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  • question_answer
    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 (S) 2006]

    A)  2

    B)                   4                    

    C)  \[\frac{1}{2}\] 

    D)         1

    Correct Answer: A

    Solution :

    Sabine's formula for reverberation time is
                            \[T=\frac{0.16\,V}{\Sigma as}\]
                where V is volume of hall in \[{{m}^{3}}\].
                            \[\Sigma as={{a}_{1}}{{s}_{1}}+{{a}_{2}}{{s}_{2}}+......=\]
                total absorption of the hall (room)
                Here, \[{{s}_{1}},{{s}_{2}},{{s}_{3}}....\] are surface areas of the absorbers and \[{{a}_{1}},{{a}_{2}},{{a}_{3}}\]....... are their respective absorption coefficients
                \[\therefore \]      \[\frac{T'}{T}=\frac{V'}{s'}\times \frac{s}{V}\]
                            \[=\frac{{{(2)}^{3}}}{{{(2)}^{2}}}=\frac{8}{4}=2\]
                Hence,  \[T'=2T=2\times 1=2s\]


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