Reverberation

Reverberation is the persistence of sound in a particular space after the original sound is removed. When sound is produced in a space, a large number of echos build up and then slowly decay as the sound is absorbed by the walls and air, creating reverberation, or reverb. This is most noticeable when the sound source stops but the reflections continue, decreasing in amplitude, until they can no longer be heard. Large chambers, especially such as cathedrals, gymnasiums, indoor swimming pools, large caves, etc., are examples of spaces where the reverberation time is long and can clearly be heard. Different types of music tend to sound best with reverberation times appropriate to their characteristics.

(Compare with echo: "If so many reflections arrive at a listener that he is unable to distinguish between them, the proper term is reverberation.")

Reverberation Time
Reverberation time is the time required for a sound in a room to decay by 60 dB (called RT60). Reverberation time is defined for wide band signals. When talking about the decay of an individual frequency, the term decay time is used.

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 a clean pair of ears he measured the time from interruption of the source to inaudibility (roughly 60dB). This time varies directly with the dimensions of room but inversely as the absorption present.

The best reverberation time for a space in which music is played depends on the size of the room and the type of music. Rooms for speech require a shorter reverberation time than for music. A longer reverberation time can make it difficult to understand speech. If the reverberation time from one syllable over laps the next syllable, it may make it difficult to identify the word. "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 studios to "smooth" sounds; the effect is commonly used on vocals to help remove inconsistencies in 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.

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


 * $$RT_{60} = \frac{c \cdot V}{Sa}$$.

where $$c$$ is a mathematical constant measuring 0.161, $$V$$ is the volume of the room in m3, $$S$$ total surface area of room in m2, $$a$$ is the average adsorption coefficient of room surfaces, and $$Sa$$ is the total adsorption in sabins.

It is worth noting that the total absorption in sabins (and hence reverberation time) generally changes depending on frequency (dependent on the which is defined by the acoustic properties of the space), and that the equation does not take into account room shape or dimensions, nor losses from the sound travelling through the air (important in larger spaces). In general most rooms adsorb less in the lower frequencies, causing a longer decay time.

The reverberation time RT60 and the volume V of the room have great influence on the critical distance dc (conditional equation):


 * $$d_c = 0{.}057 \cdot \sqrt \frac{V}{RT_{60}}$$

where critical distance $$r_H$$ is measured in metres, volume $$V$$ is measured in m3, and reverberation time $$RT_{60}$$ is measured in seconds.

Absorption
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 into 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 would have an absorption coefficient very close to 0.

Measurement of Reverberation Time
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. Modern digital sound level meters carry out this analysis automatically, on digital data.

Two basic methods exist for creating a sufficiently loud noise (which must have a defined cut off point). Impulsive 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.

Reverberation time is often given as a measurement of decay time. Decay time is the time it takes the signal to diminish 60 dB below the original sound.

Creating Reverberation Effects
It is often desirable to create a reverberation effect for recorded or live music. A number of systems have been developed to facilitate or simulate reverberation.

Chamber reverberators
The first reverb effects created for recordings used a real physical space as a natural echo chamber. A loudspeaker would play the sound, and then a microphone would pick it up again, including the effects of reverb. Whilst this is still a common technique, it requires a dedicated soundproofed room, and varying the reverb time is difficult.

Plate reverberators
A plate reverb system uses an electromechanical transducer, similar to the driver in a loudspeaker, to create vibration in a plate of sheet metal. A pickup captures the vibrations as they bounce across the plate, and the result is output as an audio signal.

Spring reverberators
A spring reverb system uses a transducer at one end of a spring and a pickup at the other, similar to those used in plate reverbs, to create and capture vibrations within a metal spring. Guitar amplifiers frequently incorporate spring reverbs due to their compact construction. Spring reverberators were once widely used in semi-professional recording due to their modest cost and small size. Due to quality problems and improved digital reverb units, spring reverberators are declining rapidly in use.

Digital reverberators
Digital reverberators use various signal processing algorithms in order to create the reverb effect. Since reverberation is essentially caused by a very large number of echoes, simple DSPs use multiple feedback delay circuits to create a large, decaying series of echoes that die out over time. More advanced digital reverb generators can simulate the time and frequency domain responses of real rooms (based upon room dimensions, absorption and other properties). In real music halls, the direct sound always arrives at the listeners ear first because it follows the shortest path. Shortly after the direct sound, the reverberant sound arrives. The time between the two is called the 'arrival time gap'. This gap is important in recorded music because it is the cue that gives the ear information on the size of the hall, better digital reverbs can incorporate this arrival time gap and hence sound more realistic. Digital reverb systems are commonly implemented as software plugins.