Calculate the velocity of sound in a mixture of two gases obtained by mixing `V_(1)` and `V_(2)` volumes of them if the velocity of sound in them be `C_(1)` and `C_(2)`. The atomicity of the gases is the same.

Options

A. `C_(1)C_(2)sqrt((V_(1)+V_(2))/(V_(1)c_(2)^(2)+V_(2)c_(1)^(2)))`
B. `C_(1)C_(2)sqrt((V_(1)+V_(2))/(V_(1)c_(1)^(2)+V_(2)c_(2)^(2)))`
C. `C_(1)C_(2)sqrt((V_(1)+V_(2))/(V_(1)^(2)c_(1)+V_(2)c_(2)^(2)))`
D. `C_(1)C_(2)sqrt((V_(1)+V_(2))/(V_(1)^(2)c_(1)+V_(2)^(2)c_(2)))`

Answer

A

Explanation

`rho_(mix)=(rho_(1)V_(1)+rho_(2)V_(2))/(V_(1)+V_(2))`
velocity of sand
`Cprop(1)/(sqrt(rho))impliesrho prop(1)/(C^(2))implies(rho_(1))/(rho_(2))(C_(2)^(2))/(C_(1)^(2))`
`impliesrho_(1)=(C_(2)^(2))/(C_(1)^(2))rho_(2)impliesrho_(mix)=((C_(2)^(2))/(C_(1)^(2))rho_(2)V_(1)+rho_(2)V_(2))/(V_(1)+V_(2))`
`rho_(mix)=((C_(2)^(2)V_(1)+C_(1)^(2)V_(2))/(V_(1)+V_(2)))(rho_(2))/(C_(1)^(2))implies(C_(mix))/(C_(2))=sqrt((rho_(2))/(rho_(mix)))`