The temperature at which the speed of sound in air becomes double of its value at `0^(@)C` is

Options

A. `546^(@)C`
B. `819^(@)C`
C. `273^(@)C`
D. `1092^(@)C`

Answer

B

Explanation

`v_(1) prop sqrtT_(1) and v_(2) prop sqrtT_(2)`
`(v_(2))/(v_(1)) = sqrt((T_(2))/(T_(1))) " " :. ((v_(2))/(v_(1)))^(2) = (T_(2))/(T_(1))`
`:. ((2v_(1))/(v_(1)))^(2) = (T_(2))/(T_(1)) " " :. 4 = (T_(2))/(T_(1))`
`:. T_(2) = 4T_(1) = 4 xx 273 = 1092 .^(@)K`
`= 1092 - 273 = 819^(@)C`