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7.7 ACOUSTIC BARRIERS

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Acoustic barriers are commonly used for the control of noise in outdoor

applications, such as reduction of highway noise to the surrounding areas,

reduction of noise from transformer stations, and reduction of noise from

construction equipment. Barriers are also used to reduce noise in indoor

applications, such as in open-plan offices and schools and for machines that

cannot be totally enclosed. For indoor applications, barriers are effective

only for those cases in which the direct sound field is predominant at the

receiver location, although the absorptive surface of the barrier will also

reduce the reverberant field somewhat. In general, barriers are more effective

in reducing high-frequency noise than for low-frequency noise.

312 Chapter 7

FIGURE 7-14 Example of door seals for an enclosure: (a) compression seal, (b)

drop seal, and (c) spring-loaded seal.

Sound interacts with a barrier in three ways: (a) reflection from the

barrier surface, (b) direct transmission through the barrier, and (c) diffraction

over the top of the barrier. The barrier should have a high transmission

loss to be effective in blocking the sound. Also, the barrier should have an

absorptive covering for indoor applications.

7.7.1 Barriers Located Outdoors

For transmission of sound across a barrier located outdoors, the following

expression has been developed for the sound pressure level Lp at the receiver

position due to a point noise source having a sound power level LW on the

opposite side of the barrier (Maekawa, 1968):

Lp ј LW юDI_20log10рAюBЮ_10log10

ab юat

_ _

_10:9 (7-89)

The quantities A and B are distances from the noise source to the top of the

barrier and from the top of the barrier to the receiver, respectively, as

illustrated in Fig. 7-16. The quantity ab is the barrier coefficient, and at is

the sound power transmission coefficient for the barrier wall.

For a point source, the barrier coefficient may be found from the

following expression:

ab ј

tanh2Ѕр2_NЮ1=2_

2_2N рfor N < 12:7Ю (7-90a)

ab ј 0:0040 рfor N 12:7Ю (7-90b)

RoomAcoustics 313

FIGURE 7-15 Typical sound trap for ventilating fans in an enclosure.

The quantity N is the Fresnel number, which is the ratio of the difference

between the direct path length d and the path length over the barrier to onehalf

of the wavelength of the sound _:

N ј

_ рA ю B _ dЮ ј

c рA ю B _ dЮ (7-91)

The quantity f is the frequency of the sound wave and c is the sonic velocity

in the air around the barrier.

For traffic noise from a roadway, the difference between the sound

pressure level at the source with the barrier Lp and without the barrier Lop

given by the following expression (Barry and Reagan, 1978):

Lop

_ Lp ј 15 log10

A ю B

_ _

ю 10 log10

a3=4

b ю at

(7-92)

The barrier coefficient ab is given by Eq. (7-90).

For effective noise control, the barrier should be sufficiently massive

that the sound transmitted directly through the barrier is negligible compared

with the sound transmitted over the wall. For design purposes, the

sound power transmission coefficient at should be less than about 1/8 of the

barrier coefficient:

at < ab=8 (design condition) (7-93)

Example 7-9. A concrete barrier 100mm (4 in) thick is to be built around a

transformer station located outdoors. The top of the barrier is 2.50m (8.2 ft)

high above the transformer and is located 10m (32.8 ft) from the transformer.

The property line (receiver) is located 30m (98.4 ft) from the transfor-

314 Chapter 7

FIGURE 7-16 Barrier dimensions.

mer. The directivity factor for the transformer may be taken as Q ј 1. The

sound power level spectrum and the transmission loss for the barrier as a

function of frequency are given in Table 7-6. Determine the sound pressure

level spectrum without the barrier in place and with the barrier.

Let us work out the calculations for the 500Hz octave band in detail.

Without the barrier, the sound pressure level may be determined from Eq.

(5-5), neglecting attenuation in the atmospheric air:

p ј LW юDI_20log10 d _10:9 ј 106ю0_20log10р30Ю_10:9

p ј 106_29:5_10:9 ј 65:5dB

The results for the other octave bands are shown in Table 7-6. If we use

these values to determine the A-weighted sound level, we find the following

value:

A ј 69:6dBA

If the transformer noise were continuous (both day and night), the day–

night level may be found from Eq. (6-8):

LDN ј 10log10Ѕр0:625Ю 106:96 юр0:375Ю 107:96_ ј 76:0dBA

If the transformer were located in an urban residential area (no corrections),

the anticipated community response, from Table 6-17, would involve vigorous

community action.

