# 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 **L _{eq}**‘. 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

**L**if A-frequency-weighting is used. However, most people use the ‘shorthand’ of

_{AT}**L**or the slightly more correct

_{eq}**L**, where ‘T’ is simply the time from the beginning of the measurement to the end.

_{AeqT}The formula for **L _{AT}** or

**L**is:-

_{AeqT}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 L_{AE}

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 **L _{AE}** has been acquired it cannot become less – it is not an average value, whereas

**L**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

_{eq}**L**and

_{eq}**L**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

_{AE}**L**is

_{eq}**L**divided by time – mathematically incorrect but a practical way of seeing it; the correct maths are shown below.

_{AE}Most sound level meters today function by frequency weighting the pressure signal (p) from the microphone and squaring this to produce (p^{2}). This is then integrated to produce p^{2} or Sound Exposure (**E _{A}**) 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

**E**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

_{A}**E**.

_{A}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 **L _{AE}** and

**L**.

_{AT}**Statistical Levels – L10 & L90**

These are two of a whole series of levels collectively known as the **L _{n}** 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 **L _{n}** 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

**L**,

_{AF}**L**,

_{AS}**L**or even

_{AT}**L**. It is important to note that the metric used will affect the resulting values to a significant degree. The metric most commonly used is

_{Cpk}**L**, probably due more to tradition than technical merit.

_{AF}The two most common **L _{n}** values used are

**L**and

_{10}**L**and these are sometimes called the ‘annoyance level’ and ‘background level’ respectively.

_{90}**L**is almost the only statistical value used for the descriptor of the higher levels, but

_{10}**L**,

_{90}**L**and

_{95}**L**are widely used by some workers to describe the background level.

_{99}**L**is the only other ‘standard’ value commonly used: the level exceeded for half the time. Mathematically

_{50}**L**is the 90% percentile and percentiles are used in every branch of statistics.

_{10}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 **L _{n}**values 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.