A) 2
B) 4
C) \[\frac{1}{2}\]
D) 1
Correct Answer: A
Solution :
The time of reverberation is defined as the time during which the intensity of sound in an auditorium becomes one millionth of initial intensity. Sabine's formula for reverberation time is \[T=\frac{0.16\,V}{\sum{as}}\] Where Vis volume of hall in \[{{m}^{3}}\] \[\sum{as}={{a}_{1}}{{s}_{1}}+{{a}_{2}}{{s}_{2}}+.......=\] 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 \[\frac{T'}{T}=\frac{T'}{s'}\times \frac{s}{V}=\frac{{{(2)}^{3}}}{{{(2)}^{2}}}=\frac{8}{4}=2\] Hence, \[T'=2T=2\,\,\,1=2s\] \[\therefore \] \[2f=f\left( \frac{v+{{v}_{0}}}{v-{{v}_{0}}} \right)\] or \[2v-2{{v}_{0}}=v+{{v}_{0}}\] or \[3{{v}_{0}}=v\] or \[{{v}_{0}}=\frac{v}{3}\]
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