Set up a relation between speed of sound in a gas and root mean sqare velocity of the molecules of that gas.

Explanation

Speed of sound in a gas is
`v=sqrt((gammaP)/(rho))` …(i)
According to kinetic theory of gasses, root mean square velocity (C) of molecules of gas is obtained from the relation
`P=(1)/(3)rhoC^(2).C=sqrt((3P)/(rho))` …(ii)
Diving (i) by (ii), we get
`(v)/(C)=sqrt((gamma)/(3)) or v=sqrt((gamma)/(3))xxC`
This is the required relation.