A) 1
B) 2
C) 3
D) 4
Correct Answer: B
Solution :
Velocity of sound increases if the temperature increases. So with \[v=n\lambda \], if \[v\] increases \[n\] will increase at \[{{27}^{o}}C,\,{{v}_{1}}=n\lambda \], at \[{{31}^{o}}C\,,\,\,{{v}_{2}}=(n+x)\lambda \] Now using \[v\propto \sqrt{T}\] \[\left( \because v=\sqrt{\frac{\gamma RT}{M}} \right)\] \[\frac{{{v}_{2}}}{{{v}_{1}}}=\sqrt{\frac{{{T}_{2}}}{{{T}_{1}}}}=\frac{n+x}{n}\] Þ \[\frac{300+x}{300}=\sqrt{\frac{(273+31)}{(273+27)}}=\sqrt{\frac{304}{300}}=\sqrt{\frac{300+4}{300}}\] Þ \[1+\frac{x}{300}={{\left( 1+\frac{4}{300} \right)}^{1/2}}=\left( 1+\frac{1}{2}\times \frac{4}{300} \right)\,\]Þ x = 2. \[[\because {{(\,1+x)}^{n}}=1+nx]\]
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