Question

what is the relation between the velocity of sound and the density of the
medium?
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Answer 1

According to Newton speed of sound=√(P/D)

Where P is the pressure and D is density.

After the corrections by Laplace it became

V=√(γP/D).

, whereγis the Adiabatic Constant . And it’s value is equal to Cp/Cv

But by experiments it was found that speed of sound is independent of pressure and density. It can be understood by considering the fact that density is directly proportional to pressure so (P/D)=constant.

It can also be proved theoretically.

By Ideal Gas Law,PV=nRT

PV=m/M×RT , where m is given mass and M is molecular mass.

m/V=PM/RT

So , density=PM/RT.

V=√(γP/D)

V=√[γP/(PM/RT)]

Which gives V=√(γRT/M)

So this proves that Velocity of sound depends only on γ and T, Temperature.