conditions. By use of the Rubinowicz theory” the interaction of the acoustical wave with an obstacle can be divided into the geometrical reflection and diffraction at edges. In a real system the multireflections of geometrical waves and born at edges diffraction waves are equivalent to an existence of image-sources and/or image-observation points.8,9,” The calculation procedure based on this concept can be easily executed in the case of a simple system, but for a complex system it results in a long computation time.“-13 In the case of the ground (floor) existence the barrier shielding efficiency (eqn (2)) assumes the form:
AL, (8 = 10log [P’ (Q, P) +p2(e’, p,] -
10log [p2 (Q, E, P) +p2(Q, E, P’>
+ p2
(Q',
(11)
E, P) + p2 (Q’, E, PI,]
The level L; (P) (Fig. l(a)) is formed
by two waves: the direct wave
p (Q, P) from the source Q and the wave p (Q’, P) from an image source
Q’9 representing the wave reflected from the ground. After a barrier application the level L; (P) (Fig. l(b)) is formed by four diffracted waves.
Barriers’ ejkiency
dependence on types of environments
297
The wave p (Q, E, P) and the wave p (Q’, E, P) reach the observation point straight after diffraction. The wave p (Q, E, P’) and the wave p (Q’, E, P’) reach the point P after being reflected from the ground, behind the barrier. Their reflections are described as reaching the point P’, being the mirror image of the point P with respect to the ground surface. When a barrier acts in the system containing a floor and a ceiling (Fig. 2), then the level L; (P) is created by the direct wave p (Q(O),P(O)) and an infinite number of waves p (Q (‘4, P(‘))reflected from the planes of the floor and ceiling. The level Li (P) is formed by diffracted waves p (Q@), E, P(O)) coming straight after diffraction to the point P(O) and waves p (Q@) ,E, P(j)), which, after diffraction, undergo reflections between the floor and the ceiling. This results in the barrier shielding efficiency:
Q”’
~ .
*
*
.
(4 ($2
t,
,
P(2)
I
\
/
\
J
\
/
\ \
/ ,
Fig. 2. The barrier applied in the system containing a floor and a ceiling with the first two image sources Q (I), Q(‘) and observation points P (‘1, Pc2) representing reflected waves. (a) Situation without a barrier; (b) situation with a barrier.
298
E. Walerian, M. Czechowicz,
ALfc = 10 log
fi:
R. Janczur
p2 (Q'k',
k=O -
10 log
P(O)) I
2
2
k=O
j=O
p2
(QCk’, Pti’)
1
(12)
The number of reflections before diffraction (k) and after diffraction (j) can be limited when the ceiling is not parallel to the floor. However, for a ceiling of complicated form, additional diffractions occur at its wedges, which makes description of the barrier shielding efficiency difficult. Generally, only the first few terms in eqn (12) have to be taken since the next ones have strongly decreasing amplitudes. When the Maekawa formula is used to express the shielding efficiency of a barrier on the ground, then eqn (11) assumes the form:
ALMg (f’) (dB) = 10 log
6, =a+b-d
(14)
&=a+b’-d
(15)
63 =a’+b-d
(16)
6, = a’ + b’ - d’
(17)
For the signal of defined power spectrum (eqn (5)) the overall shielding efficiency of a barrier on the ground is given by
ALM, [dB (A)] = 10 log
Barriers’ eficiency dependence on types of environments
299
2.3 The shielding efficiency of barrier in industrial hall The general procedure of finding the sound field description in a limited space is based on solving the wave equation for the appropriate boundary conditions. In complex systems it can be solved by the finite-difference method.‘4-‘6 This allows us to describe the field in the systems with screens which are treated as other obstacles of the given surface impedance. In industrial halls, by modeling the acoustic energy spreading, as phonons move randomly in a fitted space, a statistical description is applied. Special models, being a combination of the geometrical acoustics and the acoustical energy diffusion, are developed.‘7-28 In extreme cases, the statistical description results in the diffusion equation for acoustical energy spreading.‘9,23 Under special conditions29-3’ concerning a room size and its walls’ features, the part of the acoustical field caused by an enclosure can simply be the diffuse field. Here, this kind of mode13* is applied for the acoustical field in an industrial hall. This allows the simple estimation of the barrier shielding efficiency at the worker’s position. Here, the A-weighted acoustic energy flux: K =
10“’ L[dB(A)1-9 [(mW/m*)
(A)]
(19)
is used to determine noise at point P adequate for the position of the worker’s head.32-34 Basing on this, the overall shielding efficiency of a barrier shielding the ZE source may be expressed by:32
AL (k P) [dB(A) = LI (P) [dB (A)] - Lz (P) [dB (A)] = 10 log K(P) - 10 log KE (P)
(20)
Before a barrier application the energy flux K(P) at the point P is the sum of the direct wave energy flux KD (P) and the energy flux of the reverberant field KR:
K(P) = KD (P) + KR
(21)
The direct waves energy Ko (P) is the sum of the direct waves energy coming from all industrial sources modeled by equivalent point sources, radiating in the half-space:
300
E. Walerian, M. Czechowicz,
R. Janczur
(22) I=1
I=1
where Q (Z) is the A-weighted power of the Zth source estimated in situ. The reverberant noise field is expressed by A
N
KR=; c
Q(Z)
(23)
I=1
where R is the effective room constant determined spectrum V(i) in the analyzed room:
for an average noise
V(i)
1 -_= c R
i
(24)
R (i)
The room constant R (i) as a function of frequency is estimated from the decrease of sound pressure level with distance from the small, dominant industrial source sited in the middle of the room. After shielding the Zn-th source with a barrier the energy flux at the point P behind a barrier is: KE(~)=
The direct field component KDE
(p)
=
KD
(p>
KDE(P)+KRE(P)
(25)
is changed as follows: +
( QI
-
1) KD
[Q
(IE), P]+
AK,,
(f')
(26)
The barrier application diminishes the direct wave Ko [Q (ZE), P] from the In-th source, which is described by coefficient al. At the same time, waves from the nearest sources (different from Zn) can reach the point P through reflection from a barrier. This is described by the component AK,, (P) in eqn (26). Moreover, the barrier introduces an additional acoustic absorption to the room, and limits the share of the In-th source in generation of the reverberant field, hence: KRE=KR(~
-Qz)
(27)
Now, eqn (20), giving the barrier shielding efficiency, can be rewritten in the form:
Barriers’ eficiency dependence on types of environments
AL (IE, P) [dB (A)] = -10 log
1+
AKD,
(p>
K(P)
301
(28)
As can be seen from eqn (28), barrier shielding efficiency can be negative at some points when AK,,
(p) >
K(P)
p)
KD (IE,
(l-4
K(P)
+$
Q2
(2%
This happens when the reflections from a barrier prevail over the reduction of the direct wave from the shielded In-th source and reduction of the reverberant field. To find the explicit form of the coefficient (~1it is assumed that a barrier causes32 the exponential decay of the direct wave from the In-th shielded source. The decay factor is proportional to the relative angular dimension of a barrier seen from the observation point E(P). Thus [-E(P)]
~1 =exp
(30)
The coefficient ~1 can also be interpreted as the probability of reaching the shadow area behind the barrier by phonons from the direct wave stream. Both coefficients CX~,(~2 are related to the geometrical shielding of an observation point by a barrier E(P). The coefficient 02 (eqn (27)) describing the decay of the reverberant field is assumed to be:32 (32 =
E(P) 4n
(31)
The coefficient o2 also describes the probability of diffuse phonons scattering by a barrier. When in an industrial hall the single acting source (1~ = 1) of a power Ql is shielded by a barrier, then K(P) = KDI + KR
KD1 =-
Ql 2nd; ’
(32)
(33)
302
E. Walerian, M. Czechowicz,
AK,,
R. Janczur
(P) = 0
(35)
where &i is the direct wave energy flux and di is the distance between the source and an observation point P. The barrier shielding efficiency can be expressed according to eqn (28) as ALI
[dB
(A)]
=
Ah
r WI
[E(P),
-
-&
1 - exp [ - E(P)] [
I
(36)
r E(P) -_____ rfl
4II
1
’
where r(R)
=gzT
8IId;
(37)
is the ratio of the reverberant field energy flux and the direct wave energy flux. The overall shielding efficiency (eqn (36)) is expressed as the function of the geometrical shielding of an observation point E(P) and the room effective constant R, which appears in the parameter r definition (eqn (37)). The classical diffraction frequency dependence is absent. Only the as the average value effective room constant (eqn (24)) is calculated incorporating a room feature R (i) and noise sources spectrum V(i). When the energy flux of the reverberant field is small in relation to the direct wave energy flux: r< 1 then, calculating ,‘To
(38)
the limit in eqn (36), one achieves:
ALi = R ‘Fm
ALi = ALi [E(P),
R,]
= 4 -3 E(P)
(39)
In the highly absorbing hall, the barrier shielding efficiency (eqn (39)) is only a function of the geometrical shielding of an observation point E (P).
303
Barriers’ eficiency dependence on types of environments
In the case of two sources, one (1~ = 1) shielded by a barrier and another (IN = 2) bare source of a power Q2, the shielding efficiency, according to eqn (28), can be expressed as follows: ALi [db (A)] = -10 log
AKDT
1+ -
Jv)
1 -
exp [ - E(P)] ] -- $)
K(P) = KD~ =-
KDI
“a;$)} -
+ KDZ+ I(R
Ql
KD'~
@I
(43)
+e2)
Q2 0 2nd'
=
(41)
(42)
2nd:
Q2 KD~ = 2nd;
KR=;
(40)
(441 (45)
2
The barrier effective reflection coefficient p is related absorption coefficient Q as below:32 p=1-, 1 _Q-
(46) v(i>
ci
to the barrier
44
(47)
where a (i) is the barrier absorption coefficient for the ith octave band and V(i) (eqn (5)) is the average noise spectrum in the analyzed industriai room. By introducing the power ratio: 4 = QdQl the coefficients in eqn (40) assume the forms:
(48)
304
E. Walerian, M. Czechowicz, R. Janczur
1
KDI
K(P) -=KR K(P)
+
1 + q (&df)
(49) y:
(1 + 9)
1 l+R 8lld;
[ 1l+q
AKDI, -= K(P)
(50)
+ (d?ldZ)
&]
P4 (q/d:)
[
1 + (d#)
(51) q] + T
(1 + 4)
where di, d2, dk are distances between appropriate sources Ia, IN, I,: and the observation point, respectively. Equations (49)-(51) allow us to estimate how important the terms in eqn (40) are for the known q ratio (eqn (48)). Despite using the very simple model of a limited validity3’ for the acoustical field description in an industrial hall, the experimental results for 54 industrial halls32 have shown a good agreement with the model. It is probably due to the estimation procedure of the sources power Q (1) in situ and the use of the effective room constant R (eqn (24)). Both quantities play the role of the model parameters, which incorporate the special features of the acoustical field of each individual industrial hall. The values of the barrier shielding efficiency calculated with use of the above expressions are comparable with the results of the other models.23,28.35
3 EXPERIMENTAL
INVESTIGATIONS
The experimental investigations have been performed for a 3 m high barrier constructed of CP-1 panels (1 m x 2 m) with doors and windows (Poznan Factory of Cork Products). The panels, composed of two metal sheets with mineral wool between them, are 4.5 cm thick. The panel on one side is perforated (28%). With use of the standard sound source (B&K 4205) emitting noise within the range from 50 to 10 000 Hz, the isolation of the CP-1 panels was estimated for the overall signal: TL = 33 dB (A) The value is sufficient for the 3 m high barrier lation influence on the barrier efficiency.
