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Loud noise makers and worker safety

In some workplaces, at some construction sites, there are various machines doing all kinds of things. The issue is taken up in the following Kohler Power Systems presentation (Figure 1) at pages 18 through 25:

Figure 1 Kohler Power Systems presentation.

The underlying mathematics merits some attention.

Imagine two diesel engine driven power generators, two really intense noise makers if you will, running simultaneously. Each of which is delivering sound to some nearby location at some particular sound pressure level (SPL), measured in dBA, and let us further assume that one of them is louder than the other (Figure 2).

Figure 2 Man exposed to two noise makers.

Letting dBA1 be louder than dBA2, if we add the effect of dBA2 to the effect of dBA1, we must ask by what amount will the combination of the two, dBA12, be louder than was the case for dBA1 alone?

The underlying math and the consequences are seen as follows:

Figure 3 The number of decibels that adding dBA2 to dbA1 increases the total SPL (dBA12) when dBA1 is 106 dBA.        

Starting with some value of dBA1, starting at 106 dBA for example, the increase from dBA1 to dBA12 varies with the level of the less noisy dBA2. If for example, the dBA1 is delivering its 106 dBA and we then add a dBA2 (which is 6 dBA lower), then the dBA12 will rise to 106.97 dBA—a net rise to SPL of very nearly 7 dB, just as cited in the referenced presentation (page 20).

It may seem a bit counter intuitive, but if the starting SPL of dBA1 is different, the degree of SPL worsening as the result of introducing dBA2 does not change versus how many dB the dBA2 is lower than the dBA1. The curves of Figure 3 and of Figure 4 are the same and are correct.

Using a different dbA1 level (50 dBA), we can see this as follows:

Figure 4 The number of decibels that adding dBA2 to dbA1 increases the total SPL (dBA12) when dBA1 is 50 dBA.

In this second example, starting with the dBA1 at only 50 dBA instead of 106 dBA, the number of decibels of worsening SPL as we add in dBA2 at so many decibels down from the dBA1 remains the same as in the previous example.


[1] Kabir, R. (2021). Generator Enclosure Basics, Considerations, and Options. Kohler Power Systems Webinar.

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