Q119 / 200 · JIPMER 2008 · Physics
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 $A$ ?
- Correct answerA$2$
- B$4$
- C$\frac{1}{2}$
- D$1$
Solution
Sabine formula for reverberation time is
$T=\frac{0.16 \mathrm{~V}}{\Sigma a S}$
where $V$ is volume of hall in $\mathrm{m}^3$.
$\Sigma a S=a_1 S_1+a_2 S_2+\ldots$
$=$ total absorption of the hall (room)
Here, $S_1, S_2, S_3 \ldots \ldots$ are surface areas of the absorbers and $a_1, a_2, a_3 \ldots$. . are their respective absorption coefficients.
$\therefore \quad \frac{T^{\prime}}{T}=\frac{V^{\prime}}{S^{\prime}} \times \frac{S}{V}=\frac{(2)^3}{(2)^2}=\frac{8}{4}=2$
Hence, $\quad T^{\prime}=2 T=2 \times 1=2 \mathrm{~s}$
Hence, the correct answer is option: 'A'.