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 Leq 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 Leq” or “Fast Leq“, 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 LAy(t) if A-frequency-weighting is used.

The symbols are for example : LAF (A-frequency-weighted and F-time-weighted sound level) and LCS (C-frequency-weighted and S-time-weighted sound level.)

The formula for LAy(t) is :-

A-frequency-weighted and F-time-weighted sound level equation