Oxygen is `16` times heavier than hydrogen. At `NTP` equal volumn of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is

Options

A. `sqrt((1)/(8))`
B. `sqrt((32)/(17))`
C. `sqrt(8)`
D. `sqrt((2)/(17))`

Answer

D

Explanation

Density of mixture `(rho_(mix))=(V_(1)rho_(1)+V_(2)rho_(2))/(V_(1)+V_(2))`
`=(V(rho_(O_(2))+rho_(H_(2))))/(2V)=(rho_(H_(2))+16rho_(H_(2)))/(2)=8.5rho_(H_(2))`
Now, `vprop(1)/(sqrt(rho))`
`implies(v_(mix))/(v_(H_(2)))=sqrt((rhoH_(2))/(rho_(mix)))=sqrt((rho_(H_(2)))/(8.5rho_(H_(2))))=sqrt((2)/(17))`