# Reverberation time

The reverberation time  T 60 or simply  T , in English mostly reverberation time ( RT ), is the best-known key figure for room acoustics . The reverberation time is the time interval within which the sound pressure in a room drops to a fraction, at T 60 to a thousandth, of its initial value when the sound source suddenly falls silent, which corresponds to a decrease in sound pressure level of 60  dB .

The reverberation time of a room is usually given for the center frequency of a third-octave filter with a frequency of 500  Hz or 1 kHz or as a frequency-dependent curve, but this does not represent a frequency response of the reverberation.

## Reverberation time and sound absorption

The American physicist Wallace Clement Sabine (1868–1919) found out through experiments in 1898 that the reverberation time is proportional to the volume of a room and inversely proportional to the equivalent absorption area of the surrounding surfaces, i.e. H. the larger the room and the harder (more reflective ) the surface materials, the longer the reverberation time: ${\ displaystyle V}$ ${\ displaystyle A}$

${\ displaystyle T = k \ cdot {\ frac {V} {A}}}$

With

${\ displaystyle A = \ sum _ {i = 1} ^ {N} S_ {i} \ alpha _ {i} + 4mV}$
Are there
• ${\ displaystyle S_ {i}}$ the respective partial areas
• ${\ displaystyle \ alpha _ {i}}$the associated degrees of absorption ; a high degree of absorption corresponds to a low degree of reflection in acoustics and vice versa
• ${\ displaystyle m}$the sound attenuation of the propagation medium , e.g. B. Air; often, especially with small room volumes, the attenuation term can be neglected.${\ displaystyle 4mV}$

The constant of proportionality has the value

• ${\ displaystyle k = {\ frac {24 \ cdot \ ln 10} {340 {\ frac {\ mathrm {m}} {\ mathrm {s}}}}} = 0 {,} 163 {\ frac {\ mathrm {s}} {\ mathrm {m}}}}$, provided ${\ displaystyle \ alpha \ ll 1}$
• for the following Eyringsche formula provides better values.${\ displaystyle \ alpha> 0.2..0.3}$

In the 1920s, this equation, which made the acoustic planning of buildings possible for the first time in its design phase, was specified into Eyring's reverberation formula , which applies to everyone : ${\ displaystyle \ alpha}$

${\ displaystyle T = k \ cdot {\ frac {V} {4mV-S \ ln (1- \ alpha)}}}$

For small values ​​of , Eyring's formula goes over into Sabine’s formula with the approximation . ${\ displaystyle \ alpha}$ ${\ displaystyle \ ln x \ approx x-1}$

## Measurement

The determination of the reverberation time is done in the classic way by measuring the sound pressure in the room to be examined after switching off a noise source that must not reverberate itself or after generating an impulse sound , e.g. B. with a blank gun . Modern methods use special measurement signals , such as maximum sequences  (MLS) or sweeps  ( chirps ), which are reproduced via omnidirectional measurement speakers . From the excitation and the received signals measured in the room, the impulse response is calculated using a Hadamard transformation (MLS) or an inverse convolution on the time level or a complex division on the frequency level (sweeps) , from which a Schroeder plot can be calculated.

Various studies show that the measurement uncertainties can sometimes be considerable.

The sound pressure in the room decreases almost exponentially with the passage of time . A logarithmic measure for the sound pressure ( sound pressure level ) therefore decreases almost linearly over time, the steepness of the corresponding straight line is a measure for the reverberation time. The reverberation times can differ significantly for different frequencies; The signal is filtered accordingly for detailed calculation .

The method for measuring the reverberation time is specified in the three-part series of standards DIN EN ISO 3382 .

## Hearing sensation

Our subjective perception of the reverberation is mainly influenced by the time shortly after the initial signal, as the later reverberation is usually masked by the ambient noise. Therefore, in addition to the reverberation time and the early decay time  EDT , from English: Early Decay Time used. The early decay time EDT is defined as the time in which the level of the output signal decreases by 60 dB. However, only the time required for a decrease from 0 dB to −10 dB is taken into account for this measurement. The measured time is then extrapolated to a drop of 60 dB .

## Optimal reverberation time

The question of the optimal reverberation time is often asked, i.e. a reverberation time that the majority of the listeners and also those involved subjectively perceive as particularly suitable and is referred to as such. The optimal reverberation time depends on the purpose for which a room is used from a room acoustic point of view.

• In the case of recording and control rooms ( e.g. recording studios ), the reverberation time should be as short as possible in order to impair the recording or loudspeaker reproduction as little as possible by room reflections. (Reverberation time <0.3 s).
• In rooms that are designed for speech presentation (e.g. classrooms , lecture halls ), on the one hand, speech intelligibility must not be impaired by excessive reverberation times, on the other hand, the volume of the speaker should be increased by reverberation (reverberation times between 0.6 and 0, 8 s). For people with a different mother tongue or with impaired hearing, this value should be reduced by about 20%. Reverberation times for classrooms are recommended in DIN 18041.
• In rooms for music performance, the optimal reverberation time is the reverberation time, which most listeners and the participants consider to be particularly suitable. It depends primarily on the type of sound presentation and the volume of the room. The optimal reverberation time for the performance of symphonic music depends on the type of composition, the orchestra line-up and the taste of the time. That is why the “guideline values” for the optimal reverberation time are to be assessed carefully and scattered widely (reverberation times between 1.5 and 3 s).

The DIN 18041 " Audibility in small to medium-sized rooms", in the new version from April 2004, differentiates rooms according to their necessary speech intelligibility and divides them into groups A and B.

Group A - Good speech intelligibility over longer distances, e.g. B. Classroom. Group A rooms differ in the language scenarios and are divided into lessons, language and music. Depending on the size of the room, the target reverberation time can be calculated using a formula or read from a diagram. Rooms with a volume of up to 250 m³ cannot be overdamped because the direct sound supply is sufficient.

Group B - Good speech intelligibility over a short distance, e.g. B. offices, hallways, counter halls. DIN does not specify any target reverberation times for rooms in group B. The “recommendation” for state-of-the-art room acoustics specifies how much absorption material of which absorption class (according to DIN EN 11654) should be brought into the room in relation to the volume of the room. The arrangement of the absorbers must be observed.

Limiting room acoustics in offices to the reverberation time is often not enough. Other aspects, such as privacy and articulation class , must also be taken into account.

## Examples of reverberation times

Large opera stages have long reverberation times (medium reverberation time, fully occupied):

The Staatsoper Unter den Linden originally had a reverberation time of only 1.1 seconds and only achieved 1.6 seconds thanks to the use of electronic amplification; The elevation of the room and the sound rooms of the renovation made it possible from 2017 to achieve this reverb time without tuition. Only after this reverberation time is the sound quality in the room approximately optimal for the planned purpose; then the sound oscillation is sufficiently long, of good quality and easily audible everywhere.

Correspondingly, churches have the longest reverberation times: while the St. Michaelis Church in Hamburg lasts 6.3 seconds, the Ulm Minster is 12 seconds. The record holder with a room volume of 230,000 cubic meters is Cologne Cathedral with 13 seconds. Whoever preaches here has to speak at about 1/6 the speed of normal in order to be understood.

Furnished living spaces typically have reverberation times of 0.5 to 0.6 seconds. Recording studio rooms are dampened more and have reverberation times of 0.2 to 0.3 seconds. In anechoic rooms one can hardly speak of a reverberation time - this is around 0.01 seconds.