The time of reverberation of a room $A$ is one second. What will be the time (in seconds) of reverberation of

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 those of room $A$?

Accepted Answer

According to Sabine's formula, the reverberation time $T$ of a room is given by:
$$T = rac{kV}{S}$$
where $V$ is the volume of the room, $S$ is the total surface area (representing total absorption), and $k$ is a constant.
When all dimensions (length, breadth, and height) are doubled:
New volume, $V' = (2L) 	imes (2B) 	imes (2H) = 8V$
New surface area, $S' = 2(2L 	imes 2B + 2B 	imes 2H + 2H 	imes 2L) = 4S$
New reverberation time, $T' = \frac{kV'}{S'} = \frac{k(8V)}{4S} = 2 \left(\frac{kV}{S}ight) = 2T$
Given the initial reverberation time $T = 1 	ext{ second}$, the new reverberation time is:
$$T' = 2 	imes 1 = 2 	ext{ seconds}$$

Step-by-Step Solution

Practice All PHYSICS Questions