The velocities of sound at same temperature in two monoatomic gases densities `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. `1//4`
B. 2
C. `1//2`
D. 4

Answer

C

Explanation

Velocity of sound in the gas of density `rho_(1)` is `v_(1)` and velocity of sound in the gas of density `rho_(2)` is ` v_(2)`.
Velocity of sound is gas , `v=sqrt((gammaP)/(rho)) prop sqrt((1)/(rho))` .
Therefore `(v_(1))/(v_(2))=sqrt((rho_(2))/(rho_(1))=sqrt((1)/(4))=(1)/(2)` .