The velocity of sound in hydrogen at `0^@C` is `1200(m)/(s)`. When some amount of oxygen is mixed with hydrogen, the velocity decreases to `500(m)/(s)`. Determine the ratio of `H_2` to `O_2` by volume in this mixture, given that the density of oxygen in 16 times that of hydrogen.

Explanation

Given that
`1200=sqrt((gammaP)/(rho_H))` ..(i) ltbr. Let there be x volume of `H_2` and y volume of `O_2` then,
`(x+y)rho_(mix)=xrho_h+yrho_0=xrho_H+16yrho_H`
`impliesrho_(mix)=((x+16y))/(x+y)rho_H`
`500=sqrt((gammaP(x+y))/((x+16y)rho_H))` ..(ii)
Dividing Eq. (ii) by Eq. (i)
`(12)/(5)=sqrt((x+16y)/(x+y))`
or `(x)/(y)=(2.2)/(1)`