A gas is a mixture of two parts by volume of hyprogen and part by volume of nitrogen at `STP`. If the velocity of sound in hydrogen at `0^(@) C` is `1300 m//s` . Find the velocity of sound in the gaseous mixure at `27^(@)C`.

Explanation

Here, density of mixture,
`rho_(mix)=(2Vxxrho_(H)=1Vxxrho_(N))/(2V+V)`
`=(2Vxxrho_(H)+1Vxx14rho_(H))/(3V)`
`rho_(mix)=(16)/(3)rho_(H)`
`(v_(mix))/(v_(H))=sqrt((rho_(H))/(rho_(mix)))=sqrt((3)/(16))=(sqrt(3))/(4)`
`:. v_(mix)=(sqrt(3))/(4)xx1300=325sqrt(3)m//s`
`v_(mix)(at 27^(@)C)=(v_(mix))_(0)sqrt((273+27)/(273))`
`=325sqrt(3)xxsqrt((300)/(273))=325xx1.732xx1.048m//s`
`=590m//s`