**Measuring noise, part 5**

The “nuisance” that an observer experiences from a loud noise event is not only a function of the peak level that the noise reaches but also depends upon the duration of the event. This idea is encapsulated in the concept of “sound exposure”.

To illustrate how this concept works I have borrowed another illustration from the US Department of Transport Federal Railroad Administration (US FRA). This was figure 2-5 on page 2-7 of the October 2005 version of the manual* High-Speed Ground Transportation Noise and Vibration Impact Assessment*, but it has been deleted from the September 2012 “final” version.

This figure shows noise graphs for passes by two different trains. The left-hand graph displays data for the TGV pass that I used in my blogs of 21 May and 14 Jun. The right-hand graph is for the Eurostar train travelling at 90 mph that I also referred to in my 21 May blog.

You may notice that the shapes of the graphs are different from the versions that I have used in my previous blogs. This is because the vertical scale has been constructed differently and I shall use a little of the dreaded mathematics to explain how this has been done.

I mentioned in my blog of 14 Jun that a power level on the dBA scale is usually denoted by “L”. So we may write:

L dBA = 10log_{10}(P/P_{ref}) = 10log_{10}(P) – 10log_{10}(P_{ref}) = 10log_{10}(P) (since we have chosen P_{ref }to be the zero point on our dBA scale).

So:

L = 10log_{10}(P)

Which may be rewritten:

(L/10) = log_{10}(P)

The logarithmic function of a number is defined as the exponent to which the base must be raised to produce that number, so:

P = 10^{(L/10)}

Note that since L is A-weighted, P is also A-weighted.

If, using the above relationship between L and P, we plot P on the vertical scale instead of L we will have a linear scale, and that is what has been done in the two graphs above and why the graphs look different from the versions that I have used in previous blogs. Note also that the vertical scale has been drawn from zero, not from the threshold point.

The purpose of changing the vertical scale in this way is that the shaded areas under the traces are now a true representation of the total noise energy released by each of the train passes, which is what the “sound exposure” is.

The final trick is to create a shaded zone of one-second duration which has equal area to the shaded area under the trace, and this is what has been done to create the tall zone at the right of each of the traces. The “height” of this tall zone, when converted back to dBA, is referred to as the SEL (sound exposure level) and dBA SEL is one way in which noise nuisance may be expressed.

The point about the US FRA figure showing two traces from two different types of train at two very different speeds is that the areas under the two traces are the same. This is because, whilst the TGV trace has a comparatively high maximum value, L_{max}, of 93 dBA it has a relatively short duration of 12 seconds. Conversely, L_{max} for the Eurostar trace is only 89 dBA, but the duration is 24 seconds. Since the two traces transcribe equal areas, then the SEL is the same for both passes at 93.8 dBA SEL.

The question that I have however is, do the two passes create the same noise nuisance? If SEL is meant to be a measure of noise nuisance, then we would expect that this would be the case, since both passes have the same value of dBA SEL. Looking at the two traces reproduced above, I’m not sure that I am convinced that this is likely to be true. My instinct tells me that the louder TGV pass will possibly create more annoyance than the Eurostar.

I feel instinctively that L_{max} must have a bearing on the nuisance level and that the importance of this parameter is not really reflected in SEL. However, I am not an acoustic engineer; perhaps there’s one out there somewhere who can put my mind at rest on this one.

In the next blog I will take a look at another, but related, way of assessing noise nuisance, which is the method most commonly encountered and the one being employed by HS2 Ltd.