# Noise Measurement Terms Part 2 – Exponential and Linear Integration and Sound Level

Welcome to part 2 of our Noise Measurement Terms series. This time we are covering Exponential and Linear Integration and Sound Level.

## Exponential and Linear Integration

Many sound level descriptors – with the notable exception of **Peak** – are “averaged” in some fashion. Traditionally, exponential integration was used resulting in conventional sound level, while today the linear average resulting in **L _{eq}** is widely used. Exponential averaging methods must have a time constant of integration and this can greatly affect the reading you get. Three time constants are specified for use in noise measurement. ‘

**S**‘ (1s – was Slow), ‘

**F**‘ (0,125s – was Fast) and ‘

**I**‘ (35ms – was Impulse). The names were changed to single letters in the 1980’s to be the same in any language.

No LINEAR integral needs or can involve a time constant, so BY DEFINITION you cannot have “Slow L_{eq}” or “Fast L_{eq}“, but some bureaucrats – not in the UK – have still called for it is a few older National Standards.

The formal definition of time-weighting is:- *The exponential function of time, of a specified time constant, that weights the square of the instantaneous sound pressure*. The normal result of time weighting produces sound level.

## Sound Level

Sound Level is formally known as time-weighted sound level and is defined as:- *twenty times the base ten logarithm of the ratio of a given root-mean-square sound pressure to the reference sound pressure. Root-mean-square sound pressure being obtained with a standard frequency weighting and standard time weighting and is in decibels – symbol L_{Ay(t)} if A-frequency-weighting is used*.

The symbols are for example : **L _{AF}** (A-frequency-weighted and F-time-weighted sound level) and

**L**(C-frequency-weighted and S-time-weighted sound level.)

_{CS}### The formula for **L**_{Ay(t) }is :-

**L**

_{Ay(t) }