Velocity of sound in `O_(2)` gas is 460 `ms^(-1)` at certain temperature. Velocity of sound in He gas at the same temperature would be .......
(Consider both the gases to be ideal).

Options

A. `460sqrt((200)/(21))ms^(-1)`
B. `500sqrt((200)/(21))ms^(-1)`
C. `650sqrt(2)ms^(-1)`
D. `300sqrt(2)ms^(-1)`

Answer

A

Explanation

`v=sqrt((gammaRT)/(M)) implies (v_(1))/(v_(2)) = sqrt((gamma_(1)M_(2))/(gamma_(2)M_(1))) = sqrt(((7)/(5)xx4)/((5)/(3)xx 32))`
`implies (460)/(v_(2)) = sqrt((21)/(25xx8)) implies v_(2) = 460sqrt((200)/(21))m//s`