Reverberation

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 meters can carry out this analysis automatically.[8]

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 sources such as a blank pistol shot or balloon burst may be used to measure the impulse response of a room.

Alternatively, a 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 [9]

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 dB below the original sound. It is often difficult to inject enough sound into the room to measure a decay of 60 dB, particularly at lower frequencies. If the decay is linear, it is sufficient to measure a drop of 20 dB and multiply the time by 3, or a drop of 30 dB and multiply the time by 2. These are the so-called T20 and T30 measurement methods.

The RT₆₀ 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's reverberation equation was developed in the late 1890s in an empirical fashion. He established a relationship between the T₆₀ of a room, its volume, and its total absorption (in sabins). This is given by the equation:

${\displaystyle T_{60}={\frac {24\ln 10^{1}}{c_{20}}}{\frac {V}{Sa}}\approx 0.1611\,\mathrm {s} \mathrm {m} ^{-1}{\frac {V}{Sa}}}$.

where c₂₀ is the speed of sound in the room (at 20 °C), V is the volume of the room in m³, S total surface area of room in m², 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 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 RT₆₀ and the volume V of the room have great influence on the critical distance d_c (conditional equation):

${\displaystyle d_{\mathrm {c} }\approx 0{.}057\cdot {\sqrt {\frac {V}{RT_{60}}}}}$

where critical distance ${\displaystyle d_{c}}$ is measured in meters, volume ${\displaystyle V}$ is measured in m³, and reverberation time RT₆₀ is measured in seconds.

Eyring's reverberation time equation was proposed by Carl F. Eyring of Bell Labs in 1930.[10] 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 logarithmically scale the 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:

${\displaystyle T_{60}\approx -0.161\ {\frac {V}{S\ln(1-a)}}}$.

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.

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.