(52) in order to avoid the iso-
305
Barriers’ ejiciency dependence on types of environments
The 3 m high barrier shielding efficiency has been measured under conditions of the pseudo-free field and in the industrial hall. The pseudo-free field conditions were classified as the open air conditions and the conditions under the roof. The measurements in the industrial hall were performed for the two different sources acting alone and during operation of the two sources when only one was shielded. During measurements, signals were recorded by a Nagra IVSJ tape recorder, next, they were analyzed by use of a B&K 2033 analyzer connected to the computer system. Direct measurements by use of an SPL-meter with octave filters were performed in the open air because of sudden irregular, background noise fluctuations. 3.1 Investigation of barrier in pseudo-free field 3.1.1 Investigation of barrier in open air The measurements of the barrier efficiency were carried out in a large square, where small buildings were situated at a distance not less than 30 m from the site of measurements. The 4 m long barrier had additional 2 m long end-pieces bent at right angle in the direction to the source (Fig. 3). The measurements for the standard source (B&K 4205) emitting at the height of O-3m above the ground, were carried out at two positions: QI at a distance of 1 m from the barrier and QII at a distance of 2 m from the barrier.
t QIf
l
3mo
.
Ql 1
Pl
p9
p2 t
1.5m
.
.
1 2
.
.
.
.
.
I
I
I
4
6
8
c
D(m) (b) Fig. 3. The situation during the test in an open air for QI source (1 m from a barrier) and QII source (2 m from a barrier), and observation points positions P, (D = n[m]). (a) The horizontal
projection;
(b) the vertical projection.
E. Walerian, M. Czechowicz, R. Janczur
306
In Fig. 4 the barrier shielding efficiency ALo (f) for QI position is compared with the barrier insertion loss ILM (f) calculated from the Maekawa formula (eqn (3)) for the infinitely long screen. The curve A&r, (f), calculated according to eqn (13), represents the shielding efficiency of the barrier on the ground. The reflection coefficient of the ground has been assumed equal to one. The curve A&, (f) calculated +
[dB1
40-
Q
I
D=lm
30-
20-
f
WI
10 I
) 125
250
500
1000
2000
4000
8000
2000
4000
8000
(a)
id91 40-
30-
20-
f
[Hz1
10 ,
) 125
250
500
1000 (b)
Fig. 4. The efficiency of the barrier for the QI source position: ALO (f)-experimental curve; ILM (f)-calculated insertion loss (eqn (3)), A&, (f)-calculated shielding efficiency of the barrier on the ground (eqn (13)): (a) for PI (D = I m); (b) for Pz (D = 2 m); (c) for Ps (D = 8 m); (d) for Pg (D = 9 m) (see Fig. 3).
Barriers’ eficiency dependence on types of environments
307
with regard to the reflections from the ground is about 1.5 dB lower than the curve ILM (f). The coincidence between the experimental and theoretical curves is better for the smaller values of the distance D. Figure 5 shows the barrier shielding efficiency ALo (f) for the QI and QII positions, at three different distances from the barrier. The barrier overall shielding efficiency versus distance is presented in Fig. 6. As [dBl -.__--ALo Ib(f -
L’&ll
2
ALU,f>
/’
,’
/
f
[Hz]
10 .
b 125
250
500
1000
2m
4000
8000
(c)
[dBl 40-
01
D=9m ,I’/
-’
/’ /
,“/
f
10 I 125
250
500
1000
2000
Cd)
Fig. 4-contd
4000
EHzl
8000
E. Walerian, M. Czechowicz,
308
R. Janczur
expected, the barrier shielding efficiency for the @I position is lower than that for QI since the source nearer the barrier permits creation of a deeper shadow at the observation points behind the barrier. In Fig. 7 the barrier overall shielding efficiency ALO measured for QI is compared with the calculated AL Mg (eqn (18)). The efficiency is a weak function of the distance from the barrier. A better agreement between the calculated and measured curves can be observed for a smaller distance.
f
[Hz1 >
10 125
250
500
1000
2000
4000
8000
Fig. 5. The barrier shielding efficiency ALO (,f) for the QI and QII source distances D = 1, 3 and 9 m from a barrier (see Fig. 3).
AL 30
at
T
lo, Fig. 6. The barrier
positions
[dEWI
0
overall
,
12
,
shielding
,
3
,
4
,
5
,
6
,
7
,
8
D
,
9
[ml
)
efficiency ALo for the QI and QII source (see Fig. 3).
positions
Barriers’ efficiency dependence on types of environments
309
[WA)]
30
Ah
i *-
‘\ ‘*
Ab
‘\ ‘*
20-
10, 0
, 12
,
<*-_
--3__-t__*__~-
, 3
‘+
I
I
,
I
1
I
4
5
6
7
0
9
>
Fig. 7. The barrier shielding efficiency for the QI source position
experimental curve, A&-calculated
(Fig. 3): ALo (dB) according to (eqn (18)).
3.1.2 Investigation of barrier under roof
The measurements of the barrier efficiency under the roof for the standard source (B&K 4205) were performed to verify whether the environmental conditions can still be called the pseudo-free field conditions. The roof of a complex shape was supported by pillars. Under the roof, absorbing materials were stored. For measurements a niche with walls made of mineral wool (Fig. 8) was constructed. The niche was fully separated by the barrier in two parts; therefore, the barrier could be treated as an infinitely long one. The shielding efficiency AL,, (f) for the different observation points is shown in Fig. 9. As can be seen, the barrier efficiency is lower, the greater the frequency, which cannot be observed for the free field. As the influence of side walls is assumed to be negligible, the limited number of reflections between the floor and roof are important. The positions of the image sources and image observation points representing them are shown in Fig. 8. The waves’ interferences, which were not included in the theoretical description, can cause the decay of the shielding efficiency frequency. Figure 10 shows the barrier overall shielding efficiency AL, at the successive observation points. The curve ALMA (eqn (18)) presents the overall shielding efficiency of the barrier on the ground, with the Maekawa formula (eqn (3)) used for diffracted waves calculation. The curves ALI (R = 2719) (eqn (36)), ALi (R,) (eqn (39)) present the barrier overall shielding efficiency in a hall with the appropriate room constants (data for these calculations were collected as described in section 3.2.1). It can be
310
E. Walerian, M. Czechowicz,
R. Janczur
Q’2’
(a)
\
\
\
\
\
\. ‘\
,
.
,
,
,
/
,
,
,
(b) Fig. 8. The site of measurement observation
points
representing
under the roof with some image reflected waves. (a) The horizontal vertical projection.
sources and image projection; (b) the
Barriers’ efficiency dependence on types of environments
P,
QQoea _-__
p2
--
b
-
p4
A****
p5 pe
f
[Hz]
0
f
125
Fig. 9. The barrier
311
250
500
1000
2000
4000
8000
shielding efficiency under the roof AL,,(f) P, (n = 1, 2, 5 . 9) (see Fig. 8).
at succeeding
points
[dB(A)l
30
----
,,I
%;-_
*
;--__ 0 0
1 1
I 2
I 3
AL, Rs> t
-
-~-,---_-__ 1 4
--
I 5
D I 6
[ml
f
Fig. 10. The efficiency of barrier under the roof (Fig. 8): ALU-experimental curve; ALM,-calculated by eqn (18); AL, (R = 2719)-calculated by eqn (36); ALI (Rx)calculated by eqn (39).
seen that the conditions under the roof are nearer the conditions in a room than are the pseudo-free ones. 3.2 Investigation of barrier in industrial hall 3.2.1 Investigation of barrier shielding ejkiency for single source The site of measurements in the industrial hall (23.5 m x 15 m x 6.5 m
E. Walerian,
312
M. Czechowicz,
2
(b)
R. Janczur
4
6
8
D(m)
Fig. 11. The site of measurements in the industrial hall: (a) the horizontal (b) the vertical projection.
projection;
high) has been presented in Fig. 11. The L-800 cutter was used as the industrial noise source. The barrier at one end was attached to the wall and its opposite end was bent at right angles in the source direction. Thus, the shape of the barrier was such that it could be considered to be infinitely long. The geometrical shielding of an observation point: E(P)
(rad) = 2 tan-’
(h/D)
(53)
is determined by the difference h between the barrier height and the observation point height above the floor, and by the distance D from the barrier to the observation point. The effective room constant R has been calculated from the relationship (eqns (19) and (2 I)-(23)) d escribing the sound level decay with distance:
k
=
100” (Li-Lz)
Ll
>
L2
(55)
where the data of sound levels are taken without barrier at the points P,, (n = 1,2,5 . . 9) (Fig. 11). The points P,, have been combined in all the possible pairs, and the average value has been taken as the effective room constant R.
Barriers’ eficiency dependence on types of environments
313
The barrier shielding efficiency ALi, (f) at successive points is shown in Fig. 12. The efficiencies increase with frequency, which is not the rule for a complex system as happened in the case of a barrier under the roof (Fig. 9). The barrier overall shielding efficiency AL{ versus distance D from the barrier is shown in Fig. 13. (The lack of observation points at distances of
ALi(f)
[dB]
15-
10-
5-
f
0,
[‘+I 3
125
250
500
loo0
2000
4000
8000
Fig. 12. The barrier shielding efficiency AL{ (S) measured for the industrial successive observation points P,, (n = 1, 2, 5 9) (see Fig. II).
source at
[dB(A)l 10
*IHnHr AL: AL, R,) AL, R=2187)
Fig. 13. The barrier shielding efficiency for the industrial
mental curve; ALI (R = 2187)-calculated
by eqn eqn (39).
source (Fig. 11): AL{ -experi(36); AL, (&,)-calculated by
314
E. Walerian, M. Czechowicz,
3 and 4 m from the source microphone at these points.) eqn (36) and the curve AL1 Next, the measurements (n = 1, . . . 9) in th e same the same way, but with use
R. Janczur
was caused by difficulties in the location of a The curve ALI (R = 2187) was calculated by (R,) by eqn (39). have been performed for points P, hall as before, with the barrier mounted in of the standard source (B&K 4205) being at P.
