Two monatomic ideal gas 1 and 2 of molecular masses `m_(1) and m_(2)` respectively are enclosed in separate containers kept at same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is given by

Options

A. `sqrt((m_(1))/(m_(2)))`
B. `sqrt((m_(2))/(m_(1)))`
C. `(m_(1))/(m_(2))`
D. `(m_(2))/(m_(1))`

Answer

B

Explanation

Speed of sound in a gas given by
`v=sqrt((gammaRT)/M)`
`v prop 1/(sqrt(M))`
`:. (v_(1))/(v_(2))=sqrt((M_(2))/(M_(1)))=sqrt((m_(2))/(m_(1))`
Here `gamma=(C_(p))/(C_(v))=5/3` for both the gases `(gamma_("monoatomic")=5/3)`