# Speed of Sound greater in denser Materials linked to restoring force

I recently read a book that explained why the speed of sound is faster through a medium with a higher density.

It said -

In a denser medium, the particles are closer together. This means that there is a stronger restoring force so the vibrations are passed more rapidly from one particle to another

I am confused by the statement There is a stronger restoring force which results in the vibrations being passed more strongly.

How does a stronger restoring force cause this? I know that in a denser medium, there are more particles, hence the vibrations can be passed faster from one end to another, but I don't understand how the restoring force is involved.

Please help!

Thanks.

• look into the derivation of speed of logitudnal wave and note the role of bulk modulus in defining the final formula
– oops
Apr 1, 2017 at 8:29

## 1 Answer

I think that your book does has not given you the correct information.

The speed of sound in lead (density $11.3 \,\rm g\,m^{-3}$) is $1210\,\rm m\,s^{-1}$and in aluminium (density $2.7 \,\rm g\,m^{-3}$) is $6320\,\rm m\,s^{-1}$.

The speed of a mechanical wave depends on the properties of the solid it is travelling through.
As a wave travels through a solid the atoms are forced to oscillate ie move about their equilibrium positions.
Once an atom has been displaced from its equilibrium position how faster it returns to that position depends on the mass of the atom and the force exerted on the atom by the surrounding atoms and the faster the atom can back to its equilibrium the larger will be the speed of the sound wave through the solid.

An atom of larger mass given the same restoring force will return to its equilibrium position slower resulting in the wave speed being lower.
An atom with a larger restoring force will return to its equilibrium position faster resulting in the wave speed being higher.

So the two important properties of a solid as far as the speed of propagation of sound waves through a solid are the density of the solid which is related to the mass of an atom of the solid and ta modulus of elasticity of the solid which is related to the restoring force for a given displacement.