P2 P3 p4 P5 Pb P7 P8 PP
f 125
Fig. 14. The barrier
250
500
2000
loo0
4.000
[Hz]
6000
shielding efficiency AL; (J) for the standard source observation points P, (n = 1, 9) (see Fig. 11).
10
[d’J(A)l
AL,(L)
-
--__ 0
at successive
I
I
0123456769
Fig. 15. The barrier shielding efficiency mental curve; AL, (R = 518)-calculated
I
I
*44+# ---
AL; AL,(R=518)
----_
D [ml
I
)
for the standard source (Fig. 11): AL;-experiby eqn (36); ALI (R,)-calculated by eqn (39).
Barriers’ ejiciency dependence on types of environments
315
the same distance from the barrier as the industrial source (about 2 m), but at the height of 1.2 m. The shielding efficiencies AL! (f) (Fig. 14) at the successive points P&z= 1, . . . 9) (Fig. 11) for the standard source have again the characteristic feature of decreasing with frequency, which does not appear in the free field. The barrier overall shielding efficiency AL: versus distance D from the barrier is shown in Fig. 15. The curves ALI (&) (eqn (39)) and ALi (R = 518) (eqn (36)) p resent the barrier shielding efficiency in the absorbing and reverberant room, respectively. The standard source, due to its position, was less shielded than the industrial source. Also, the industrial source had its maximum at 4 kHz while the standard source had its maximum at 1 kHz. From the diffraction point of view the standard source, being at the same position as the industrial source, has to be less effectively shielded since the maximum of its relative power spectrum occurs at the lower frequency. Moreover, during the measurements for the standard source (B&K 4205) the amount of cork materials stored in the hall was smaller (R = 5 18) than during the measurements (R = 2187) for the industrial source (L-800 cutter). All these facts connected with the source position, its power spectrum and the amount of absorbing materials have led to a greater barrier shielding efficiency AL{ (Fig. 13) for the industrial source than that for the standard source AL! (Fig. 15). 3.2.2 Investigation of barrier shielding eficiency with presence of unshielded source The measurements have been performed under the same conditions as previously. The standard source Qi (B&K 4205) has been shielded by the barrier. The additional unshielded strong noise source Q2 (siren) has been acting. Its position is shown in Fig. 16. The ratio q (eqn (48)) of the A-weighted acoustical power of the sources Qr, Q2 was equal to q = Qz/Ql = 4 The barrier shielding efficiency ALS2 (f) (Fig. 17) at the successive measuring points P, (n = 1, . . . 6) decreases with frequency as in the case when the standard source acts alone (Fig. 14). Now, the decrease is stronger, assuming also the negative values at the higher frequency. In Fig. 18 are shown the barrier overall shielding efficiencies ALS2 versus distance D. The theoretical curve ALi2 is obtained from eqn (40).
E. Walerian, M. Czechowicz,
316
R. Janczur
As can be observed, the waves from the source Q2 reflected from the barrier cause the negative value of the barrier shielding efficiency ALS2 measured at the points P,, (n = 2,4). The calculated shielding efficiency (eqn (40)) decreases, becoming zero at the point P5 which is the nearest to the source Q2: ALlz (P5, q = 4) = 0 dB (A) 1
PI
.Ql
Q2
PI
0
I
I
p9
p5
.o...ee*.
41
Q2
.
.
.
i
p5
.
.
.
.
PY
2.5m I
I
2
4
t
I
I
6
8
w
D(m)
(b)
Fig. 16. The position during measurements
of observation points P, (n = 1, 9) and of Ql, and Q2 sources when both sources operate: (a) the horizontal projection; (b) the vertical projection.
A&(f)
[dB] lo-
5-
f -10
I
f
125
Fig.
17. The
[Hz1
250
500
1000
2000
barrier shielding efficiency AL;,(f) at P,, (n = 1, 6) (Fig. 16), during operation
4.000
BOO0
successive observation of two sources.
points
317
Barriers’ efficiency dependence on types of environments
[dB(A>l 5
! !I *
I
D [ml I
-2 b
i
13
I 4
I 5
I 6
I 7
I 6
I 9
)
Fig. 18. The barrier shielding efficiency during operation of Ql and Q2 sources Al:,-experimental curve; ALIzcalculated by eqn (40).
(Fig. 16):
Assuming that the relation between the acoustical power of the sources Qi, Q2 is inverse to that given by eqn (56) i.e. q =
Q2/Qi = 0.25
(58)
the positive value of the shielding efficiency can still be achieved from eqn (40): AL12 (J’s,
q =
0.25) = 1.7 dB (A)
(59)
The above calculation results and the experimental results (Fig. 18) underline the fact that, when applying a barrier in an industrial hall, attention has to be paid to unshielded sources.
4 COMPARISON OF SHIELDING EFFICIENCIES DIFFERENT ENVIRONMENTS
IN
During the measurements the barrier was constructed in a way allowing us to treat it as an infinitely long, opaque screen. Its insertion loss has to be equal to that given by the Maekawa formula. When the barrier was sited on the ground its shielding efficiency could be calculated by eqn (18) where the diffraction wave amplitude was expressed after Maekawa (eqn (3)).
E. Walerian. M. Czechowicz,
318
R. Janczur
The comparison (Fig. 19) between the barrier overall shielding efficiencies ALO for the source position QI, measured in the open air, and the calculated A&s (eqn (18)) gives the difference, which increases with distance. Its average value is about 3 dB (A). The geometry of the source-barrier-observation point system, during measurements in the open air for the QII source position, corresponds to the geometry of the system used during the measurements under the roof.
[dB(A>l 5
Fig. 19. The differences between the calculated overall shielding efficiency for QI position ALMp (eqn (I 8) and (eqn (12)) and that measured in the open air AL”.
D [ml 10 , 0
I
I
I
I
I
1
2
3
4
5
v 6
1
Fig. 20. The differences between the barrier shielding efficiency measured for the QII source position in the open air A& and under the roof AL, (in both cases the same equivalent source position).
Barriers’ efficiency dependence on types of environments
319
Hence, the difference between the barrier overall shielding efficiency in the open air ALo (Fig. 6) and under the roof AL, (Fig. 10) can be presented (Fig. 20). The barrier in the open air is more effective than that under the roof. The average value of the difference is about 13 dB (A). As the equivalent sources’ positions were the same during the measurements under the roof and in the industrial hall, the difference between the overall shielding efficiencies of the barrier under the roof AL,, (R = 2719) (Fig. 10) and in the industrial hall ALi, (R = 2187) (Fig. 13) has been shown in Fig. 21. The differences were not only due to the different surroundings, but also due to application of the sources with different power spectra. In the first case it was the standard source, in the second case the industrial source. The average difference value is about 3 dB (A). In the same industrial hall the barrier was investigated for the industrial source and standard source. In the second case the equivalent source position was nearer the barrier’s upper edge, and the amount of stored absorbing materials was smaller. The difference between the barrier’s overall shielding efhciency for the industrial source ALi, (R = 2187) (Fig. 13) and the standard source ALi (R = 518) (Fig. 15) is shown in Fig. 22. The effect of the unshielded source action, i.e. the difference between the overall shielding efficiencies AL! (Fig. 17), for the standard source acting alone ALS2 (Fig. 21) and with the second unshielded source, is presented in Fig. 23.
Fig. 21. The difference between the barrier shielding efficiency AL,, measured under the roof (R = 2719) for the standard source (B&K 4205), and the shielding efficiency AL’, in the industrial hall (R = 2187) for the industrial source (L-800 cutter) (in both cases the same equivalent source position).
E. Walerian, M. Czechowicz,
320
R. Janczur
Based on the investigations in the industrial rier action can be distinguished: l l
hall, two areas of the bar-
the active range at the distance from the barrier not greater than 4 m; the passive range at the distance from the barrier greater than 4 m.
T [dBtA)l 5 1
l 2
*,*----____ 4-
$
*
_-J
I I
I I
a
I I I 1 I I , 1 , ,
3-
2-
j
, II
,
12
,
,
, p;
3
4
5
6
[ml, 7
a
9
Fig. 22. The difference between the barrier shielding efficiency AL; measured in the hall R = 2187) for the industrial source, and the shielding efficiency AL: measured in the hall (R = 5 18) for the standard source (in the second case the source is nearer the barrier upper edge).
T [WA)1
5-i 0,
4-
P “J a
3-
-1;
I
0
12
,
,
,
,
/
I
,
,
3
4
5
6
7
6
9
,
Fig. 23. The difference between the barrier shielding efficiency AL; for one source and AL;, for two sources when the second one is unshielded (in both cases the same effective room constant R = 518).
321
Barriers’ eficiency dependence on types of environments
The average values of the barrier’s overall shielding efficiency in the active range AL, and in the passive range AL,, for the different noise sources in a changeable environment (described by the effective room constant R), are presented in Table 2. Generally, it might not be expected that the overall shielding efficiency of the 3 m high barrier in an industrial hall could exceed the value of 10 dB(A) at a distance of 1 m from the barrier. In the most absorbing room under the roof, AL, has been 9 dB(A). Moreover, the barrier shielding efficiency is smaller, the greater the distance from the barrier. In estimating the barrier shielding efficiency in the case when only one of the sources is shielded, one should bear in mind that at some points the shielding efficiency can even be negative. The changes met in the surrounding space due to varying amounts of the absorbing materials stored in the hall result in variations of the effective room constant. This might cause the temporally varying barrier TABLE 2
The Barrier Shielding Efficiency in the Active Range AL, (0 < D < 4 m) and in the Passive Range ALP (D > 4 m) Case
Difference between barrier and source height
Eflective room constant,
(m)
R (m2)
B&K 4205
2.7
2719”
8.0
5.5
L-800 cutter
2.7
2181b
6.5
2.5
L-800 cutter
2.7
2187’
6.5
2.5
B&K 4205
1.8
528’
2.5
1.5
5
B&K 4205
1.8
528’
2.5
1.5
6
B&K 4205 &IS siren
1.8
518’
0.5
0.5
no.
Type of noise source
Average barrier shielding efficiency. AL
(dB (A))
Average barrier shieiding eficiency, AL, (dB (A))
OMeasurement in semienclosure, constructed by walls of mineral wool, under roof. bMeasurement in industrial hall with large amount of absorbing materials. ‘Measurement in industrial hall with small amount of absorbing materials.
