The previous set of notes illustrated the ubiquity of wave behavior by
showing that the displacements in strings and sound (y and s,
respectively) and that the electromagnetic fields in vacuum ( 
,
, 
, 
) all satisfy the same wave equation,
where q represents either y, s or (or , , or
) for strings, sound or electromagnetic systems, respectively.
We now turn to the problem of finding a general solution to this
equation. Once we have such a solution, we are then able to explore
readily all possible wave solutions and therefore all possible wave
phenomena.
Along the way to the general solution, we shall also discover a new,
important sub-class of solutions to the wave equation, traveling
waves
. These traveling solutions will
clarify greatly why we interpret the constant c in the wave equation
(1) to be the wave speed.
