Intensity of sound :
It is related to power, loudness, sound level of the sound wave.
Intensity is the power incident on a unit surface area, at a distance from the the sound source.
Intensity is defined as the average energy incident/crossing a unit cross sectional (surface) area perpendicular to the direction (velocity) of propagation of sound wave in unit time.
I = ω² s₀² B / (2 v) = 2 π² B s₀² f ² / v = p₀² / (2 ρ v)
where I = intensity
ω = angular frequency of sound wave
f = frequency of sound wave
B = bulk modulus of the medium
v = speed of sound wave
s₀ = amplitude of the particles vibrating in the medium
p₀ = pressure amplitude (maximum excess pressure at compression region)
ρ = density of the medium
Intensity of sound is measured by sound level as :
β in decibels = 120 + 10 Log I
Higher decibels towards 120 db means intolerable sound level.
In a concert hall when a speaker speaks or a musician plays instruments , the sound waves are supposed to reach all the audience. Also, the effect of the sounds is expected to last a little more than what normally happens in open air.
The sound waves reach the ears of the audience directly. Also, they get reflected from the walls and the ceiling. The design of the shapes and curves of the walls and ceiling are done in such a way that the waves get reflected from walls and ceiling multiple times and reach the ears one wave after another. Thus all audience receive the sounds. Also, sound waves, which are reflected, reach the ear a little later than those which are received directly.
Thus multiple reflections of waves reach one after another in the ear, so the effect of same sound lasts longer. This is more effective and pleasing to the ear.
These multiple reflections are called reverberations.
Also, the delay introduced by the reverberations should not be too long, as that will interfere with the next sound from the stage. So the design is done in such a way that reverberations are there, but not for too long.
Perhaps higher the intensity , longer will be the reverberations.