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

Since we know that
`V=sqrt((gammaP)/rho_H) , therefore 1200=sqrt((gammaP)/rho_H`….(1)
Let there be x volume of `H_2` and y volume of `O_2`
Then (x+y) `rho_"mix"= x rho_H yrho_0 =x rho_H + 16 y rho_H`
`rArr rho_"mix" =((x+16y))/(x+y) rho_H , 500=sqrt((gamma P(x+y))/((x+16y) rho_H)`....(2)
Dividing (1) by (2)
`12/5=sqrt((x+16y)/(x+y))`
or `x/y=2.2/1`