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JIPMER 2008
Exam
JIPMER
Year
2008
Subject
Physics
Chapter
Waves and Sound

JIPMER 2008 · Physics · Waves and Sound

The time of reverberation of a room A is one second. What will be...

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 of those of room AA ?

Options

  1. A22
  2. B44
  3. C12\frac{1}{2}
  4. D11

Correct answer

A. 22

Step-by-step solution

Sabine formula for reverberation time is T=0.16 VΣaST=\frac{0.16 \mathrm{~V}}{\Sigma a S} where VV is volume of hall in m3\mathrm{m}^3. ΣaS=a1S1+a2S2+…\Sigma a S=a_1 S_1+a_2 S_2+\ldots = total absorption of the hall (room) Here, S1,S2,S3……S_1, S_2, S_3 \ldots \ldots are surface areas of the absorbers and a1,a2,a3…a_1, a_2, a_3 \ldots. . are their respective absorption coefficients. ∴T′T=V′S′×SV=(2)3(2)2=84=2\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, T′=2T=2×1=2 s\quad T^{\prime}=2 T=2 \times 1=2 \mathrm{~s}
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