NOISE 771
hours, 24 hours, etc. The time period may be identified by the
subscript, e.g. L eq24 for a 24 hour averaging time.
Integrating sound level meters compute and display
equivalent sound level directly. If equivalent sound level is
to be determined from a number of representative instanta-
neous measurements or predictions, the above equation may
be rewritten as follows:(^)
LNL
i
N
eq^10 lg^110
10
1
( ⁄ )
⎡
⎣
⎢
⎤
⎦
⎥
⁄
∑ i.
(4.2)
If a large number of readings are involved, it is con-
venient to incorporate the above equation into a computer
program. If the base-10 logarithm is not available on the
computer it may be obtained from
lg(xx)^11 n( )⁄ n 10( ) (4.3)
where ln is the natural (base-e) logarithm.
Example Problem: Equivalent Sound Level
Considering four consecutive 15-minute intervals, during
which representative sound levels are 55, 58, 56 and 70 dBA
respectively. Determine equivalent sound level for that hour.
Solution:
Leq lg 1 4
dBA.
10 10 10 10 10
64 5
(⁄ ) 55 10 58 10 56 10 70 10
()
⁄⁄⁄⁄
.
It can be seen that higher sound levels tend to dominate when
determining L eq. Note that the mean average sound level (55
58 56 70)/4 59.8 has no significance.
DAY–NIGHT SOUND LEVEL
Day–night sound level takes into account the importance of
quiet during nighttime hours by adding a 10 dBA weighting
to noise during the period from 10 pm to 7 am. It is given by
(^)
Lt
t
L
L
DN am
pm
pm
am
lg 1/24 d
10 10
10
10
7
10
10
7
{[]⎡⎣⎢
⎤
⎦
⁄
∫
∫
( 10) 10 d
⎥⎥}
(5.1)
where L DN day–night sound level and t time (hours).
COMBINING NOISE FROM SEVERAL SOURCES
Correlated sound waves. Sound waves with a precise time
and frequency relationship may be considered correlated.
A sound wave arriving directly from a source may have a
precise phase relationship with a reflected sound wave from
the same source. The sound level resulting from combining
two correlated sound waves of the same frequency depends
on the phase relationship between the waves. Reactive muf-
flers and silencers are designed to produce reflections that
cancel the progressive sound wave.
Active noise control is accomplished by generating
sound waves out-of-phase with the noise which is to be
cancelled. Active noise control systems employ continuous
measurement, signal processing, and sound generation.
Uncorrelated noise sources. Most noise sources are not
correlated with one another. The combined effect of two or
more uncorrelated sources is obtained by combining the energy
from each at the receiver. To do this, we may add mean-square
sound pressures. In terms of sound levels, the result is
(^)
L L
i
N
i
T=
⁄
(^10) ∑ 10
10
1
lg
(6.1)
where L T total sound level due to N contributions L i (dBA
as measured or predicted at the receiver).
For two contributions, the total sound level is
L
L
LL
T
DIF 10
lg 10
lg 1 10
10 10
10
110 2 10
1
⁄⁄
⁄
⎡⎣ ⎤⎦
⎡⎣ ⎤⎦ (6.2)
where L 1 the greater sound level and DIF L 1 L 2 , the
difference between the two sound levels.
The last term in equation 6.2 may be identified as L (add), the
quantity to be added to L 1 to obtain total sound level L T. L (add)
is tabulated against DIF, the difference in levels, in Table 3.
Values are given to the nearest one-tenth decibel. Although
measured and predicted sound levels are often reported to the
TABLE 2
A-weighted sound levels
Approximate
sound level Noise source or criterion
140 Threshold of pain
122 Supersonic aircraftA
120 Threshold of discomfort
112 Stage I aircraftA
110 Leaf blower at operator
105 OSHA 1 hr/da limitB
99 EEC 1 hr/da limitB
90 OSHA and EEC 8 hr/da limitB
70 EPA criterion for hearing conservationC
67 DOT worst hour limitD
65 Daytime limit, typical community ordinance
45 Noise limit for virtually 100% indoor speech intelligibility
35 Acceptable for sleep
0 Threshold of hearing
Notes:
A: Aircraft measurements 500 ft beyond end of runway, 250 ft to side.
Stage 3 aircraft in current use are quieter.
B: Criteria for worker exposure (US Occupational Safety and Health
Administration and European Economic Community).
C: Environmental Protection Agency identified 24-hr equivalent sound level.
D: Department of Transportation design noise level for residential use.
C014_003_r03.indd 771C014_003_r03.indd 771 11/18/2005 10:46:07 AM11/18/2005 10:46:07 AM