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

Options

A. `4:1`
B. `2:1`
C. `1:2`
D. `1:4`

Answer

C

Explanation

The velocity of sound is given by `v=sqrt((gammaP)/(rho))`
where P is pressure `rho` is density and `gamma` is adiabatic constant.
`implies(v_1)/(v_2)=sqrt((rho_2)/(rho_1))=sqrt((1)/(4))=1:2`