Suppose that there is a pulse moves to the right.
  There is a upward transverse motion along the leading edge of the pulse.
  The transverse motion vanishes at the peak, and there is downward transverse motion along the trailing edge .
Let us consider the superposition of two pulses of identical shape moving relative to each other.

---

Usage :

1. Click right mouse to toggle the animation.

When the animation stops. The blue curves show the current pulses.
 while those red curves show the pulse at the next time interval.
Those red arrows indicate the relative motion of pulses.
 Blue arrows are moving directions of those pulses.
For transverse wave blue arrow and red arrow are perpendicular to each other.

2. Click right mouse button twice quickly will reset all the parameters.

Even though the wave is flat
for a brief moment, It is not at rest.