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The time of reverberation of a room AA is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double those of room AA?

A

2

B

4

C

1/2

D

1

Step-by-Step Solution

According to Sabine's formula, the reverberation time TT of a room is given by: T=kVST = \frac{kV}{S} where VV is the volume of the room, SS is the total surface area (representing total absorption), and kk is a constant. When all dimensions (length, breadth, and height) are doubled: New volume, V=(2L)×(2B)×(2H)=8VV' = (2L) \times (2B) \times (2H) = 8V New surface area, S=2(2L×2B+2B×2H+2H×2L)=4SS' = 2(2L \times 2B + 2B \times 2H + 2H \times 2L) = 4S New reverberation time, T=kVS=k(8V)4S=2(kVS)=2TT' = \frac{kV'}{S'} = \frac{k(8V)}{4S} = 2 \left(\frac{kV}{S}\right) = 2T Given the initial reverberation time T=1 secondT = 1 \text{ second}, the new reverberation time is: T=2×1=2 secondsT' = 2 \times 1 = 2 \text{ seconds}

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