Wave equations and their solution
2.1 Wave equations
We have discussed qualitatively in the previous chapter how wave motions result from the delayed response to an adjacent displacement. But how can we quantify the motion? How can we determine the speed of propagation, the energy contained within the wave, whether the wave shape changes as it propagates, and so on? The answer is that we must first quantify the physics of the wave system by writing explicit equations that describe how the adjacent disturbance influences a given point and how the response is delayed.
Pain  pp. 108–112French  pp. 161–167Crawford  pp. 48–56