The speed of sound in oxygen `(O_(2))` at a certain temperature is `460 ms^(-1)`. The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

Answer

`1800 m//s`

Explanation

`v = sqrt((gammaRT)/(M))`
since termperature, `T` is constant,
`(v_(H_(2)))/(v_(H_(1))) = sqrt((M_(O_(2)))/(M_(O_(2)))) = sqrt((32)/(2)) = 4`
`v(H_(2)) = 4 xx 450 = 1800 m//s`
Aliter : The speed of sound in a gas is given by `u = sqrt((gammaP)/(rho))`. At `STP, 22.4` liters of oxygen has a mass of `32 g` whereas the same volume of hydrogen has a mass of `2 g`. Thus, the density of oxygen is `16` times the density of hydrogen at the same temperature and pressure. As `gamma` is same for both the gases,
`v_(("hydrogen"))/(v_(("oxygen"))) = sqrt((rho_(("oxygen")))/(rho_(("hydrogen"))))`
or, `v_(("hydrogen") = 4v_(("oxygen"))`
`= 4 xx 450 m//s = 1800 m//s`