Reverberation Time

Reverberation General

In rooms sound energy is reflected on walls, ceiling and floor. With all reflections and reflections of reflections the sound is 'prolonged'. The reverberation time is defined as the time until the sound pressure level would be decreased by 60 dB after the sound source is switched off abruptly. Because this time normally cannot be measured because of too high ambience noise, the equivalent in a shorter time will be measured.
Reverberation time is the primary characterization of an acoustic environment. All other acoustic parameters are more or less connected to the reverberation time. The 'optimum' reverberation time depends on the use of the space. Speech needs a more dry environment, there as music demands a certain richness and liveliness in the room. Different styles of music require different acoustic conditions with different reverberation times.
Measurements of reverberation time are divided in four different measurements: EDT, T10, T20, T30. Each of these parameters and the relationship between them can reveal more inside into the room's specification.

'dry' signal short reverberation long reverberation

See: RT Measurements     Concert Hall Acoustics

Reverberation Time (sec)

Reverberation Time is the global quantitative criterion of the sound field in the room.

Two types of reverberation time are measured. One is EDT (Early Decay Time), the second is Reverberation Time RT as T10, T20 and T30.

Early Decay Time EDT (sec)

The EDT is a reverberation time derived from the initial 10 dB of decay. It is the length of time that it takes for the sound to decay 10 dB after the sound source is turned off. EDT more closely corresponds to subjective evaluation of the reverberation time then RT. It affects principally the hall's support to the voice and adds definition to the higher tones of music.
The measurement is multiplied by the factor of 6 to make it comparable with RT60.

T10, T20, T30 (sec)

RT is the time it takes for a loud sound to decay to inaudibility after its source is cut off. It is defined as the level difference of -60 dB.
It is evaluated with three different parameters:
T10 as the decay from -5 to -15 dB
T20 as the decay from -5 to -25 dB
T30 as the decay from -5 to -35 dB

T10 is multiplied with the factor 6, T20 with the factor 3 and T30 with the factor 2 to be comparable with the classical term RT60 (decay over 60 dB).

EDT is the subjectively more important parameter and is strongly related to the perceived reverberance. T20 and T30 are more related to the physical properties of the room.

Calculation of Reverberation Time

Reverberation time can roughly be calculated by the formula of Sabine. Wallace Clemens Sabine developed this formula during his work to improve the room acoustic of the Lecture Hall of the Fogg Art Museum in the late 1890s. This 'Sabine' formula works well for rooms with straight and even walls. For more complicated rooms other more complicated formulas were developed later. Today room acoustic simulations should be carried out to get all the details in consideration.

Sabine based his empirical formula on the sound decay of 60dB (1/1000 SPL) after the abruptly end of a test tone (shot, shooting, etc.).

Sabine's RT formula

V: volume of the room in square meter
a: total average absorption coefficient of all wall, ceiling and floor surfaces
S: total surface area of the room in square meter (all walls, ceiling, floor)

The absorption coefficient of a surface is a number between 0 and 1, there '0' indicates no absorption at all and '1' indicated total absorption (as with an 'open window', there all sound energy striking this area leaves the room completely equal to a 100% absorption of the sound energy).
It must be kept in consideration that this calculations are frequency neutral, but the frequency dependency of reverberation is very important for the overall sound impression of a room (see below).

See: Absorber.

Reverberation versus Frequency

Reverberation time specifications without reference to frequency are often misleading. The same reverberation time but with different frequency dependencies sound very different and can make the difference between good acoustic and non-usable acoustic.
The low frequency range of the reverberation is depending on low-frequency absorption. Low-frequency absorption is often caused by plywood or gypsum walls that resonate and therefore absorb energy. Concrete or stone walls have nearly no low-frequency absorption. Because of that the 'cold' looking stone walls create a more 'warm' sounding acoustic, there as 'warm' looking wooden walls can create a 'cold' sounding acoustic because of lacking low frequency energy (absorbed by resonating wooden plates).

typical concert hall reverberation

high low frequency damping (often caused by plywood and gypsum walls)

perfect reverberation for speech oriented roomstoo high low frequency reverberation (booming sound)

Initial Time Delay Gap ITDG (msec)

The time difference between the arrival of the direct sound and the earliest and most significant reflection (at listener's position), excluding floor reflections. It corresponds to the subjective impression of 'intimacy'. ITDG is measured in msec.

Early Reflections

The early reflections are the first reflections arriving at a listeners ears. Because of the shortest path lengths these reflections are isolated events during the first 5 to 100 milliseconds. First reflections are the reflections of the first order but can be also reflections of the second or higher orders (reflections of reflections on a second or third surface). Part of the 'early reflections' by definition are all arriving reflections of walls, ceilings and floor (other than the Initial Time Delay Gap (see above), there the reflections over the floor are excluded). Early reflections arrive later than the direct sound but before the onset of the full reverberation. These reflections cause psychoacoustic reactions to get a sense of room size and distances in the room.

first reflections in a room between source and listener these first reflections as 'early reflections'

Reverberation Time and Room Size

Reverberation time is only indirectly depending on room size. It depends on the interaction of room size and absorption. With different room sizes mainly the Initial Time Delay Gap (ITDG) changes drastically because of different travel paths of the first significant reflections.

reverberation of 2 sec in a bath room reverberation of 2 sec in a concert hall
reverberation of 2 sec in a wide factory hall

DIN 18041

The German standard DIN 18041 ("acoustical quality in small to medium size rooms") recommends reverberation times for class rooms, meeting rooms and conference rooms. It was revised the last time in 2004. It corresponds to the Swiss standard SIA 181 and the Austrian standard ÖľNORM EN 12354-6 [3]. For a frequency range from 500Hz to 1kHz the following equations should be used to calculate appropriate reverberation times for fully occupied rooms:

For empty rooms the RT can be raised for about 0.2 sec. For instance, a room with 770qm should have no longer reverberation time than 0.75 sec for the fully occupied room and 0.95 sec for the empty room.

To reach a high speech intelligibility the overall performance of the room is important. It is necessary to prevent focused reflections by the use of sufficient sound diffusion especially on the walls of the room. A reflective ceiling can help to improve speech intelligibility and strength by carrying energy from the talker to the audience.

DIN 18041: suggested reverberation time versus room size
DIN 18041: tolerance range for speech DIN 18041: tolerance range for music
time axis indicating the relation between suggested and real reverberation time
1,0: measured reverberation time equals suggested reverberation time for 500Hz to 1kHz

ANSI standard S12.60-2002 specifies a reverberation time of 0.6 sec for normal classrooms and 0.7 sec for large classrooms.