E. Walerian, M. Czechowicz.
322
R. Janczur
shielding efficiency. In the active range, the 3 m high barrier shielding efficiency might decrease to about 4 dB(A) due to the variations of the sources’ type, the position behind the barrier, and the effective room constants. 5 CONCLUSIONS When the barrier is arranged in a way which allows one to treat the barrier as an infinitely long, opaque screen, then its efficiency is near the insertion loss. The decisive factor of the barrier insertion loss in the free field is the geometry of the source-barrier-observation point system, i.e. the position of the source and the observation points relative to the barrier edge. The diminishing of efficiency, when the barrier is placed in a real system, is caused by interactions with the environment, due to multiple reflections from neighbouring objects’ surfaces. In the simplest cases, reflections from the ground, or between a floor and a ceiling, appear. In an industrial hall the reflected waves field assumes a very complex form. An approximate measure of the reflected waves field is the effective room constant which, in practice, can vary, depending upon the amount of the materials being temporarily stored in the hall. The investigations, carried out for the shielding efficiency of the 3 m high barrier in the open air, have shown that the theoretically achieved value with use of the Maekawa expression is about 3 dB (A) higher than the measured one. The barrier shielding efficiency after placing under the roof is about 13 dB (A) lower than that in the open air. In a room, in the most favourable circumstances, the achieved value within the barrier active range (at a distance from the barrier not greater than 4 m), was equal to 9 dB (A). For the smaller room constant, and for the source placed nearer the barrier upper edge, the barrier shielding efficiency decreased to 4 dB(A). The additional unshielded strong sources, present in the barrier vicinity, can cause further decrease of the barrier shielding efficiency. It can finally give even a negative value of the barrier shielding efficiency, while the barrier predominantly acts as an additional reflecting surface. With regard to all the discussed factors, the simple expressions presented in this paper for the barrier overall shielding efficiency in an industrial hall might be accepted as accurate enough, especially in the barrier active range. REFERENCES 1. Bowman, J. J., Senior, T. B. A. & Uslenghi, P. L. E. (eds), Electromagnetic and Acoustical Scattering by Simple Shapes. North-Holland, Amsterdam, 1970.
Barriers’ efficiency dependence on types of environmenfs
2.
3. 4.
5. 6. 7. 8. 9.
10. 11.
323
Kending, R. P. & Hayek, S. I., Diffraction by a hard-soft barrier. J. Acoust. sot. Am., 70 (1981) 115665. Rawlings, A. D., Plane-wave diffraction by rational wedge. Proc. Roy. Sot. London, A 411 (1987) 265-83. Walerian, E. & Janczur, R., Theories of diffraction applied for description of acoustical field screen efficiency. Inst. Fundam. Technol. Res. Rep., 25 (1985) (in Polish). Maekawa, Z., Noise reduction by screen. Memoirs of the Faculty of Engineering, Kobe University, 11 (1965). Yuzuwa, M. & Sone, T., Noise reduction by various shape barriers. Appl. Acoust., 14 (1981) 65-73. Maekawa, Z., Simple estimation method for noise reduction by variously shaped barriers. Arch. Acoust., 10 (1985) 369-82. L’Esperance, A., The insertion loss of finite length barrier on the ground. J. Acoust. Sot. Am., 86 (1989) 179-83. Janczur, R., Theoretical and scale-model investigation of a point source acoustical field in the presence of reflecting surfaces and screen. PhD thesis, Inst. Fundam. Technol. Res. Rep., 8 (1990) (in Polish). Rubinowicz, W., Die Beugungswelle in der Kirchhoffschen Theorie der Beugung. PWN, Warsaw, 1957. Walerian, E., Multiple diffraction at edges and right angle wedges. Acustica,
78 (1993) 201-9. 12. Janczur, R., Walerian,
E. & Oglaza, J., Acoustical field in space with obstacles. Part I: Description of geometrical field. Acustica, 78 (I 993) 15462. 13. Walerian, E. & Janczur, R., Acoustical field in space with obstacles. Part II: Propagation between buildings. Acustica, 78 (1993) 2lCk-19. 14. Terai, T., On calculation of sound fields around three dimensional objects by integral methods. J. Sound & Vibr., 69 (1980) 71-100. 15. Kawai, Y. & Terai, T., The application of integral equation methods to the calculation of sound attenuation by barriers. Appl. Acoust., 31 (1990) 101-17. 16. Hothersall,
D. C., Chandler-Wild, S. N. & Hajmirzae, M. N., Efficiency of single noise barriers. J. Sound & Vibr., 142 (1991) 303-22. 17. Kruzins, E. & Fricke, F., The prediction of sound field in non-diffuse spaces by ‘random walk’ approach. J. Sound & Vibr., 81 (1982) 549964. 18. Kruzins, E., The prediction of sound fields inside non-diffuse space: transmission loss consideration. J. Sound & Vibr., 91 (1983) 43945. 19. Kuttruff, H., Sound decay in reverberation chamber with diffusing elements. J. Acoust. Sot. Am., 69 (1981) 171623. 20. Kuttruff, H., Stationare Schallausbreitung in Flachraumen. Acustica, 57 (1985) 62-70. 21. Linqvist, E. A., Sound attenuation in large factory space. Acustica, 50 (1982) 313-28. 22. Linqvist, E. A., Noise attenuation in factory. Appl. Acoust., 16 (1983) 183241. 23. Kurze, H., Scattering of sound in industrial spaces. J. Sound & Vibr., 98 (1985) 349964. 24. Ondet, A. M. & Barry, J. L., Sound propagation in fitted rooms-comparison of different models. J. Sound & Vibr., 125 (1988) 13749.
324
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R. Janczur
25. Ondet, A. M. & Barry, J. L., Modeling of sound propagation in fitted workshops using ray tracing. J. Acousl. Sot. Am., 85 (1989) 787-96. 26. Ondet, A. M. & Barry, J. L., Note in connection with a comparison of different models for predicting sound level in fitted industrial rooms. J. Sound & Vibr., 143 (1990) 343-50. 27. Hodgson, M., On accuracy of models for predicting factory sound propagation in fitted rooms. J. Acoust. Sot. Am., 88 (1990) 871-8. 28. Hodgson, M., Case history: factory noise prediction using ray tracingexperimental validation and the effectiveness of noise control measures. Noise Control Engng J., 33 (1989) 97-104. 29. Joyce, W. B., Exact effect of surface roughness on the reverberation time of a uniformly absorbing spherical enclosure. J. Acoust. Sot. Am., 64 (1978) 1429-36. 30. Janecek, P., A model for the sound energy distribution in work spaces based on the combination of direct and diffuse field. Acustica, 74 (1991) 149-56. 31. Fujiwara. K., Steady state sound field in an enclosure with diffusely and specularly reflected boundary. Acustica, 54 (1984) 26673. 32. Rybarczyk, W., Selection method for technical solutions reducing noise in woodworking and paper industry. Works Inst. Wood Technol., 13 (1980) 13357 (in Polish). 33. Rybarczyk, W., Walerian, E. & Czechowicz, M., Principles of noise control in industrial structures. Proc. Noise Control ‘85, pp. 427-33. 34. Rybarczyk, W., Walerian, E. & Kowal, E., Designing and Application oj Noise Control Measures. IWZZ, Warsaw, 1988 (in Polish). 35. Orlowski, R. J., Scale modeling for predicting noise propagation in factory. Appl. Acoust., 31 (1990) 147-71.
0003-682X(94)00028-X
Barriers’ Efficiency Dependence on Types of Environments* E. Walerian, M. Czechowicz$ & R. Janczur Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland (Received 5 January 1994; revised version received 18 June 1994; accepted 8 July 1994)
ABSTRACT Real, thin barriers are limited in length and have a finite isolation. Thus, it is hard to treat them as ideal half-planes for which the insertion loss in the free space is defined, The real features of barriers and interactions with the environment cause their efjiciencies (the barrier shielding efficiencies) to be drastically lower than the insertion loss. In this paper, simple means for allowing one to avoid the influence of the real barrier features, i.e. its length and isolation, are given. Also, simple expressions for the barrier shielding eficiency in dtflerent environments are presented. The experimental results for a barrier in the pseudo-free field: on the ground and under the roof, are shown. Further investigation in a more densely occupied space, such as an industrial hall, is also represented.
NOTATION a b
zl
Distance from source to barrier edge (Fig. 1) Distance from observation point to barrier edge (Fig. 1) Sound speed Distance between source and observation point (Fig. 1) Distance between barrier and observation point (Fig. 3) Coefficient describing the geometrical shielding of observation point P by barrier
*Sponsored by PZWK (Poznan Factory of Cork Products), Poland. STo whom correspondence should be addressed. 291
ul. Ksiazeca
1, Poznan,
292
E. Walerian, M. Czechowicz,
R. Janczur
Center frequency of ith octave band Insertion loss of ideal barrier in free space A-weighted acoustical energy flux at point P,in industrial hall Sound (pressure) level at point P,in free space L”, (P) Sound (pressure) level at point P,behind barrier, in free space L2 (P) Sound (pressure) level at point P,in real system with reflecting 4 (P> panels Sound (pressure) level at point P,behind barrier, in real system 4 (P) with reflecting panels Barrier shielding efficiency in real system AL N Fresnel number Acoustical pressure in ith octave band Pw p x p(O) Observation point located at worker’s head position, 1.5 m above floor p’, p(i=I) First-order image observation point Q = Q(O) Noise source @, Q@=‘) First-order image noise source A-weighted power of Ah source expressed in mW (A) Q (0 Effective room constant R Room constant measured for ith octave band R (4
f(i)
IL
a!
a (4 Ql (32
P s
Barrier effective absorption coefficient Barrier absorption coefficient for ith octave band Coefficient describing decrease of direct wave energy from In-th shielded source Coefficient describing change of reverberant field after barrier application Barrier effective reflection coefficient Difference between wave path through edge and direct distance from source to observation point
1 INTRODUCTION Barriers are frequently applied as protectors against noise, where the so-called shadow area is used. The barrier efficiency as a noise control measure depends on the barrier itself and its interactions with the environment. All these factors cause degradation of the barrier efficiency. In the free space the barrier efficiency is determined by barrier acoustical features and the source-barrier-observation point geometry, and is defined as the insertion loss:
Barriers’ esciency
dependence on types
of environments
IL = Li (P) - L2 (P)
293
(1)
In the case of the ideal half-plane in the shadow area there is only the wave diffracted at the half-plane edge. As a real barrier is never the ideal half-plane it is less efficient than the ideal one. For the real barrier some special means have to be undertaken to prevent a decreasing of its efficiency caused chiefly by its limited length and finite isolation. In a real system, containing obstacles of reflecting surfaces, an inserted barrier acts not only as a screen, but also as an additional reflecting panel. This causes further degradation of a barrier efficiency. To distinguish between the insertion loss (eqn (1)) defined in the free space, and the barrier efficiency in the real system, the notion of shielding efficiency is introduced: AL = L; (P) - L; (P)
(2)
In this paper, it is shown how the barrier efficiency decreases with a growing number of obstacles in a space. A prediction of the barrier shielding efficiency needs the assumption of a barrier model and a model of the acoustical field in the system. The accuracy of prediction depends on the applied models’ accuracy and accuracy of the model parameters’ estimation. Here, simple expressions, accurate enough for technical purposes, are given for calculation of the barrier shielding efficiency in different environments.
