Criteria
4.3 HEARING DAMAGE RISK
4.3.6 Some Alternative Interpretations
In Europe and Australia, the assumption is implicit in regulations formulated to protect people exposed to excessive noise, that hearing loss is a function of the integral of pressure squared with time as given by Equation (4.1). In the United States the same assumption is generally accepted, but a compromise has been adopted in formulating regulations where it has been assumed that recovery, during periods of non-exposure, takes place and reduces the effects of exposure. The situation may be summarised by rewriting Equation (4.1) more generally as in the following equation.
The prime has been used to distinguish the quantity from the traditional, energy averaged LAeq,8h, defined in Equation (4.1).
Various trading rules governing the equivalence of increased noise level versus decreased exposure time are used in regulations concerning allowed noise exposure.
For example, in Europe and Australia it is assumed that, for a fixed sound exposure, the noise level may be increased by 3 dB(A) for each halving of the duration of exposure, while in United States industry, the increase is 5 dB(A) and in the United States Military the increase is 3 dB(A).
Values of n in Equation (4.36), corresponding to trading rules of 3 or 5 dB(A), are approximately 1 and 3/5 respectively. If the observation that hearing loss due to noise exposure is a function of the integral of r.m.s pressure with time, then n = ½ and
n ' 3.01/L (4.37)
L)Aeq,8h ' L
0.301log10 1 8m
T
0
100 301(LA(t)&LB) /L 100 301LB/Ldt (4.38)
L)Aeq,8h ' L
0.301log10 1 8m
T
0
100 301(LA(t)&LB) /L dt % LB (4.39)
L)Aeq,8h ' L
0.301log10 1 8m
T
0
2(LA(t)&LB) /L dt % LB (4.40)
L)Aeq,8h ' L
0.301log10 1 8j
m i'1
2(LAi&LB) /L ×ti % LB (4.41)
Ta ' 8 × 2&(LAeq,8h) &LB) /L (4.42) the trading rule is approximately 6 dB(A). The relationship between n and the trading rule is:
where L is the decibel trading level which corresponds to a change in exposure by a factor of two for a constant exposure time. Note that a trading rule of 3 results in n being slightly larger than 1, but it is close enough to 1, so that for this case, it is often assumed that it is sufficiently accurate to set L)Aeq,8h ' LAeq,8h.
Introduction of a constant base level criterion, LB, which L)Aeq,8h should not exceed and use of Equation (4.37) allows Equation (4.36) to be rewritten in the following form:
Equation (4.38) may, in turn be written as follows:
or,
Note that if discrete exposure levels were being determined with a sound level meter as described above, then the integral would be replaced with a sum over the number of discrete events measured for a particular person during a working day. For example, for a number of events, m, for which the ith event is characterised by an A- weighted sound level of LA i, Equation (4.40) could be written as follows.
When L)Aeq,8h ' LB reference to Equation (4.40) shows that the argument of the logarithm on the right-hand side of the equation must be one. Consequently, if an employee is subjected to higher levels than LB, then to satisfy the criterion, the length of time, T, must be reduced to less than eight hours. Setting the argument equal to one, and evaluating the integral using the mean value theorem, the LA(t) ' LB ' LAeq,8h)
maximum allowed exposure time to an equivalent noise level, LAeq,8h) is:
If the number of hours of exposure is different to 8, then to find the actual allowed exposure time to the given noise environment, denoted LAeq,T) , the “8” in Equation (4.42) is replaced by the actual number of hours of exposure, T.
DND ' 2(LAeq,8h) &90) /L (4.43)
LAeq,8h ' 10 log10 1
8 7.2 × 1085/10 % 0.8 × 1096/10 ' 88.3 dB(A)
LAeq,8h ' 85.0 dB(A) ' 10 log10 Ta
8 0.9 × 1085/10 % 0.1 × 1096/10
Ta ' 8×2&(88 34&85 0) / 3 ' 8/21 11 ' 3.7 hours
The daily noise dose (DND), or “noise exposure”, is defined as equal to 8 hours divided by the allowed exposure time, Ta with LB set equal to 90. That is:
In most developed countries (with the exception of USA industry), the equal energy trading rule is used with an allowable 8-hour exposure of 85 dB(A), which implies that in Equation (4.39), L = 3 and LB = 85. In industry in the USA, L = 5 and LB= 90, but for levels above 85 dB(A) a hearing conservation program must be implemented and those exposed must be given hearing protection. Interestingly, the US Military uses L = 3 and LB = 85. Additionally in industry and in the military in the USA, noise levels less than 80 dB(A) are excluded from Equation (4.39). No levels are excluded for calculating noise dose (or noise exposure) according to Australian and European regulations, but as levels less than 80 dB(A) contribute such a small amount to a person’s exposure, this difference is not significant in practice.
Ex ample 4.1
An Australian timber mill employee cuts timber to length with a cut-off saw. While the saw idles it produces a level of 85 dB(A) and when it cuts timber it produces a level of 96 dB(A) at the work position.
1. If the saw runs continuously and actually only cuts for 10% of the time that it is switched on, compute the A-weighted, 8-hour equivalent noise level.
2. How much must the exposure be reduced in hours to comply with the 85 dB(A) criterion?
Solution:
1. Making use of Equation (4.2) (or Equation (4.38) with L= 3, in which case ), the following can be written:
LAeq,8h . LAeq,8h)
2. Let Ta be the allowed exposure time. Then:
Solving this equation gives Ta = 3.7 hours. The required reduction = 8 - 3.7
= 4.3 hours. Alternatively, use Equation (4.42) and let L = 3, LB = 85:
Ta ' 8×2&(87 2&90 0) / 5 ' 8×20 56 ' 11.8 hours
Alternatively, for an American worker, L = 5 and use of Equation (4.41) gives Equation (4.42) with L= 5 and LB = 90 gives for the allowed exposure LAeq,8h) ' 87.2.
time Ta: