Encyclopedia of Environmental Science and Engineering, Volume I and II

772 NOISE

nearest whole decibel, fractional values are often retained for

comparison purposes, and to insure accuracy of intermediate

calculations.

Note that addition of the contributions of two equal but

uncorrelated sources produces a total sound level 3 decibels

higher than the contribution of one source alone.

If the difference between contributions is 10 or more

decibels, then the smaller contribution increases total sound

level by less than one-half decibel. If the difference is 20

or more decibels, the smaller contribution has no significant

effect; for DIF  20, L (add) 1/20. This is an important

consideration when evaluating noise control efforts. If sev-

eral individual contributions to overall sound level can be

identified, the sources producing the highest sound levels

should be considered first. Figure 1 is a graph showing the

effect of combining noise levels.

Example Problem: Combining Noise Contributions

The individual contributions of five machines are as follows

when measured at a given location: 85, 88, 80, 70 and 95 dBA.

Find the sound level when all five are operating together.

Solution:

Using equation 6.1, the result is L T 
 10 lg[10 85/10 

10 88/10  10 80/10  10 70/10  10 95/10 ] 
 96.25 dBA. We could

use Table 3 instead. Combining the levels in ascending order,

the result is

70  80 
 80.4 and

80.4  85 
 86.3 and

86.3  88 
 90.3 and

90.3  95 
 96.3 dBA

Fractional parts of one dBA are only retained for purposes

or illustration.

For several sources which contribute equally to sound

level at the receiver, total sound level is given by

LLT
 1 10 lgn (6.3)

where L 1 
 sound level contribution at the receiver due to

a single source and n 
 the number of sources. Table 3 and

Figure 2 show the effect of combining n equal (but uncor-

related) contributions.

SOUND FIELDS

The region within one or two wavelengths of a noise source

or within one or two typical source dimensions is called the

near field. The region where reflected sound waves have a

significant effect on total sound level is called the reverber-

ant field. Consider an ideal nondirectional noise source which

generates a spherical wave. For regions between the near field

and the reverberant field, sound intensity is given by

IW
 ⁄⎡⎣^4 r⎤⎦

p^2

(7.1)

TABLE 3

Combining noise from two uncorrelated sources

DIF L(add) DIF L(add)

0.0 3.0 5.0 1.2

0.2 2.9 5.5 1.1

0.4 2.8 6.0 1.0

0.6 2.7 6.5 0.9

0.8 2.6 7.0 0.8

1.0 2.5 7.5 0.7

1.2 2.5 8.0 0.6

1.4 2.4 8.5 0.6

1.6 2.3 9.0 0.5

1.8 2.2 9.5 0.5

2.0 2.1 10.0 0.4

2.2 2.0 10.5 0.4

2.4 2.0 11.0 0.3

2.6 1.9 11.5 0.3

2.8 1.8 12.0 0.3

3.0 1.8 12.5 0.2

3.2 1.7 13.0 0.2

3.4 1.6 13.5 0.2

3.6 1.6 14.0 0.2

3.8 1.5 14.5 0.2

4.0 1.5 15.0 0.1

4.2 1.4 15.5 0.1

4.4 1.3 16.0 0.1

4.6 1.3 16.5 0.1

4.8 1.2 17.0 0.1

— — 17.5 0.1

— — 18.0 0.1

— — 18.5 0.1

— — 19.0 0.1

— — 19.5 0.0

L1 
 greater sound level, L2 
 lower sound level. DIF 


L1  L2, Combined sound level LT 
 L1  L(add).

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

Difference in levels

3.5

3

2.5

2

1.5

1

0.5

0

Add to higher level

FIGURE 1 Combining noise levels.

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