The temperature at which the speed of sound in air becomes double of its value at `27^(@)C` is

Options

A. `54^(@)C`
B. `327^(@)C`
C. `927^(@)C`
D. None of these

Answer

C

Explanation

The speed of sound in air is defined as,
`v=sqrt((gammaRT)/M) implies v prop sqrt(T)`
`:. v_(1)/v_(2)=sqrt(T_(1)/T_(2))` ...(i)
But according to question,
`v_(1)=v, v_(2)=2v, T_(1)=27^(@)C=(27+273)K=300 K`,
On pulling these value in Eq. (i), we have
`v/(2v)=sqrt(300/T_(2)) implies 1/2 =sqrt(300/T_(2))`
or `1/4=300/T_(2) implies T_(2)=1200 K`
or `T_(2)=(1200-273)^(@)C=927^(@)C`