2 THE EFFECT
OF THE BARRIER
APPLICATION
2.1 The efficiency of ideal barrier in free space Treating the Kirchhoff diffraction theory, which assumes a nonreflective, opaque half-plane screen, as a good approximation,i4 Maekawa gives the expression for reduction of the sound pressure level of frequency fat the point P in the shadow area (Fig. l), where only the wave diffracted at the upper edge exists:’ ILM (f, P) = LI (f, P) - L2 (f, P) = 10 log (20N + 3) (dB) N=; 2f (a+b-d)
=O.O058fS
(3)
(4)
294
E. Walerian, M. Czechowicz. R. Janczur
\
Q,,l-
\
\ P’ .
(b)
Fig. 1. The barrier applied in the system containing only the ground, Q-a real source; Q’-an image source; P-an observation point; P’-an image observation point. (a) Situation without a barrier; (b) situation with a barrier.
Thus, the sound pressure level reduction ILM (1; P) gives the insertion loss (eqn (1)) of a barrier in the free space. 2.1 .I Eficiency of barrier for signal of defined spectrum ]It is possible to calculate the barrier insertion loss for a signal of the defined A-weighted, relative power spectrum: V(i) =
P’ (i) a(i) T p2 (i) a (i)
(5)
where the A-weighting coefficient a (i) is related to the A-weighting curve ALA (i) as below: a
(i)
=
100”
“A
(i) (6)
When the barrier insertion loss for the ith octave band is known IL [f(i)] = IL (i)
(7)
then the barrier overall insertion loss is given by
IL [dB (A)] = -10 log
10Po” iLCi)V(i)
c i
(8)
295
Barriers’ efficiency dependence on types of environments
By use of the Maekawa formula (eqn (3)) for the barrier insertion loss IL (i) calculation, the barrier overall insertion loss can be expressed as
ILM [dB(A)l =-l”log
7
o_ll$;a+3
1
which gives the sound level reduction. 2.1.2 Eficiency of jinite size barrier The real barrier is always sited on the ground. When there is no gap between a barrier lower edge and the ground (floor), then there is no diffraction at the lower barrier edge. The diffraction effect caused by the junction of the ground and a screen, in the first approximation, can be omitted.’ Thus, when the barrier is thin and opaque, it can be treated as a half-plane screen, for which diffraction occurs only at its upper edge. For barriers being screens of limited length, and for screens with edges of more complicated shape, the theories can be applied independently to each straight line segment of the edge.“’ In the case of a barrier of limited length the diffraction at side-edges makes the barrier efficiency lower. To avoid this the barrier ends can be folded in the direction of a source or an observation point. Then, the side diffraction waves have negligible amplitudes as their Fresnel numbers N (eqn (4)) are large. In the case of a barrier applied in a room the side diffraction can be eliminated by a barrier extension up to the room wall. For the wall-screen junction the same assumption is valid as for the groundscreen one. 2.1.3 Eficiency offinite isolation barrier When a barrier has a finite isolation, then a portion of the acoustical energy is transmitted into the shadow area through a barrier. In effect, the insertion loss ILr of a barrier of a finite isolation may be diminished’ and in this case is given by ILr = -10 log [10-O” IL + 10-O”rr]
(10)
where IL is the insertion loss of an opaque barrier, and TL is the transmission loss of the real barrier. Equation (10) can be used for a pure tone or for a signal of defined spectrum. For some typical values of IL and TL, the barrier insertion loss ILr is calculated in Table 1.
E. Walerian, M. Czechowicz,
296
The Insertion
R. Janczur
TABLE 1 Loss of a Barrier of Finite Isolation
IL
TL
TL - IL
IL-r
30 25 20
20 20 20
-10 -5 0
19.59 18.81 17.00
Light barriers of about 3 m height, when applied in industry, have the insertion loss for high frequency of about 20 dB. For this range of frequencies one should assume that the isolation of barriers should not be smaller than 25 dB. 2.2 The shielding efficiency of barrier in pseudo-free field The simplest real systems in which a barrier can be applied are the systems containing the ground, or a floor and ceiling. The shielding efficiency of a barrier is affected by reflections from the ground and reflections between a floor and a ceiling. When the influence is small then the conditions under which the barrier acts can be called the pseudo-free field conditions. By use of the Rubinowicz theory” the interaction of the acoustical wave with an obstacle can be divided into the geometrical reflection and diffraction at edges. In a real system the multireflections of geometrical waves and born at edges diffraction waves are equivalent to an existence of image-sources and/or image-observation points.8,9,” The calculation procedure based on this concept can be easily executed in the case of a simple system, but for a complex system it results in a long computation time.“-13 In the case of the ground (floor) existence the barrier shielding efficiency (eqn (2)) assumes the form:
AL, (8 = 10log [P’ (Q, P) +p2(e’, p,] -
10log [p2 (Q, E, P) +p2(Q, E, P’>
+ p2
(Q',
(11)
E, P) + p2 (Q’, E, PI,]
The level L; (P) (Fig. l(a)) is formed
by two waves: the direct wave
p (Q, P) from the source Q and the wave p (Q’, P) from an image source
Q’9 representing the wave reflected from the ground. After a barrier application the level L; (P) (Fig. l(b)) is formed by four diffracted waves.
Barriers’ ejkiency
dependence on types of environments
297
The wave p (Q, E, P) and the wave p (Q’, E, P) reach the observation point straight after diffraction. The wave p (Q, E, P’) and the wave p (Q’, E, P’) reach the point P after being reflected from the ground, behind the barrier. Their reflections are described as reaching the point P’, being the mirror image of the point P with respect to the ground surface. When a barrier acts in the system containing a floor and a ceiling (Fig. 2), then the level L; (P) is created by the direct wave p (Q(O),P(O)) and an infinite number of waves p (Q (‘4, P(‘))reflected from the planes of the floor and ceiling. The level Li (P) is formed by diffracted waves p (Q@), E, P(O)) coming straight after diffraction to the point P(O) and waves p (Q@) ,E, P(j)), which, after diffraction, undergo reflections between the floor and the ceiling. This results in the barrier shielding efficiency:
Q”’
~ .
*
*
.
(4 ($2
t,
,
P(2)
I
\
/
\
J
\
/
\ \
/ ,
Fig. 2. The barrier applied in the system containing a floor and a ceiling with the first two image sources Q (I), Q(‘) and observation points P (‘1, Pc2) representing reflected waves. (a) Situation without a barrier; (b) situation with a barrier.
298
E. Walerian, M. Czechowicz,
ALfc = 10 log
fi:
R. Janczur
p2 (Q'k',
k=O -
10 log
P(O)) I
2
2
k=O
j=O
p2
(QCk’, Pti’)
1
(12)
The number of reflections before diffraction (k) and after diffraction (j) can be limited when the ceiling is not parallel to the floor. However, for a ceiling of complicated form, additional diffractions occur at its wedges, which makes description of the barrier shielding efficiency difficult. Generally, only the first few terms in eqn (12) have to be taken since the next ones have strongly decreasing amplitudes. When the Maekawa formula is used to express the shielding efficiency of a barrier on the ground, then eqn (11) assumes the form:
ALMg (f’) (dB) = 10 log
6, =a+b-d
(14)
&=a+b’-d
(15)
63 =a’+b-d
(16)
6, = a’ + b’ - d’
(17)
For the signal of defined power spectrum (eqn (5)) the overall shielding efficiency of a barrier on the ground is given by
ALM, [dB (A)] = 10 log
Barriers’ eficiency dependence on types of environments
299
2.3 The shielding efficiency of barrier in industrial hall The general procedure of finding the sound field description in a limited space is based on solving the wave equation for the appropriate boundary conditions. In complex systems it can be solved by the finite-difference method.‘4-‘6 This allows us to describe the field in the systems with screens which are treated as other obstacles of the given surface impedance. In industrial halls, by modeling the acoustic energy spreading, as phonons move randomly in a fitted space, a statistical description is applied. Special models, being a combination of the geometrical acoustics and the acoustical energy diffusion, are developed.‘7-28 In extreme cases, the statistical description results in the diffusion equation for acoustical energy spreading.‘9,23 Under special conditions29-3’ concerning a room size and its walls’ features, the part of the acoustical field caused by an enclosure can simply be the diffuse field. Here, this kind of mode13* is applied for the acoustical field in an industrial hall. This allows the simple estimation of the barrier shielding efficiency at the worker’s position. Here, the A-weighted acoustic energy flux: K =
10“’ L[dB(A)1-9 [(mW/m*)
(A)]
(19)
is used to determine noise at point P adequate for the position of the worker’s head.32-34 Basing on this, the overall shielding efficiency of a barrier shielding the ZE source may be expressed by:32
AL (k P) [dB(A) = LI (P) [dB (A)] - Lz (P) [dB (A)] = 10 log K(P) - 10 log KE (P)
(20)
Before a barrier application the energy flux K(P) at the point P is the sum of the direct wave energy flux KD (P) and the energy flux of the reverberant field KR:
K(P) = KD (P) + KR
(21)
The direct waves energy Ko (P) is the sum of the direct waves energy coming from all industrial sources modeled by equivalent point sources, radiating in the half-space:
300
E. Walerian, M. Czechowicz,
R. Janczur
(22) I=1
I=1
where Q (Z) is the A-weighted power of the Zth source estimated in situ. The reverberant noise field is expressed by A
N
KR=; c
Q(Z)
(23)
I=1
where R is the effective room constant determined spectrum V(i) in the analyzed room:
for an average noise
V(i)
1 -_= c R
i
(24)
R (i)
The room constant R (i) as a function of frequency is estimated from the decrease of sound pressure level with distance from the small, dominant industrial source sited in the middle of the room. After shielding the Zn-th source with a barrier the energy flux at the point P behind a barrier is: KE(~)=
The direct field component KDE
(p)
=
KD
(p>
KDE(P)+KRE(P)
(25)
is changed as follows: +
( QI
-
1) KD
[Q
(IE), P]+
AK,,
(f')
(26)
