Editing Reverberation (section)

== {{visible anchor | Reverberation time}} ==
[[File: Reverberation time diagram.svg|thumb|Sound level in a reverberant cavity excited by a pulse, as a function of time (very simplified diagram)]]
'''Reverberation time''' is a measure of the time required for the sound to "fade away" in an enclosed area after the source of the sound has stopped.

When it comes to accurately measuring reverberation time with a meter, the term ''T<sub>60</sub>'' <ref>{{Cite web|url=https://www.nti-audio.com/en/applications/room-building-acoustics/reverberation-time#What-is-reverberation-time|title=Reverberation Time|website=www.nti-audio.com}}</ref> (an abbreviation for reverberation time 60&nbsp;dB) is used. T<sub>60</sub> provides an objective reverberation time measurement. It is defined as the time it takes for the sound pressure level to reduce by 60&nbsp;[[Decibel|dB]], measured after the generated test signal is abruptly ended.

Reverberation time is frequently stated as a single value if measured as a wideband signal (20&nbsp; Hz to 20&nbsp;kHz). However, being frequency-dependent, it can be more precisely described in terms of frequency bands (one octave, 1/3 octave, 1/6 octave, etc.). Being frequency dependent, the reverberation time measured in narrow bands will differ depending on the frequency band being measured. For precision, it is important to know what ranges of frequencies are being described by a reverberation time measurement.

In the late 19th century, [[Wallace Clement Sabine]] started experiments at Harvard University to investigate the impact of absorption on the reverberation time. Using a portable wind chest and organ pipes as a sound source, a [[stopwatch]] and his ears, he measured the time from interruption of the source to inaudibility (a difference of roughly 60&nbsp;dB). He found that the reverberation time is proportional to room dimensions and inversely proportional to the amount of absorption present.

The optimum reverberation time for a space in which music is played depends on the type of music that is to be played in the space. Rooms used for speech typically need a shorter reverberation time so that speech can be understood more clearly.  If the reflected sound from one [[syllable]] is still heard when the next syllable is spoken, it may be difficult to understand what was said.<ref>{{cite web|url=http://www.mcsquared.com/y-reverb.htm|title=So why does reverberation affect speech intelligibility?|publisher=MC Squared System Design Group, Inc|access-date=2008-12-04}}</ref> "Cat", "cab", and "cap" may all sound very similar. If on the other hand the reverberation time is too short, tonal balance and loudness may suffer. Reverberation effects are often used in [[recording studio|studios]] to add depth to sounds. Reverberation changes the perceived spectral structure of a sound but does not alter the pitch.

Basic factors that affect a room's reverberation time include the size and shape of the enclosure as well as the materials used in the construction of the room. Every object placed within the enclosure can also affect this reverberation time, including people and their belongings.

=== Measurement ===

[[File:RT60 measurement.jpg|thumb|240px|right|Automatically determining T20 value - 5dB trigger - 20dB measurement - 10dB headroom to noise floor]]
Historically, reverberation time could only be measured using a level recorder (a plotting device which graphs the noise level against time on a ribbon of moving paper). A loud noise is produced, and as the sound dies away the trace on the level recorder will show a distinct slope. Analysis of this slope reveals the measured reverberation time. Some modern digital [[sound level meter]]s can carry out this analysis automatically.<ref>{{Cite web|url=https://www.nti-audio.com/en/applications/room-building-acoustics/reverberation-time|title=Reverberation Time|website=www.nti-audio.com}}</ref>

Several methods exist for measuring reverberation time.  An impulse can be measured by creating a sufficiently loud noise (which must have a defined cut-off point). [[Impulse noise (audio)|Impulse noise]] sources such as a [[Blank (cartridge)|blank]] pistol shot or balloon burst may be used to measure the impulse response of a room.

Alternatively, a [[Colors of noise|random noise signal]] such as [[pink noise]] or [[white noise]] may be generated through a loudspeaker, and then turned off. This is known as the interrupted method, and the measured result is known as the interrupted response.

A two-port measurement system can also be used to measure noise introduced into a space and compare it to what is subsequently measured in the space. Consider sound reproduced by a loudspeaker into a room. A recording of the sound in the room can be made and compared to what was sent to the loudspeaker. The two signals can be compared mathematically. This two port measurement system utilizes a [[Fourier transform]] to mathematically derive the impulse response of the room. From the impulse response, the reverberation time can be calculated. Using a two-port system allows reverberation time to be measured with signals other than loud impulses. Music or recordings of other sounds can be used. This allows measurements to be taken in a room after the audience is present.

Under some restrictions, even simple sound sources like handclaps can be used for measurement of reverberation <ref>{{cite journal |last1=Papadakis |first1=Nikolaos M. |last2=Stavroulakis |first2= Georgios E. |title=Handclap for Acoustic Measurements: Optimal Application and Limitations.  |journal=Acoustics |year=2020 |volume=2 |issue=2 |pages=224–245 |doi=10.3390/acoustics2020015 |doi-access=free }}</ref>

Reverberation time is usually stated as a decay time and is measured in seconds. There may or may not be any statement of the frequency band used in the measurement. Decay time is the time it takes the signal to diminish 60&nbsp;dB below the original sound. It is often difficult to inject enough sound into the room to measure a decay of 60&nbsp;dB, particularly at lower frequencies. If the decay is linear, it is sufficient to measure a drop of 20&nbsp;dB and multiply the time by 3, or a drop of 30&nbsp;dB and multiply the time by 2. These are the so-called T20 and T30 measurement methods.

