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?
[AIPMT (Prelims)-2006)
(1) 2
(2) 4
(3)
(4) 1​

Answer 1

Answer:

option (1)  2 is correct.

Explanation:

since, Reverberation time is directly proportional to Volume per unit surface area.

i.e.    Reverberation time (t)  ∝ $\frac{V}{S}$

         ⇒ $t_{1}$ / $t_{2}$ = $V_{1}$ $S_{2}$ / $V_{2}$ $S_{1}$

since   $t_{1}$ = 1 second , $V_{1}$ = l×b×h

             $V_{2}$ = 2l×2b×2h = 8 l×b×h = 8 $V_{1}$

              $S_{1}$ = 2 ( lb+bh+hl )

             $S_{2}$ = 2(2l×2b+2b×2h+2h×2l) =  4×2( lb+bh+hl ) = 4×  $S_{1}$

  $t_{2}$ = $\frac{S_{1} V_{2} t_{1}}{S_{2} V_{1} }$

                          = (S1×8 V1 ×1)÷(4×S1× V1) =2

Hence new time will be 2 second.

Know More

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