The barrier application diminishes the direct wave Ko [Q (ZE), P] from the In-th source, which is described by coefficient al. At the same time, waves from the nearest sources (different from Zn) can reach the point P through reflection from a barrier. This is described by the component AK,, (P) in eqn (26). Moreover, the barrier introduces an additional acoustic absorption to the room, and limits the share of the In-th source in generation of the reverberant field, hence: KRE=KR(~
-Qz)
(27)
Now, eqn (20), giving the barrier shielding efficiency, can be rewritten in the form:
Barriers’ eficiency dependence on types of environments
AL (IE, P) [dB (A)] = -10 log
1+
AKD,
(p>
K(P)
301
(28)
As can be seen from eqn (28), barrier shielding efficiency can be negative at some points when AK,,
(p) >
K(P)
p)
KD (IE,
(l-4
K(P)
+$
Q2
(2%
This happens when the reflections from a barrier prevail over the reduction of the direct wave from the shielded In-th source and reduction of the reverberant field. To find the explicit form of the coefficient (~1it is assumed that a barrier causes32 the exponential decay of the direct wave from the In-th shielded source. The decay factor is proportional to the relative angular dimension of a barrier seen from the observation point E(P). Thus [-E(P)]
~1 =exp
(30)
The coefficient ~1 can also be interpreted as the probability of reaching the shadow area behind the barrier by phonons from the direct wave stream. Both coefficients CX~,(~2 are related to the geometrical shielding of an observation point by a barrier E(P). The coefficient 02 (eqn (27)) describing the decay of the reverberant field is assumed to be:32 (32 =
E(P) 4n
(31)
The coefficient o2 also describes the probability of diffuse phonons scattering by a barrier. When in an industrial hall the single acting source (1~ = 1) of a power Ql is shielded by a barrier, then K(P) = KDI + KR
KD1 =-
Ql 2nd; ’
(32)
(33)
302
E. Walerian, M. Czechowicz,
AK,,
R. Janczur
(P) = 0
(35)
where &i is the direct wave energy flux and di is the distance between the source and an observation point P. The barrier shielding efficiency can be expressed according to eqn (28) as ALI
[dB
(A)]
=
Ah
r WI
[E(P),
-
-&
1 - exp [ - E(P)] [
I
(36)
r E(P) -_____ rfl
4II
1
’
where r(R)
=gzT
8IId;
(37)
is the ratio of the reverberant field energy flux and the direct wave energy flux. The overall shielding efficiency (eqn (36)) is expressed as the function of the geometrical shielding of an observation point E(P) and the room effective constant R, which appears in the parameter r definition (eqn (37)). The classical diffraction frequency dependence is absent. Only the as the average value effective room constant (eqn (24)) is calculated incorporating a room feature R (i) and noise sources spectrum V(i). When the energy flux of the reverberant field is small in relation to the direct wave energy flux: r< 1 then, calculating ,‘To
(38)
the limit in eqn (36), one achieves:
ALi = R ‘Fm
ALi = ALi [E(P),
R,]
= 4 -3 E(P)
(39)
In the highly absorbing hall, the barrier shielding efficiency (eqn (39)) is only a function of the geometrical shielding of an observation point E (P).
303
Barriers’ eficiency dependence on types of environments
In the case of two sources, one (1~ = 1) shielded by a barrier and another (IN = 2) bare source of a power Q2, the shielding efficiency, according to eqn (28), can be expressed as follows: ALi [db (A)] = -10 log
AKDT
1+ -
Jv)
1 -
exp [ - E(P)] ] -- $)
K(P) = KD~ =-
KDI
“a;$)} -
+ KDZ+ I(R
Ql
KD'~
@I
(43)
+e2)
Q2 0 2nd'
=
(41)
(42)
2nd:
Q2 KD~ = 2nd;
KR=;
(40)
(441 (45)
2
The barrier effective reflection coefficient p is related absorption coefficient Q as below:32 p=1-, 1 _Q-
(46) v(i>
ci
to the barrier
44
(47)
where a (i) is the barrier absorption coefficient for the ith octave band and V(i) (eqn (5)) is the average noise spectrum in the analyzed industriai room. By introducing the power ratio: 4 = QdQl the coefficients in eqn (40) assume the forms:
(48)
304
E. Walerian, M. Czechowicz, R. Janczur
1
KDI
K(P) -=KR K(P)
+
1 + q (&df)
(49) y:
(1 + 9)
1 l+R 8lld;
[ 1l+q
AKDI, -= K(P)
(50)
+ (d?ldZ)
&]
P4 (q/d:)
[
1 + (d#)
(51) q] + T
(1 + 4)
where di, d2, dk are distances between appropriate sources Ia, IN, I,: and the observation point, respectively. Equations (49)-(51) allow us to estimate how important the terms in eqn (40) are for the known q ratio (eqn (48)). Despite using the very simple model of a limited validity3’ for the acoustical field description in an industrial hall, the experimental results for 54 industrial halls32 have shown a good agreement with the model. It is probably due to the estimation procedure of the sources power Q (1) in situ and the use of the effective room constant R (eqn (24)). Both quantities play the role of the model parameters, which incorporate the special features of the acoustical field of each individual industrial hall. The values of the barrier shielding efficiency calculated with use of the above expressions are comparable with the results of the other models.23,28.35
3 EXPERIMENTAL
INVESTIGATIONS
The experimental investigations have been performed for a 3 m high barrier constructed of CP-1 panels (1 m x 2 m) with doors and windows (Poznan Factory of Cork Products). The panels, composed of two metal sheets with mineral wool between them, are 4.5 cm thick. The panel on one side is perforated (28%). With use of the standard sound source (B&K 4205) emitting noise within the range from 50 to 10 000 Hz, the isolation of the CP-1 panels was estimated for the overall signal: TL = 33 dB (A) The value is sufficient for the 3 m high barrier lation influence on the barrier efficiency.
(52) in order to avoid the iso-
305
Barriers’ ejiciency dependence on types of environments
The 3 m high barrier shielding efficiency has been measured under conditions of the pseudo-free field and in the industrial hall. The pseudo-free field conditions were classified as the open air conditions and the conditions under the roof. The measurements in the industrial hall were performed for the two different sources acting alone and during operation of the two sources when only one was shielded. During measurements, signals were recorded by a Nagra IVSJ tape recorder, next, they were analyzed by use of a B&K 2033 analyzer connected to the computer system. Direct measurements by use of an SPL-meter with octave filters were performed in the open air because of sudden irregular, background noise fluctuations. 3.1 Investigation of barrier in pseudo-free field 3.1.1 Investigation of barrier in open air The measurements of the barrier efficiency were carried out in a large square, where small buildings were situated at a distance not less than 30 m from the site of measurements. The 4 m long barrier had additional 2 m long end-pieces bent at right angle in the direction to the source (Fig. 3). The measurements for the standard source (B&K 4205) emitting at the height of O-3m above the ground, were carried out at two positions: QI at a distance of 1 m from the barrier and QII at a distance of 2 m from the barrier.
t QIf
l
3mo
.
Ql 1
Pl
p9
p2 t
1.5m
.
.
1 2
.
.
.
.
.
I
I
I
4
6
8
c
D(m) (b) Fig. 3. The situation during the test in an open air for QI source (1 m from a barrier) and QII source (2 m from a barrier), and observation points positions P, (D = n[m]). (a) The horizontal
projection;
(b) the vertical projection.
E. Walerian, M. Czechowicz, R. Janczur
306
In Fig. 4 the barrier shielding efficiency ALo (f) for QI position is compared with the barrier insertion loss ILM (f) calculated from the Maekawa formula (eqn (3)) for the infinitely long screen. The curve A&r, (f), calculated according to eqn (13), represents the shielding efficiency of the barrier on the ground. The reflection coefficient of the ground has been assumed equal to one. The curve A&, (f) calculated +
[dB1
40-
Q
I
D=lm
30-
20-
f
WI
10 I
) 125
250
500
1000
2000
4000
8000
2000
4000
8000
(a)
id91 40-
30-
20-
f
[Hz1
10 ,
) 125
250
500
1000 (b)
Fig. 4. The efficiency of the barrier for the QI source position: ALO (f)-experimental curve; ILM (f)-calculated insertion loss (eqn (3)), A&, (f)-calculated shielding efficiency of the barrier on the ground (eqn (13)): (a) for PI (D = I m); (b) for Pz (D = 2 m); (c) for Ps (D = 8 m); (d) for Pg (D = 9 m) (see Fig. 3).
Barriers’ eficiency dependence on types of environments
307
with regard to the reflections from the ground is about 1.5 dB lower than the curve ILM (f). The coincidence between the experimental and theoretical curves is better for the smaller values of the distance D. Figure 5 shows the barrier shielding efficiency ALo (f) for the QI and QII positions, at three different distances from the barrier. The barrier overall shielding efficiency versus distance is presented in Fig. 6. As [dBl -.__--ALo Ib(f -
L’&ll
2
ALU,f>
/’
,’
/
f
[Hz]
10 .
b 125
250
500
1000
2m
4000
8000
(c)
[dBl 40-
01
D=9m ,I’/
-’
/’ /
,“/
f
10 I 125
250
500
1000
2000
Cd)
Fig. 4-contd
4000
EHzl
8000
E. Walerian, M. Czechowicz,
308
R. Janczur
expected, the barrier shielding efficiency for the @I position is lower than that for QI since the source nearer the barrier permits creation of a deeper shadow at the observation points behind the barrier. In Fig. 7 the barrier overall shielding efficiency ALO measured for QI is compared with the calculated AL Mg (eqn (18)). The efficiency is a weak function of the distance from the barrier. A better agreement between the calculated and measured curves can be observed for a smaller distance.
f
[Hz1 >
10 125
250
500
1000
2000
4000
8000
Fig. 5. The barrier shielding efficiency ALO (,f) for the QI and QII source distances D = 1, 3 and 9 m from a barrier (see Fig. 3).
AL 30
at
T
lo, Fig. 6. The barrier
positions
[dEWI
0
overall
,
12
,
shielding
,
3
,
4
,
5
,
6
,
7
,
8
D
,
9
[ml
)
efficiency ALo for the QI and QII source (see Fig. 3).
positions
Barriers’ efficiency dependence on types of environments
309
[WA)]
30
Ah
i *-
‘\ ‘*
Ab
‘\ ‘*
20-
10, 0
, 12
,
<*-_
--3__-t__*__~-
, 3
‘+
I
I
,
I
1
I
4
5
6
7
0
9
>
Fig. 7. The barrier shielding efficiency for the QI source position
experimental curve, A&-calculated
(Fig. 3): ALo (dB) according to (eqn (18)).
