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. $\therefore \frac{T'}{T}=\frac{V'}{S'} \times \frac{S}{V}=\frac{(2)^{3}}{(2)^{2}}=\frac{8}{4}=2$ Hence, $T'=2 T=2 \times 1=2 s$