As what temperature the speed of sound in air will because double of its value at `27^(@)`?

Options

A. `54^(@)C`
B. `627^(@)C`
C. `927^(@)C`
D. `327^(@)C`

Answer

c

Explanation

Speed of sound is given by
`v = sqrt((gamma P)/(A))` ..(1)
where rho is ratio of specific heat P is pressure and d is density
Also `PV = RT,`
where `V` is volume R gas constant and T is temperature
`P (m)/(d) = RT`
`rArr (P)/(d) = (RT)/(m)`
putting the value in Eqs (i) we get
`v = sqrt((gamma RT)/(m))`
Given ` v_(1) = v, T_(1) = 27 + 273= 330 K`
`v_(2) = 2v`
`:. (v_(1))/(v_(2)) = (v)/(2v) = sqrt((T_(1))/(T_(2))) = sqrt((300)/(T_(2)))`
`rArr T_(2) = 4 xx 300 = 1200 K`
`rArr T_(2) = (1200 - 273)^(@)C = 927^(@)C `