Question 515: Waves

Question

The time of reverberation of a room A is one second. What will be the time (in seconds of reverberation of a room, having all the dimensions double of those of room A ?

Accepted Answer

Reverberation time is defined as the time during which the intensity of sound in the auditorium becomes one millionth of the initial intensity.
Sabine has shown that standard reverberation time for an auditorium is given by the formula
$${T_R} = K{V \over {\alpha S}}$$
Here, V is volume of the auditorium, S is the surface area.
$$ 	herefore {T_R} = {{K.V} \over {\alpha S}} = 1$$ (given)
$$ \Rightarrow {T_R} = {{K.{l^3}} \over {6\alpha {l^2}}} = {K \over {6\alpha }}l$$ $${T_R} = {{K.{l^3}} \over {6\alpha {l^2}}} = {K \over {6\alpha }}l$$
(Assuming auditorium to be cubic in shape)
$$ 	herefore {T_R} \propto l$$
If dimension is doubled, reverberation time t will be doubled.
So, New T
R
= 2 sec.

Answer

1

Answer

2

Answer

4

Answer

1/2

Waves

The time of reverberation of a room A is one second. What will be the time (in seconds of reverberation of a room, having all the dimensions double of those of room A ?

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