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. `330 m s^(-1)`
B. `1420 m s^(-1)`
C. `500 m s^(-1)`
D. `650 m s^(-1)`

Answer

C

Explanation

Speed of sound in a gas is `v=sqrt((gammaRT)/(M))`
As the temperature remains constant,
`therefore (v_(He))/(v_(O_(2)))=sqrt((gamma_(He)M_(O_(2)))/(gamma_(O_(2))M_(He)))or (v_(He))/(460)=sqrt((((5)/(3))xx32)/(((7)/(5))xx4))=sqrt((200)/(21))`
or `v_(He)=460sqrt((200)/(21))~~1420ms^(-1)`