# Reverberation Time (RT)

## Table of Contents

**Definition**: The reverberation time in a room at a given frequency is the time required for the mean-square sound pressure in that room to decay from a steady state value by 60dB after the sound suddenly ceases. This is one of the most vital , though not the only, measures of a rooms acoustic properties and can be a guide to the suitability of a room for a given purpose.

Several diferent definitions for the reverberation time are available and have different applications. I will mention the three primary ones, though mostly Sabine and Eyring are used in practice.

**Sabines** equation provides most accurate results when the average absorption coefficient < 0.2. In this respect the effects air absorption is neglected above 4 kHz (where it becomes dominant). This is the classical and oldest RT equation developed by W.C. Sabine at the turn of the century.

and with air absorption

where

Where *T* = Reverberation time (s), *V* = room volume (m^3), *S* = total surface area of room (m^2),
= the average absortption coefficient (dimensionless), *m* = attenuation constant of air

Typically 4*mV* is small for small room and can be neglected (as for Eyring)

**Eyring** - For use when the average absorption coefficient > 0.2 alsoapplied to frequencies below 4kHz. The second term in the denominator is added to take inot account the air absorption at high frequencies

**Fitzroy** - applies when absorption is unevenly distributed. RT can be estimated indepenently for each room axis, and the total RT can be estimated from the sum of these three (*x*, *y*, *z*) components.

Where *x*, *y*, *z* = total area of two oposite parallel walls (m^2), , ,
= average absorption coefficients of a pair of opposite wall

The air absorption term may also be applied to the Fitzroy formula if required.

Other reverberation formulae exist but these are the three primary ones of interest (CADP2 incorporates all others, but they are of little use over these main three above).