The speed of sound in oxygen `(O_2)` at a certain temperature is `460ms^-1`. The speed of sound in helium (He) at the same temperature will be (assume both 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`