The velocity of sound in a gas depends on its pressure and density . Obtain the relation between velocity , pressure and density.

Explanation

Let the relationship be expressed as `v=kp^(a)rho^(c )`, where p is pressure, `rho` is density and v is velocity of sound.
Now,`" "[v]=[LT^(-1)],[p]=[ML^(-1)T^(-2)],[rho]=[ML^(-3)]`
`therefore" "[M^(@)LT^(-1)]=[ML^(-1)T^(2)]^(a)[ML^(-2)]^(c)`
`"or "[M^(@)LT^(-1)]=[M^(a+c)L^(-a-3c)T^(-2a)]`
Equating the powers of M, L and T, we have `a+c=0, -a-3c=1, -2a=-1`
`rArr" "a=(1)/(2), c=(-1)/(2)`
`therefore" "`Expression for velocity of sound is of the form `V=Ksqrt((P)/(rho)).`