The constant `gamma` of oxygen as well as for hydrogen is 1.40. If the speed of sound in oxygen is `470 ms^-1,` What will be the speed in hydrogen at the same temperature and pressure?

Explanation

The speed of sound in a gas is given by `v=sqrt((gammaP)/rho)`. At STP 22.4 litres of oxygen has a mass of 32 whereas the same volume of hydrogen has a mass of 2g. 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)`
`=4xx470ms=1880ms^-1`