3.1.2 Investigation of barrier under roof
The measurements of the barrier efficiency under the roof for the standard source (B&K 4205) were performed to verify whether the environmental conditions can still be called the pseudo-free field conditions. The roof of a complex shape was supported by pillars. Under the roof, absorbing materials were stored. For measurements a niche with walls made of mineral wool (Fig. 8) was constructed. The niche was fully separated by the barrier in two parts; therefore, the barrier could be treated as an infinitely long one. The shielding efficiency AL,, (f) for the different observation points is shown in Fig. 9. As can be seen, the barrier efficiency is lower, the greater the frequency, which cannot be observed for the free field. As the influence of side walls is assumed to be negligible, the limited number of reflections between the floor and roof are important. The positions of the image sources and image observation points representing them are shown in Fig. 8. The waves’ interferences, which were not included in the theoretical description, can cause the decay of the shielding efficiency frequency. Figure 10 shows the barrier overall shielding efficiency AL, at the successive observation points. The curve ALMA (eqn (18)) presents the overall shielding efficiency of the barrier on the ground, with the Maekawa formula (eqn (3)) used for diffracted waves calculation. The curves ALI (R = 2719) (eqn (36)), ALi (R,) (eqn (39)) present the barrier overall shielding efficiency in a hall with the appropriate room constants (data for these calculations were collected as described in section 3.2.1). It can be
310
E. Walerian, M. Czechowicz,
R. Janczur
Q’2’
(a)
\
\
\
\
\
\. ‘\
,
.
,
,
,
/
,
,
,
(b) Fig. 8. The site of measurement observation
points
representing
under the roof with some image reflected waves. (a) The horizontal vertical projection.
sources and image projection; (b) the
Barriers’ efficiency dependence on types of environments
P,
QQoea _-__
p2
--
b
-
p4
A****
p5 pe
f
[Hz]
0
f
125
Fig. 9. The barrier
311
250
500
1000
2000
4000
8000
shielding efficiency under the roof AL,,(f) P, (n = 1, 2, 5 . 9) (see Fig. 8).
at succeeding
points
[dB(A)l
30
----
,,I
%;-_
*
;--__ 0 0
1 1
I 2
I 3
AL, Rs> t
-
-~-,---_-__ 1 4
--
I 5
D I 6
[ml
f
Fig. 10. The efficiency of barrier under the roof (Fig. 8): ALU-experimental curve; ALM,-calculated by eqn (18); AL, (R = 2719)-calculated by eqn (36); ALI (Rx)calculated by eqn (39).
seen that the conditions under the roof are nearer the conditions in a room than are the pseudo-free ones. 3.2 Investigation of barrier in industrial hall 3.2.1 Investigation of barrier shielding ejkiency for single source The site of measurements in the industrial hall (23.5 m x 15 m x 6.5 m
E. Walerian,
312
M. Czechowicz,
2
(b)
R. Janczur
4
6
8
D(m)
Fig. 11. The site of measurements in the industrial hall: (a) the horizontal (b) the vertical projection.
projection;
high) has been presented in Fig. 11. The L-800 cutter was used as the industrial noise source. The barrier at one end was attached to the wall and its opposite end was bent at right angles in the source direction. Thus, the shape of the barrier was such that it could be considered to be infinitely long. The geometrical shielding of an observation point: E(P)
(rad) = 2 tan-’
(h/D)
(53)
is determined by the difference h between the barrier height and the observation point height above the floor, and by the distance D from the barrier to the observation point. The effective room constant R has been calculated from the relationship (eqns (19) and (2 I)-(23)) d escribing the sound level decay with distance:
k
=
100” (Li-Lz)
Ll
>
L2
(55)
where the data of sound levels are taken without barrier at the points P,, (n = 1,2,5 . . 9) (Fig. 11). The points P,, have been combined in all the possible pairs, and the average value has been taken as the effective room constant R.
Barriers’ eficiency dependence on types of environments
313
The barrier shielding efficiency ALi, (f) at successive points is shown in Fig. 12. The efficiencies increase with frequency, which is not the rule for a complex system as happened in the case of a barrier under the roof (Fig. 9). The barrier overall shielding efficiency AL{ versus distance D from the barrier is shown in Fig. 13. (The lack of observation points at distances of
ALi(f)
[dB]
15-
10-
5-
f
0,
[‘+I 3
125
250
500
loo0
2000
4000
8000
Fig. 12. The barrier shielding efficiency AL{ (S) measured for the industrial successive observation points P,, (n = 1, 2, 5 9) (see Fig. II).
source at
[dB(A)l 10
*IHnHr AL: AL, R,) AL, R=2187)
Fig. 13. The barrier shielding efficiency for the industrial
mental curve; ALI (R = 2187)-calculated
by eqn eqn (39).
source (Fig. 11): AL{ -experi(36); AL, (&,)-calculated by
314
E. Walerian, M. Czechowicz,
3 and 4 m from the source microphone at these points.) eqn (36) and the curve AL1 Next, the measurements (n = 1, . . . 9) in th e same the same way, but with use
R. Janczur
was caused by difficulties in the location of a The curve ALI (R = 2187) was calculated by (R,) by eqn (39). have been performed for points P, hall as before, with the barrier mounted in of the standard source (B&K 4205) being at P.
P2 P3 p4 P5 Pb P7 P8 PP
f 125
Fig. 14. The barrier
250
500
2000
loo0
4.000
[Hz]
6000
shielding efficiency AL; (J) for the standard source observation points P, (n = 1, 9) (see Fig. 11).
10
[d’J(A)l
AL,(L)
-
--__ 0
at successive
I
I
0123456769
Fig. 15. The barrier shielding efficiency mental curve; AL, (R = 518)-calculated
I
I
*44+# ---
AL; AL,(R=518)
----_
D [ml
I
)
for the standard source (Fig. 11): AL;-experiby eqn (36); ALI (R,)-calculated by eqn (39).
Barriers’ ejiciency dependence on types of environments
315
the same distance from the barrier as the industrial source (about 2 m), but at the height of 1.2 m. The shielding efficiencies AL! (f) (Fig. 14) at the successive points P&z= 1, . . . 9) (Fig. 11) for the standard source have again the characteristic feature of decreasing with frequency, which does not appear in the free field. The barrier overall shielding efficiency AL: versus distance D from the barrier is shown in Fig. 15. The curves ALI (&) (eqn (39)) and ALi (R = 518) (eqn (36)) p resent the barrier shielding efficiency in the absorbing and reverberant room, respectively. The standard source, due to its position, was less shielded than the industrial source. Also, the industrial source had its maximum at 4 kHz while the standard source had its maximum at 1 kHz. From the diffraction point of view the standard source, being at the same position as the industrial source, has to be less effectively shielded since the maximum of its relative power spectrum occurs at the lower frequency. Moreover, during the measurements for the standard source (B&K 4205) the amount of cork materials stored in the hall was smaller (R = 5 18) than during the measurements (R = 2187) for the industrial source (L-800 cutter). All these facts connected with the source position, its power spectrum and the amount of absorbing materials have led to a greater barrier shielding efficiency AL{ (Fig. 13) for the industrial source than that for the standard source AL! (Fig. 15). 3.2.2 Investigation of barrier shielding eficiency with presence of unshielded source The measurements have been performed under the same conditions as previously. The standard source Qi (B&K 4205) has been shielded by the barrier. The additional unshielded strong noise source Q2 (siren) has been acting. Its position is shown in Fig. 16. The ratio q (eqn (48)) of the A-weighted acoustical power of the sources Qr, Q2 was equal to q = Qz/Ql = 4 The barrier shielding efficiency ALS2 (f) (Fig. 17) at the successive measuring points P, (n = 1, . . . 6) decreases with frequency as in the case when the standard source acts alone (Fig. 14). Now, the decrease is stronger, assuming also the negative values at the higher frequency. In Fig. 18 are shown the barrier overall shielding efficiencies ALS2 versus distance D. The theoretical curve ALi2 is obtained from eqn (40).
E. Walerian, M. Czechowicz,
316
R. Janczur
As can be observed, the waves from the source Q2 reflected from the barrier cause the negative value of the barrier shielding efficiency ALS2 measured at the points P,, (n = 2,4). The calculated shielding efficiency (eqn (40)) decreases, becoming zero at the point P5 which is the nearest to the source Q2: ALlz (P5, q = 4) = 0 dB (A) 1
PI
.Ql
Q2
PI
0
I
I
p9
p5
.o...ee*.
41
Q2
.
.
.
i
p5
.
.
.
.
PY
2.5m I
I
2
4
t
I
I
6
8
w
D(m)
(b)
Fig. 16. The position during measurements
of observation points P, (n = 1, 9) and of Ql, and Q2 sources when both sources operate: (a) the horizontal projection; (b) the vertical projection.
A&(f)
[dB] lo-
5-
f -10
I
f
125
Fig.
17. The
[Hz1
250
500
1000
2000
barrier shielding efficiency AL;,(f) at P,, (n = 1, 6) (Fig. 16), during operation
4.000
BOO0
successive observation of two sources.
points
317
Barriers’ efficiency dependence on types of environments
[dB(A>l 5
! !I *
I
D [ml I
-2 b
i
13
I 4
I 5
I 6
I 7
I 6
I 9
)
Fig. 18. The barrier shielding efficiency during operation of Ql and Q2 sources Al:,-experimental curve; ALIzcalculated by eqn (40).
(Fig. 16):
Assuming that the relation between the acoustical power of the sources Qi, Q2 is inverse to that given by eqn (56) i.e. q =
Q2/Qi = 0.25
(58)
the positive value of the shielding efficiency can still be achieved from eqn (40): AL12 (J’s,
q =
0.25) = 1.7 dB (A)
(59)
The above calculation results and the experimental results (Fig. 18) underline the fact that, when applying a barrier in an industrial hall, attention has to be paid to unshielded sources.
4 COMPARISON OF SHIELDING EFFICIENCIES DIFFERENT ENVIRONMENTS
IN
During the measurements the barrier was constructed in a way allowing us to treat it as an infinitely long, opaque screen. Its insertion loss has to be equal to that given by the Maekawa formula. When the barrier was sited on the ground its shielding efficiency could be calculated by eqn (18) where the diffraction wave amplitude was expressed after Maekawa (eqn (3)).
