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

The formula for L_Ay(t) is :-