We start with the equation for a simple harmonic wave. This equation (for a wave propagating along the positive x–axis) has the form
\(\xi\) is thus a function of time, t, as well as the position co–ordinate, x. We, therefore, have
We thus find that
We call this equation as the differential equation for (one-dimensional) wave motion. It turns out that the differential form of the wave equation, namely
is also valid for waves that may not be simple harmonic waves. We, therefore, regard the above differential equation as the ‘general equation’ for (one–dimensional) wave motion. The equation of the simple harmonic wave, namely,
is just one of the many possible ‘solutions’ of this differential equation.
