# REVERBERATION

#### Reverberation:

The persistence or existence of sound in a room, even when the sound source has stopped to emit sound is called reverberation.

• When sound waves are produced in a hall, they spread out, scatter and strike the various objects in the hall such as ceiling, walls, floor, etc.  i.e., sound waves undergo reflection, absorption, transmission, and is converted into heat by friction. Therefore, in such a hall, the listener receives, not only the direct sound waves from the source, but also receives the sound waves that undergo reflection. Normally, sound waves suffer 2 to 300 reflections before it becomes inaudible.
• I.e., the listener receives a series of sound waves of diminishing intensities since part of the energy of sound waves is lost at each reflection from the direct sound wave. As a result, the listener will not hear a sharp sound but a roll of sound.
• In such a situation, if the source of sound is cut off, the sound does not stop immediately, as far as the listener is concerned, because he will continue to pick up the successive reflection until they are too weak to stimulate his ears.

#### Reverberation Time:

• The duration for which the sound persists after the source cutoff is called the reverberation time and this is measured from the instant the source stops emitting the sound to the time at which the sound becomes inaudible.
• I.e., The time taken for the sound to fall below the minimum audibility, measured from the instant when the source stopped sounding. Normally, it is 0.5 sec to 1 sec for speech and 1 sec to 2 sec for music.

#### Optimum Reverberation Time:

• A certain amount of reverberation is, of course, desirable, as it adds a pleasing characteristic to the acoustical qualities of a room, especially for giving richness in music, but too much reverberation is most undesirable since it leads to the overlap. Obtaining the right amount of reverberation is the secret of good acoustics.
• An optimum value of reverberation time depends on the volume of the hall and also upon the use to which the hall is put to. Stephen’s and Bate’s empirical formula for the optimum reverberation time is,
• $T_o_p_t=(0.0036V^{-1/3}&space;+0.107)^n$
•  Where V is the volume in cubic feet
• n = 4 for speech
• n = 6 for music

Sabine’s Formula For Reverberation Time

• The standard reverberation time is the time taken by the intensity of sound to fall to one -millionth $(10^{-6})$ of its original sound intensity after the source is cut off.
• I.e., $I_{T}=I_{0}(10^{-6})$
• Where $I_T$= Intensity after T secs
• $I_0$= original intensity ; T=Reverberation  time in secs
• Using this, one can derive the Sabine’s formula, as $T=\frac{0.165V}{A}$
• Where V = Volume of the hall in cubic meter; A = Total sound absorption in the hall
• The Sabine’s formula is applicable only under certain conditions. So, let us consider the assumptions in driving the same.

#### Assumptions

• The energy density (energy/unit volume) of the sound is uniform throughout the room.
• Energy transmitted equally in all directions.
• The rate of emission of sound from the sources is constant.
• The effects of superposition are neglected.
• The dissipation of energy is confirmed to the bounding surface, i.e., attenuation due to the viscosity of air is negligible.
• The coefficient of sound absorption is independent of the frequency of sound.