The RT<sub>60</sub> reverberation time measurement is defined in the [[ISO]] 3382-1 standard for performance spaces, the [[ISO]] 3382-2 standard for ordinary rooms, and the [[ISO]] 3382-3 for open-plan offices, as well as the [[ASTM]] E2235 standard.

The concept of reverberation time implicitly supposes that the decay rate of the sound is exponential, so that the sound level diminishes regularly, at a rate of so many dB per second. It is not often the case in real rooms, depending on the disposition of reflective, dispersive and absorbing surfaces. Moreover, successive measurement of the sound level often yields very different results, as differences in phase in the exciting sound build up in notably different sound waves. In 1965, [[Manfred R. Schroeder]] published "A new method of Measuring Reverberation Time" in the ''Journal of the Acoustical Society of America''. He proposed to measure, not the power of the sound, but the energy, by integrating it. This made it possible to show the variation in the rate of decay and to free acousticians from the necessity of averaging many measurements.

=== Sabine equation ===
[[Wallace Clement Sabine|Sabine]]'s reverberation equation was developed in the late 1890s in an [[empirical]] fashion. He established a relationship between the ''T''<sub>60</sub> of a room, its volume, and its total absorption (in [[Sabin (unit)|sabin]]s). This is given by the equation:

:<math>T_{60} = \frac{24 \ln 10^1}{c_{20}} \frac{V}{Sa} \approx 0.1611\,\mathrm{s}\mathrm{m}^{-1} \frac{V}{Sa}</math>.

where ''c''<sub>20</sub> is the speed of sound in the room (at 20&nbsp;°C), ''V'' is the volume of the room in m<sup>3</sup>, ''S'' total surface area of room in m<sup>2</sup>, ''a'' is the average absorption coefficient of room surfaces, and the product ''Sa'' is the total absorption in sabins.

The total absorption in sabins (and hence reverberation time) generally changes depending on frequency (which is defined by the [[acoustics|acoustic properties]] of the space). The equation does not take into account room shape or losses from the sound traveling through the air (important in larger spaces). Most rooms absorb less sound energy in the lower frequency ranges resulting in longer reverb times at lower frequencies.

Sabine concluded that the reverberation time depends upon the reflectivity of sound from various surfaces available inside the hall. If the reflection is coherent, the reverberation time of the hall will be longer; the sound will take more time to die out.

The reverberation time ''RT''<sub>60</sub> and the [[volume]] ''V'' of the room have great influence on the [[critical distance]] ''d''<sub>c</sub> (conditional equation):
:<math>
d_\mathrm{c} \approx 0{.}057 \cdot \sqrt \frac{V}{RT_{60}}
</math>

where critical distance <math>d_c</math> is measured in meters, volume <math>V</math> is measured in m³, and reverberation time ''RT''<sub>60</sub> is measured in [[second]]s.

=== Eyring equation ===
Eyring's reverberation time equation was proposed by [[Carl F. Eyring]] of [[Bell Labs]] in 1930.<ref>{{cite journal |last1=Eyring |first1=Carl F. |title=Reverberation Time in "Dead" Rooms  |journal=The Journal of the Acoustical Society of America |year=1930 |volume=1 |issue=2A |pages=217–241 |doi=10.1121/1.1915175 |bibcode=1930ASAJ....1..217E |doi-access= }}</ref>  This equation aims to better estimate the reverberation time in small rooms with relatively large quantities of sound absorption, identified by Eyring as "dead" rooms.  These rooms tend to have lower reverberation times than larger, more acoustically live rooms.  Eyring's equation is similar in form to Sabine's equation, but includes modifications to [[natural logarithm|logarithmically]] scale the [[absorption (acoustics)|absorption]] term. The units and variables within the equation are the same as those defined for Sabine's equation.  The Eyring reverberation time is given by the equation:

:<math>T_{60} \approx -0.161\ \frac{V}{S \ln (1-a)}</math>.

Eyring's equation was developed from first principles using an image source model of sound reflection, as opposed to Sabine's [[empirical]] approach.  The experimental results obtained by Sabine generally agree with Eyring's equation since the two formulae become identical for very live rooms, the type in which Sabine worked. However, Eyring's equation becomes more valid for smaller rooms with large quantities of absorption.  As a result, the Eyring equation is often implemented to estimate the reverberation time in [[recording studio]] control rooms or other critical listening environments with high quantities of sound absorption.  The Sabine equation tends to over-predict reverberation time for small rooms with high amounts of absorption.  For this reason, reverberation time calculators available for smaller recording studio environments, such as [[home recording]] studios, often utilize Eyring's equation.

=== Absorption coefficient ===
The absorption coefficient of a material is a number between 0 and 1 which indicates the proportion of sound which is absorbed by the surface compared to the proportion which is reflected back to the room. A large, fully open window would offer no reflection as any sound reaching it would pass straight out and no sound would be reflected. This would have an absorption coefficient of 1. Conversely, a thick, smooth painted concrete ceiling would be the acoustic equivalent of a mirror and have an absorption coefficient very close to 0.