The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300K is

Options

A. `sqrt(2//7)`
B. `sqrt(1//7)`
C. `sqrt(3//5)`
D. `sqrt(6//5)`

Answer

C

Explanation

Speed of sound in an ideal gas is given by
`V = sqrt((gammaRT)/(M))`
`V prop sqrt((gamma)/(M))` , [`T` is same for both the gasses] '
`(V_(N_(2)))/(V_(He))=sqrt((gamma_(N_(2)))/(gamma_(He))xx(M_(H_(e)))/(M_(N_(2))))=sqrt(((7//5))/((5//3))((4)/(28)))=sqrt(3)//5`
`gamma_(N_(2)) = 7//5` , (Distomic)
`gamma_(He) = 5//3` , (Monoatomic)