The ratio of the sound in a monatomic gas at `27^(@)C` and rms speed of the molecules of the same gas at a temperature of `127^(@)` C is

Options

A. `1:2`
B. `sqrt(5):sqrt(12)`
C. `3:4`
D. `sqrt(13): sqrt(17)`

Answer

B

Explanation

Speed of sound in gas
`v= sqrt((gammaRT_(1))/(M)) " " cdots (i)`
rms speed of molecules ,
` c= sqrt((3RT)/(M)) " " cdots (ii)`
For monoatonic gas r `= (5)/(3)`
Also `T_(1)= 300 K , T_(2)= 400 K `
`:. " " "Ration ", (v)/(c)= sqrt((gamma.T_(1))/(3.T_(2)))=sqrt((5//3xx300)/(3xx400))`
`(v)/(c)=(sqrt(5))/(sqrt(12))`