Taking the composition of air to be `75%` of nitrogen and `25%` of oxygen by weight, calculate the velocity of sound through air.

Explanation

The molecular weight of a mixture is given by
`(m_(1) + m_(2) + m_(3) + . . . . . )/(M) = (m_(1))/(M_(1)) + (m_(1))/(M_(2)) + . . . . `
`:. (75 + 25)/(M) = (75)/(28) + (25)/(32)`
or, M = 28 . 9
`gamma` of a mixture is given by
` = (n_(1) + n_(2))/(gamma - 1) = (n_(1))/(gamma_(1) - 1) = (n_(2))/(gamma_(2)-1) + . . . `
`rArr((75)/(28)+(25)/(32))/(gamma-1) = ((75)/(28))/(1.4 - 1) + ((25)/(32))/(1.4 - 1)`
`rArr (3.46)/(gamma-1) = 6 . 70 + 1.95 rArr gamma = 1.4`
`:' v = sqrt((gammaP)/(rho))`
By the prefect gas equation
`P p = (rho RT)/(M) " ":' (p)/(rho) = ((RT)/(M))`
`v = sqrt((gammaRT)/(M)) = sqrt((1 . 4 xx 8 . 3 xx 1000 xx 273)/(28.9))`
`rArr v = 331 . 3 ms^(-1)`