velocity of sound

Some textbooks mistakenly state that the speed of sound increases with increasing density.

But in fact,

c = √( C / ρ )

c = The speed of sound
C = a coefficient of stiffness
ρ = density

The coefficient of stiffness relates to the strength of the bond between particles of a material. The stronger the bond, the higher the speed.

The higher the density, the greater the force is required to move the particles, hence the slower the speed.


For sound in air,

C = γ p
γ = adiabatic index
p = pressure

But p = ρ R T for ideal gas, so the effects of density and pressure cancel out. Hence

c = √( γ R T )

The total internal reflection of sound is more or less like that of light. It is a property of wave. But since the speed of sound is greater in solid or liquid, the total internal reflection occurs when sound travels from air to solid or liquid.