Is it possible to create a visual model (stop motion) of a wave motion using the differential equation for simple harmonic oscillation and how so?

Explanation:

A particular solution for the 1D wave equation has the form

where A its the amplitude, k the wavenumber, ω the angular frequency and φ the phase angle.

Now, for any given position , we can use:

so, the equation its:

.

This is the equation for a simple harmonic oscillation!

So, for any given point, we can use a simple harmonic oscillation as visual model. Now, when we move a distance from the original position, we got:

and

now, this its

So, there its a phase angle difference of . We can model this simply by starting the simple harmonic oscillation with a different phase angle.