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Waves

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?

2

4

$\frac{1}{2}$

1

Solution

Sabine formula for reverberation time is

$T = \frac{0.16}{Σ a S}$

Where V is volume of hall in m³

∑ $a S$ = $a_{1} S_{1} + a_{2} S_{2} + a_{3} S_{3} . . . .$

= total absorption of the hall (room)

Here, S₁, S₂ , S₃, ..... are surface areas of the absorbers and a₁_,a₂ , a₃ .... their respective absorption coefficients

$\frac{T'}{T} = \frac{V'}{S'} \times \frac{S}{V} = \frac{{(2)}^{3}}{{(2)}^{2}} = \frac{8}{4}$

$\frac{T'}{T} = 2$

T' = 2T = 2 × 1

T' = 2 s