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

Answer

B

Explanation

Let V be the volume of each gas. Then Density mixture, `rho_("mix")=("total mass")/("total volume")`
`=(Vrho_(H_(2))+Vrho_(O_(2)))/(V+V)=(Vrho_(H_(2))+V(16rho_(H_(2))))/(2V)=(17)/(2)rho_(H_(2))`
As `v=sqrt((gammaP)/(rho))or vprop(1)/(sqrt(rho))therefore (v_(mix))/(v_(H_(2)))=sqrt((rho_(H_(2)))/(rho_(mix)))=sqrt((2)/(17))`