The velocities of sound at same temperature in two monoatomic gases of density `rho_(1)` and `rho_(2)` are `v_(1)` and `v_(2)` repectively , if `(rho_(1))/(rho_(2)) = 4 `, then the value of `(v_(1))/(v_(2))` will be

Options

A. `4`
B. `2`
C. `(1)/(2)`
D. `(1)/(4)`

Answer

c

Explanation

Since both hases are monoatomic ratio of speed heat is same for both
The velocity of speed sound is given by both
`v = sqrt(( gamma P )/(rho))`
where p is pressure p is density and `gamma` is ratio of specific heat
`:. (v_(1))/(v_(2)) = sqrt((p_(2))/(p_(1)))` (Since `rho` and `gamma` are same for body)
Given `(rho_(2))/(rho_(1)) = (1)/(4) `
`:. (v_(1))/(v_(2)) =sqrt((1)/(4)) = (1)/(2)`