E. Walerian. M. Czechowicz,
318
R. Janczur
The comparison (Fig. 19) between the barrier overall shielding efficiencies ALO for the source position QI, measured in the open air, and the calculated A&s (eqn (18)) gives the difference, which increases with distance. Its average value is about 3 dB (A). The geometry of the source-barrier-observation point system, during measurements in the open air for the QII source position, corresponds to the geometry of the system used during the measurements under the roof.
[dB(A>l 5
Fig. 19. The differences between the calculated overall shielding efficiency for QI position ALMp (eqn (I 8) and (eqn (12)) and that measured in the open air AL”.
D [ml 10 , 0
I
I
I
I
I
1
2
3
4
5
v 6
1
Fig. 20. The differences between the barrier shielding efficiency measured for the QII source position in the open air A& and under the roof AL, (in both cases the same equivalent source position).
Barriers’ efficiency dependence on types of environments
319
Hence, the difference between the barrier overall shielding efficiency in the open air ALo (Fig. 6) and under the roof AL, (Fig. 10) can be presented (Fig. 20). The barrier in the open air is more effective than that under the roof. The average value of the difference is about 13 dB (A). As the equivalent sources’ positions were the same during the measurements under the roof and in the industrial hall, the difference between the overall shielding efficiencies of the barrier under the roof AL,, (R = 2719) (Fig. 10) and in the industrial hall ALi, (R = 2187) (Fig. 13) has been shown in Fig. 21. The differences were not only due to the different surroundings, but also due to application of the sources with different power spectra. In the first case it was the standard source, in the second case the industrial source. The average difference value is about 3 dB (A). In the same industrial hall the barrier was investigated for the industrial source and standard source. In the second case the equivalent source position was nearer the barrier’s upper edge, and the amount of stored absorbing materials was smaller. The difference between the barrier’s overall shielding efhciency for the industrial source ALi, (R = 2187) (Fig. 13) and the standard source ALi (R = 518) (Fig. 15) is shown in Fig. 22. The effect of the unshielded source action, i.e. the difference between the overall shielding efficiencies AL! (Fig. 17), for the standard source acting alone ALS2 (Fig. 21) and with the second unshielded source, is presented in Fig. 23.
Fig. 21. The difference between the barrier shielding efficiency AL,, measured under the roof (R = 2719) for the standard source (B&K 4205), and the shielding efficiency AL’, in the industrial hall (R = 2187) for the industrial source (L-800 cutter) (in both cases the same equivalent source position).
E. Walerian, M. Czechowicz,
320
R. Janczur
Based on the investigations in the industrial rier action can be distinguished: l l
hall, two areas of the bar-
the active range at the distance from the barrier not greater than 4 m; the passive range at the distance from the barrier greater than 4 m.
T [dBtA)l 5 1
l 2
*,*----____ 4-
$
*
_-J
I I
I I
a
I I I 1 I I , 1 , ,
3-
2-
j
, II
,
12
,
,
, p;
3
4
5
6
[ml, 7
a
9
Fig. 22. The difference between the barrier shielding efficiency AL; measured in the hall R = 2187) for the industrial source, and the shielding efficiency AL: measured in the hall (R = 5 18) for the standard source (in the second case the source is nearer the barrier upper edge).
T [WA)1
5-i 0,
4-
P “J a
3-
-1;
I
0
12
,
,
,
,
/
I
,
,
3
4
5
6
7
6
9
,
Fig. 23. The difference between the barrier shielding efficiency AL; for one source and AL;, for two sources when the second one is unshielded (in both cases the same effective room constant R = 518).
321
Barriers’ eficiency dependence on types of environments
The average values of the barrier’s overall shielding efficiency in the active range AL, and in the passive range AL,, for the different noise sources in a changeable environment (described by the effective room constant R), are presented in Table 2. Generally, it might not be expected that the overall shielding efficiency of the 3 m high barrier in an industrial hall could exceed the value of 10 dB(A) at a distance of 1 m from the barrier. In the most absorbing room under the roof, AL, has been 9 dB(A). Moreover, the barrier shielding efficiency is smaller, the greater the distance from the barrier. In estimating the barrier shielding efficiency in the case when only one of the sources is shielded, one should bear in mind that at some points the shielding efficiency can even be negative. The changes met in the surrounding space due to varying amounts of the absorbing materials stored in the hall result in variations of the effective room constant. This might cause the temporally varying barrier TABLE 2
The Barrier Shielding Efficiency in the Active Range AL, (0 < D < 4 m) and in the Passive Range ALP (D > 4 m) Case
Difference between barrier and source height
Eflective room constant,
(m)
R (m2)
B&K 4205
2.7
2719”
8.0
5.5
L-800 cutter
2.7
2181b
6.5
2.5
L-800 cutter
2.7
2187’
6.5
2.5
B&K 4205
1.8
528’
2.5
1.5
5
B&K 4205
1.8
528’
2.5
1.5
6
B&K 4205 &IS siren
1.8
518’
0.5
0.5
no.
Type of noise source
Average barrier shielding efficiency. AL
(dB (A))
Average barrier shieiding eficiency, AL, (dB (A))
OMeasurement in semienclosure, constructed by walls of mineral wool, under roof. bMeasurement in industrial hall with large amount of absorbing materials. ‘Measurement in industrial hall with small amount of absorbing materials.
E. Walerian, M. Czechowicz.
322
R. Janczur
shielding efficiency. In the active range, the 3 m high barrier shielding efficiency might decrease to about 4 dB(A) due to the variations of the sources’ type, the position behind the barrier, and the effective room constants. 5 CONCLUSIONS When the barrier is arranged in a way which allows one to treat the barrier as an infinitely long, opaque screen, then its efficiency is near the insertion loss. The decisive factor of the barrier insertion loss in the free field is the geometry of the source-barrier-observation point system, i.e. the position of the source and the observation points relative to the barrier edge. The diminishing of efficiency, when the barrier is placed in a real system, is caused by interactions with the environment, due to multiple reflections from neighbouring objects’ surfaces. In the simplest cases, reflections from the ground, or between a floor and a ceiling, appear. In an industrial hall the reflected waves field assumes a very complex form. An approximate measure of the reflected waves field is the effective room constant which, in practice, can vary, depending upon the amount of the materials being temporarily stored in the hall. The investigations, carried out for the shielding efficiency of the 3 m high barrier in the open air, have shown that the theoretically achieved value with use of the Maekawa expression is about 3 dB (A) higher than the measured one. The barrier shielding efficiency after placing under the roof is about 13 dB (A) lower than that in the open air. In a room, in the most favourable circumstances, the achieved value within the barrier active range (at a distance from the barrier not greater than 4 m), was equal to 9 dB (A). For the smaller room constant, and for the source placed nearer the barrier upper edge, the barrier shielding efficiency decreased to 4 dB(A). The additional unshielded strong sources, present in the barrier vicinity, can cause further decrease of the barrier shielding efficiency. It can finally give even a negative value of the barrier shielding efficiency, while the barrier predominantly acts as an additional reflecting surface. With regard to all the discussed factors, the simple expressions presented in this paper for the barrier overall shielding efficiency in an industrial hall might be accepted as accurate enough, especially in the barrier active range. REFERENCES 1. Bowman, J. J., Senior, T. B. A. & Uslenghi, P. L. E. (eds), Electromagnetic and Acoustical Scattering by Simple Shapes. North-Holland, Amsterdam, 1970.
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2.
3. 4.
5. 6. 7. 8. 9.
10. 11.
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Kending, R. P. & Hayek, S. I., Diffraction by a hard-soft barrier. J. Acoust. sot. Am., 70 (1981) 115665. Rawlings, A. D., Plane-wave diffraction by rational wedge. Proc. Roy. Sot. London, A 411 (1987) 265-83. Walerian, E. & Janczur, R., Theories of diffraction applied for description of acoustical field screen efficiency. Inst. Fundam. Technol. Res. Rep., 25 (1985) (in Polish). Maekawa, Z., Noise reduction by screen. Memoirs of the Faculty of Engineering, Kobe University, 11 (1965). Yuzuwa, M. & Sone, T., Noise reduction by various shape barriers. Appl. Acoust., 14 (1981) 65-73. Maekawa, Z., Simple estimation method for noise reduction by variously shaped barriers. Arch. Acoust., 10 (1985) 369-82. L’Esperance, A., The insertion loss of finite length barrier on the ground. J. Acoust. Sot. Am., 86 (1989) 179-83. Janczur, R., Theoretical and scale-model investigation of a point source acoustical field in the presence of reflecting surfaces and screen. PhD thesis, Inst. Fundam. Technol. Res. Rep., 8 (1990) (in Polish). Rubinowicz, W., Die Beugungswelle in der Kirchhoffschen Theorie der Beugung. PWN, Warsaw, 1957. Walerian, E., Multiple diffraction at edges and right angle wedges. Acustica,
78 (1993) 201-9. 12. Janczur, R., Walerian,
E. & Oglaza, J., Acoustical field in space with obstacles. Part I: Description of geometrical field. Acustica, 78 (I 993) 15462. 13. Walerian, E. & Janczur, R., Acoustical field in space with obstacles. Part II: Propagation between buildings. Acustica, 78 (1993) 2lCk-19. 14. Terai, T., On calculation of sound fields around three dimensional objects by integral methods. J. Sound & Vibr., 69 (1980) 71-100. 15. Kawai, Y. & Terai, T., The application of integral equation methods to the calculation of sound attenuation by barriers. Appl. Acoust., 31 (1990) 101-17. 16. Hothersall,
D. C., Chandler-Wild, S. N. & Hajmirzae, M. N., Efficiency of single noise barriers. J. Sound & Vibr., 142 (1991) 303-22. 17. Kruzins, E. & Fricke, F., The prediction of sound field in non-diffuse spaces by ‘random walk’ approach. J. Sound & Vibr., 81 (1982) 549964. 18. Kruzins, E., The prediction of sound fields inside non-diffuse space: transmission loss consideration. J. Sound & Vibr., 91 (1983) 43945. 19. Kuttruff, H., Sound decay in reverberation chamber with diffusing elements. J. Acoust. Sot. Am., 69 (1981) 171623. 20. Kuttruff, H., Stationare Schallausbreitung in Flachraumen. Acustica, 57 (1985) 62-70. 21. Linqvist, E. A., Sound attenuation in large factory space. Acustica, 50 (1982) 313-28. 22. Linqvist, E. A., Noise attenuation in factory. Appl. Acoust., 16 (1983) 183241. 23. Kurze, H., Scattering of sound in industrial spaces. J. Sound & Vibr., 98 (1985) 349964. 24. Ondet, A. M. & Barry, J. L., Sound propagation in fitted rooms-comparison of different models. J. Sound & Vibr., 125 (1988) 13749.
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