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. `330m//s`
B. `460m//s`
C. `1420m//s`
D. `920m//s`

Answer

C

Explanation

`V=sqrt((gammaRT)/(M))` as R and T are constant
`therefore(V_(HE))/V_(O_(2))=sqrt((gamma_(He))/(M_(He))xx(M_(O_(2)))/(gamma_(O_(2))))`
but `gamma_(He)=5//3` (monoatomic)
`gamma_(O_(2))=7//3` (diatomic)
`M_(O_(2))=32andM_(He)=4andV_(0)=460`
`thereforeV_(HE)=460xxsqrt(5/3xx32/4xx5/7)`
`=460sqrt(200/21)`
`=460xx3.08=1419m//s=1420m//s`