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 $A$
AIPMT 2006, Medium
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The time of reverberation is defined as the time during which the intensity of sound in an autitorium becomes one millionth of initial initensity. Sabine's formula for reverberation time is
$T=\frac{0.16 V }{\sum a s}$
Where $V$ is volume of hall in $m^3$
$\sum a s=a_1 s_1+a_2 s_2+\ldots \ldots=$ Total absorption of the hall (room)
Here $s_1, s_2, s_3 \ldots \ldots \ldots$ are surface area of the absorbers and $a_1, a_2, a_3 \ldots \ldots \ldots$ are their respective absorbption coefficients
$\frac{T^{\prime}}{T}=\frac{V^{\prime}}{s^{\prime}} \times \frac{s}{V}=\frac{(2)^3}{(2)^2}=\frac{8}{4}=2$
Hence, $T^{\prime}=2 T=2 \times 1=2\; s$.
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