The barrier could be placed around the transformer station to alleviate

this negative community response. The dimensions for the barrier, assuming

the source (transformer) and the receiver are at the same elevation, are as

follows:

A ј р102 ю 2:502Ю1=2 ј 10:308m р33:82 f tЮ

B ј р202 ю 2:502Ю1=2 ј 20:156m р66:13 f tЮ

рA ю B _ dЮ ј 10:308 ю 20:156 _ 30:0 ј 0:463m р1:520 ftЮ

The Fresnel number at 500 Hz, for a sonic velocity of c ј 347 m/s, corresponding

to an air temperature of 300K (808F), is calculated from Eq.

(7-91):

N ј р20Юр500Юр0:463Ю

р347Ю ј 1:335 < 12:7

2_N ј р2_Юр1:335Ю ј 8:391

The barrier coefficient is found from Eq. (7-90a):

ab ј

tanh2р

ffiffiffiffiffiffiffiffiffiffiffi

p8:391 Ю

р_Юр8:391Ю ј 0:03748

Room Acoustics 315

316 Chapter 7

TABLE 7-6 Solution for Example 7-9

Item

Octave band center frequency, Hz

63 125 250 500 1,000 2,000 4,000 8,000

Given data:

LW, dB 112 116 110 106 106 100 95 89

TL, dB 36 38 38 38 38 44 50 56

Without the barrier in place:

Lop

, dB 71.6 75.6 69.6 65.6 65.6 59.6 54.6 48.6

With the barrier in place:

N 0.167 0.334 0.667 1.335 2.671 5.342 10.68 21.4

ab 0.1807 0.1216 0.0710 0.0375 0.0189 0.0095 0.0047 0.0040

at 0.0003 0.0002 0.0002 0.0002 0.0002 4 _ 10

_5 1 _ 10

_5 3 _ 10

_10 log10

рab

ю at

Ю 7.4 9.1 11.5 14.2 17.2 20.2 23.2 24.0

Lp, dB 64.0 66.3 57.9 51.2 48.2 39.2 31.2 24.4

The sound power transmission coefficient at 500Hz is as follows:

at ј 10_TL=10 ј 10_3:8 ј 0:00016 < р0:03748Ю=р8Ю ј 0:00469

ab юat ј 0:03748ю0:00016 ј 0:03764

The sound pressure level in the 500Hz octave band with the barrier in

place is found from Eq. (7-89):

Lp ј 106ю0_20log10р10:308ю20:156Ю_10log10р1=0:03764Ю_10:9

Lp ј 106_29:7_14:2_10:9 ј 51:2 dB

The results for the other octave bands are given in Table 7-6. The corresponding

A-weighted sound level is as follows:

LA ј 55:3dBA (with the barrier in place)

The day–night level, for continuous noise day and night, is found as in the

previous calculation:

LDN ј 61:7dBA

If the transformer were located in an urban residential area (no corrections),

the anticipated community response, from Table 6-17, would be ‘‘no reaction.’’

We may make the following observations relative to this example.

First, we see that the barrier is most effective in reducing high-frequency

noise. For the 63Hz octave band, the barrier reduces the sound pressure

level by р71:6_64:0Ю ј 7:6dB. On the other hand, the barrier reduces the

sound pressure level by (48:6_24:4Ю ј 24:2dB in the 8000Hz octave band.

The reduction in the 8000Hz octave band is more than 3 times that for the

63Hz octave band.

Secondly, we note that the A-weighted sound level is reduced by

р69:6_55:3Ю ј 14:3dBA. The use of a barrier changes the anticipated community

response from ‘‘vigorous pursuit of legal action’’ to ‘‘no reaction,’’

without the need for a complete enclosure of the transformer station.

7.7.2 Barriers Located Indoors

When a barrier is located indoors, it will primarily affect the direct sound

field; however, there will also be an effect on the reverberant sound field due

to surface absorption of the barrier wall, as illustrated in Fig. 7-17.

The acoustic energy density associated with the direct sound field, if

attenuation in the room air is negligible, is given by the following expression:

Room Acoustics 317

DD ј

WQрab ю atЮ

4_рA ю BЮ2c

(7-94)

The quantity W is the acoustic power for the sound source and Q is the

directivity factor for the source.

The room constant is changed by the insertion of the barrier, because

additional surface is exposed to the reverberant field. The room constant

with the barrier in place is given by the following expression:

Rb ј

__So ю Sbр_1 ю _2Ю

1 _ __ _ рSb=SoЮр_1 ю _2Ю

(7-95)

The quanity __ is the average surface absorption coefficient for the room and

So is the surface area of the room (excluding the surface area of the barrier).

The quantities _1 and _2 are the surface absorption coefficients for the front

and back sides of the barrier and Sb is the surface area of one side of the

barrier.

