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_2/M_2+…..`
`therefore (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)+(35/32))/(gamma-1) =(75/28)/(1.4-1)+(25/35)/(1.4-1)`
`rArr 3.46/(gamma-1) =6.70+1.95`
`rArr gamma=1.4`
`because v=sqrt((gammaP)/P)`
By the perfect gas equation
`P=(rho RT)/M " " therefore P/rho =((RT)/(M))`
`v=sqrt((gammaRT)/M)=sqrt((1.4xx8.3xx1000xx273)/28.9)=331.3 ms^(-1)`