# Noise Measurement Terms Part 3 – Time Average Sound Level, Sound Exposure Level (SEL) / LAE and Statistical Levels L10 & L90

In part 3 of our Noise Measurement Terms series, we cover Time Average Sound Level, Sound Exposure Level (SEL) / LAE and Statistical Levels L10 and L90.

## Time-Average Sound Level

The averaged linear integral is properly known as time-average sound level or more traditionally the equivalent continuous sound level or simply as ‘the Leq‘. It is defined as :- twenty times the base ten logarithm of the ratio of a root-mean-square sound pressure during a stated time interval to the reference sound pressure, sound pressure being obtained with a standard frequency weighting and is in decibels – symbol LAT if A-frequency-weighting is used. However, most people use the ‘shorthand’ of Leq or the slightly more correct LAeqT, where ‘T’ is simply the time from the beginning of the measurement to the end.

The formula for LAT or LAeqT is:-

The most obvious difference between the two methods of integration is that when using a linear integral ALL the sound since the start of the measurement is included with equal importance in the final value. By contrast, in an exponential average, the further back in time the sound occurred, the less it contributes to the final level on an exponentially decaying curve; thus, exponentially averaged or conventional sound level is often said to be a ‘snapshot’ of the noise.

## Sound Exposure Level (SEL) or LAE

This can be looked at as the ‘amount’ of noise, being based as it is on Sound Exposure, that is the time integral of the square of the pressure. Once LAE has been acquired it cannot become less – it is not an average value, whereas Leq can and will fall if the noise level reduces. While often ignored and usually poorly defined by most workers, in many ways it is the most useful metric available. The main problem with it is that because after a 1 second measurement the Leq and LAE have the same value, it leads people to call it the ‘1-second equivalent” or some such nonsense. Indeed, possibly the best way to regard these two metrics is that effectively Leq is LAE divided by time – mathematically incorrect but a practical way of seeing it; the correct maths are shown below.

Most sound level meters today function by frequency weighting the pressure signal (p) from the microphone and squaring this to produce (p2). This is then integrated to produce p2 or Sound Exposure (EA) and this is the basic quantity used for hearing damage risk, no matter what ‘spin’ bureaucrats put on it by inventing complex variants of it. By taking a new value of EA a few times every second, the meter than computes all the other metrics needed. Subject to a few practical constraints, virtually everything – except peak – can be computed from EA.

Formally, Sound Exposure is :-

The level equivalent is :-

In both formulae t1 and t2 are simply the times of starting and ending the measurement and the second part of the equation shows the formal relationship between LAE and LAT.

## Statistical Levels – L10 & L90

These are two of a whole series of levels collectively known as the Ln values. ‘n’ can be any number from 0.1 to 99.9 assuming the system has a 0.1dB resolution. There is no international standard to describe these, despite them being very widely used in environmental noise work. They are usually defined as :- the level – in decibels – exceeded for n% of the time. The critical word is ‘exceeded’ and this has caught out many workers who failed to see the maths behind the word.

Because there is no internationally agreed standard for the Ln values, the user must specify what basic metric was used to create them, as they are simply statistical descriptors. It could be any of the sound level metrics, for example LAFLAS , LAT or even LCpk. It is important to note that the metric used will affect the resulting values to a significant degree. The metric most commonly used is LAF, probably due more to tradition than technical merit.

The two most common Ln values used are L10 and L90 and these are sometimes called the ‘annoyance level’ and ‘background level’ respectively. L10 is almost the only statistical value used for the descriptor of the higher levels, but L90L95 and L99 are widely used by some workers to describe the background level. L50 is the only other ‘standard’ value commonly used: the level exceeded for half the time. Mathematically L10 is the 90% percentile and percentiles are used in every branch of statistics.

The most annoying feature is that because these metrics are statistical, they can only be computed after the measurement period has ended and statistical values over different time periods cannot be combined. Thus, if you need to measure the Lnvalues every hour and also overnight and during the day, three separate measurements are needed. The Cirrus Noise Pole solves this problem by having three separate statistical groups that can be set to almost any time periods.