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 $A$?

• A. 2
• B. 4
• C. $\frac{1}{2}$
• D. 1

Answer 1

Answer: (A)

2

Answer 2

Sabine formula for reverberation time is
$T=\frac{0.16\, V }{\Sigma a S}$
where $V$ is volume of hall in $m ^{3}$.
$\Sigma a S=a_{1} S_{1}+a_{2} S_{2}+\ldots$
$=$ total absorption of the hall (room)
Here, $S_{1}, S_{2}, S_{3} \ldots \ldots$ are surface areas of the absorbers and $a_{1}, a_{2}, a_{3} \ldots \ldots$ are their respective absorption coefficients.
$\therefore \frac{T^{\prime}}{T}=\frac{V^{\prime}}{S^{\prime}} \times \frac{S}{V}=\frac{(2)^{3}}{(2)^{2}}=\frac{8}{4}=2$
Hence, $T^{\prime}=2 T=2 \times 1=2 s$