The sound pressure level, with the barrier in place, is found from the

following expression, for an indoor application:

Lp ј LW ю 10 log10

Rb ю

Qрab ю atЮ

4_рA ю BЮ2

_ _

ю 0:1 (7-96)

318 Chapter 7

FIGURE 7-17 Barrier located indoors.

For indoor applications, the barrier is most effective in reducing noise

for the situations in which the term associated with the direct sound field,

Q=4_r2, is much larger (say, more than 6 times larger) than the term associated

with the reverberant sound field, 4=R, in Eq. (7-17).

Example 7-10. A machine has an octave band sound power level of 109 dB

for the 1000 Hz octave band. The machine is located in a room having

dimensions of 30m _ 30m _ 5m high (98:4 ft _ 98:4 ft _ 16:4 ft high),

with an average surface absorption coefficient of 0.35. The machine has a

directivity factor of 2.0, and the operator is located at a distance of 3.00m

(9.84 ft) from the machine. It is desired to reduce the noise received by the

operator by placing a barrier 5.00m long _ 3.00m high (16.40 ft _ 9.84 ft)

at a distance of 1.00m (3.28 ft) from the machine, as shown in Fig. 7-18. The

operator’s ear and the machine center are both 1.50m (59 in) above the

floor. The transmission loss for the barrier is 31 dB in the 1000 Hz octave

band. The surface absorption coefficient for one side (facing the operator) of

the barrier is 0.90, and the absorption coefficient for the other side is 0.20.

Determine the sound pressure level in the 1000 Hz octave band at the

operator’s ear without the barrier and with the barrier in place.

The surface area of the room is as follows:

So ј р2Юр30 ю 30Юр5Ю ю р2Юр30Юр30Ю ј 2400m2 р25,830 ft2Ю

The room constant without the barrier is found from Eq. (7-13):

R ј

__So

1 _ __ ј р0:35Юр2400Ю

1 _ 0:35 ј 1292m2

Room Acoustics 319

FIGURE 7-18 Diagram for Example 7-10.

The sound pressure level, without the barrier in place, is given by Eq. (7-18):

Lop

ј 109 ю 10 log10

1292 ю

2:0

р4_Юр3:00Ю2

_ _

ю 0:1

Lop

ј 109 ю 10 log10р0:003095 ю 0:017674Ю ю 0:1 ј 92:3dB

At this point, we may note that the barrier should be effective in reducing

the noise to the operator, because the direct field is р0:017675=0:003095Ю ј 5:7 or about 6 times as large as the reverberant field.

The room constant, with the barrier in place, is calculated from Eq.

(7-95):

Rb ј р0:35Юр2400Ю ю р5:00Юр3:00Юр0:90 ю 0:20Ю

1 _ 0:35 _ р15=2400Юр0:90 ю 0:20Ю ј 1332m2

The presence of the barrier in the room increases the room constant by

about 3%.

The distances for the barrier are found as follows:

A ј р1:002 ю 1:502Ю1=2 ј 1:8028m р5:915 ftЮ

B ј р2:002 ю 1:502Ю1=2 ј 2:5000m р8:2021 ftЮ

A ю B _ d ј 1:8028 ю 2:5000 _ 3:00 ј 1:3028m р4:274 ftЮ

The Fresnel number from Eq. (7-91) is as follows:

N ј

2f рA ю B _ dЮ

c ј р2Юр1000Юр1:3028Ю

р347Ю ј 7:509 < 12:7

2_N ј р2_Юр7:509Ю ј 47:18

The barrier coefficient is found from Eq. (7-90a):

ab ј

tanh2Ѕр47:18Ю1=2_

р_Юр47:18Ю ј 0:006747

The sound power transmission coefficient for the barrier is as follows:

at ј 10_TL=10 ј 10_3:10 ј 0:000794

The sound power level at the operator’s location with the barrier in

place is found from Eq. (7-96):

Lp ј 109 ю 10 log10

1332 ю р2:0Юр0:006747 ю 0:000794Ю

р4_Юр1:8028 ю 2:500Ю2

_ _

ю 0:1

Lp ј 109 ю 10 log10р0:003004 ю 0:0000648Ю ю 0:1 ј 84:0dB

320 Chapter 7

The use of the barrier reduced the noise in the 1000 Hz octave band

from 92.3 dB to 84.0 dB, or a reduction of 8.3 dB. The reverberant field

contribution is reduced from 0.003095 to 0.003004, or a reduction of

about 3%. On the other hand, the direct field contribution is reduced

from 0.017674 to 0.0000648, or a reduction of more than 99%.

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