The diagrams of this section are based on original animations by Petr Lobaz, from the University of West Bohemia, Czech Republic.
Below are two charged particles, represented by green circles. Each charge affects the electrical field around it.
If you click the particle on the left, an external force starts oscillating it. This causes changes in its electrical field to propagate outward, at the speed of light (of course, much slowed down for this illustration).
When these changes reach the second particle (5 seconds later), they stimulate it into an identical motion pattern. The propagation distance makes such motion to occur with a slight delay compared to the original particle's.
The wave "effect" caused by this propagation delay becomes clear once we observe what happens when several more particles are added to this setup: (click the first one to start the animation)
Essentially, charged particles "drag" each other along, and the closer they are to each other, the faster the influence of one reaches the next.
According to this page, a sinusoidal function is the result of the simplest system that produces an oscillation.
The following is just a draft for text to be added.
\begin{equation} \sin ( t ) \\ A \sin ( \omega t + \varphi ) \\ \boxed{A} \sin \left( \boxed{\omega}t + \boxed{\varphi} \right) \\ y = \boxed{\mathsf{A}} \sin \left( \boxed{\mathsf{B}}x + \boxed{\mathsf{C}} \right) + \boxed{\mathsf{D}} \\ y = \boxed{\mathsf{1}} \sin \left( \boxed{\mathsf{1}}x + \boxed{\mathsf{0}} \right) + \boxed{\mathsf{0}} \\ y = \sin ( x ) \end{equation}| ...in the input (x) axis. |
...in the output (y) axis. | |
|---|---|---|
| slides the wave... | C | D |
| stretches the wave... | B | A |