Substituting the constitutive relation (11) into the law of motion (5) we find the equation of motion for sound,
Thus, we see that sound obeys precisely the same wave equation as do waves on a string. In particular, we now have the wave speed of sound,
As with waves on a string, we again find that the wave speed is the square root of the ratio of a measure of the restoring forces in the system to the inertia. Once again, a ``stiffer'' system (stronger restoring forces) leads to faster wave motion and increased inertia (mass density) leads to slower wave motion.
