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))rArr v prop sqrt(T)`
`rArr (v_(1))/(v_(2)) = sqrt((T_(1))/(T_(2)))`
But according to question,
`v_(1) = v_(1)v_(2) = 2v`,
`T_(1) = 27^(@)C = (27 + 273) K = 300K`
On putting these values in Eq. (i) we have
`(v)/(2v) = sqrt((300)/(T^(2))) or (1)/(2) = sqrt((300)/(T^(2)))`
ON squaring both sides.
`(1)/(4) = (300)/(T^(2)) =rArr = 1200K`
or `T_(2) = (1200 -273)^(@)C = 927^(@)C`