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Mechanical Properties Of Fluids

Question
CBSEENPH11020802

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

  • 1 half
  • 1

Solution

A.

2

Sabine's formula for reverberation time is
                          straight T space equals space fraction numerator 0.16 space straight V over denominator begin display style sum for blank of end style as end fraction
where V is volume of hall in m3.
sum from blank to blank of as space equals space straight a subscript 1 straight s subscript 1 plus straight a subscript 2 straight s subscript 2 plus.......... space equals space total absorption of the hall (room)
Here s1, s2, s3 ...... are the surface areas of the absorbers and a1, a2, a3.......are their respective absorption coefficients.
therefore space space space space space space space fraction numerator straight T apostrophe over denominator straight T end fraction space equals space fraction numerator straight V apostrophe over denominator straight s apostrophe end fraction cross times straight s over straight V
                  equals space fraction numerator left parenthesis 2 right parenthesis cubed over denominator left parenthesis 2 right parenthesis squared end fraction equals space 8 over 4 space equals space 2
Hence comma space space space straight T apostrophe space equals space 2 straight T space equals space 2 cross times 1 space equals space 2 straight s