12 July, 2021

# Why am I getting LA,eq values below the LA,90. Surely that’s impossible?

No, it’s not impossible at all, and probably it is related to measuring low levels. By having a think about how statistical levels are calculated, all should become clear.

Firstly, the LAeq is the A-weighted equivalent energy over a certain period. It’s independent of time weighting (e.g. F), and the measurement range of the instrument will be defined by the linearity range in the specifications, as defined by IEC 61672:2013-1. Anything outside this range will be flagged as underrange or overload.

The LA,n values are calculated from a statistical analysis of the sampled sound pressure levels, in dB, and there is no standardised definition of the calculation procedure. This means that it can vary between instrument types/manufacturers. However, most instruments work in a similar way, despite the calculation of statistics not being standardised.

To calculate statistics, the measurement range is split up into counting ‘bins’, with a resolution of, typically, 0.1dB. So, for a measurement range of, say, 80dB, there will be 800 ‘bins’ or levels. As a sample comes along, it is put into the appropriate bin, and at the end of the measurement period, we count up the number of samples in each bin to get our Level Distribution. You can normally view this distribution on the display of Svantek instruments.

We can then calculate the Cumulative Distribution by accumulating all the sample progressively from the lowest bin to the highest bin.

The LA,90 will then be the value for 90% on the Cumulative Distribution.

Now, it’s possible that there will be SPL measurement values below the measurement range of the instrument, particularly if the levels are low, or the measurement range selected is too high. Where does the analyser put those samples – it can’t just throw those away? The solution is simply to put it in the lowest bin, and worry about it afterwards. For periods where there is a lot of low level data, this will have the effect of collapsing the distribution onto the lowest bin, while the lowest period LA,eq data may well be below range. This will give the possibility that low level values (e.g. LA,90) will end up higher than the reported LA,eq.

The only solutions are to select a lower measurement range, or, if that’s not possible, to simply flag the data for that period as invalid or contaminated by instrument noise.

Example
Here’s an example of a multifile from a Svan 958A instrument. The 15 minute summary results have been merged to create a time history of LA,eq and LA,90.

You can see that during the night, the LA,90 (blue) bottoms out at 38.1dBA, while the LA,eq (red) drops even lower, reaching 34.7dBA at around 2am.

Let’s take a look at the instrument settings in the header of the file…..

This is just part of the header, but shows the key settings of the channels. Channel 4 in the 958A is the one typically used for sound measurement, and the Measurement Range is shown as ‘High’ (the 958A has two measurement ranges, Low and High).

Taking a look at the manual and technical specifications, the 958A with a nominal 50mV/Pa microphone will have two linearity ranges of 45-130dB (High) and 24-115dB (Low). These are the linearity ranges of the instrument, which conform to IEC61672-1:2013 to Class 1. It is possible to measure results below 44dBA (High) and 24dBA (Low) but they would be flagged as underrange.

The statistics bins will be set around 7dB below the bottom of the linearity range, as this is the bottom limit of the dynamic range, so in this case, around 38dBA (this may vary depending on the calibration factor of the instrument).

So, in this example, you can see that you will not get a Ln value of any kind below 38dBA (in this case 38.1dBA), however, the underrange Leq will drop to the noise floor of the instrument.

In fact, if we draw a graph of 9 values of Ln, from L10 to L90, you’ll clearly see this effect.

This example shows that it would have been better to use the ‘Low’ measuring range on the 958A, which would still have been high enough to manage the daytime sound levels.