A) \[{{54}^{o}}C\]
B) \[{{627}^{o}}C\]
C) \[{{927}^{o}}C\]
D) \[{{327}^{o}}C\]
Correct Answer: C
Solution :
According to Laplace, the formula for speed of sound in a gas is \[v=\sqrt{\frac{\gamma \,RT}{M}}\] where \[\gamma \] is ratio of specific heats, R is gas constant, T is temperature and M is molecular weight. Given, \[{{v}_{1}}=v,\,{{v}_{2}}=2\,v,\,{{T}_{1}}={{27}^{o}}C\] \[=273+27=300\,K\] \[\therefore \] \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] \[\Rightarrow \] \[\frac{v}{2\,v}=\sqrt{\frac{300}{{{T}_{2}}}}\] \[\Rightarrow \] \[{{T}_{2}}=300\times 4=1200\,K\] \[=1200-273={{927}^{o}}C\]. Note: In general the velocity of sound in air increases roughly by \[0.61\,m{{s}^{-1}}\] per degree centigrade rise in temperature.
You need to login to perform this action.
You will be redirected in
3 sec
