Drag the sliders. The pattern moves, but every point in the medium just oscillates in place — that single idea unlocks the whole topic.
A wave transfers energy from one place to another without transferring matter. Everything about a wave's shape and speed follows from that.
In a transverse wave, particles of the medium oscillate perpendicular to the direction the wave travels — light and waves on a string are transverse. In a longitudinal wave, particles oscillate parallel to the direction of travel, bunching into compressions and spreading into rarefactions — sound is the classic example. Flip the toggle on the simulator to see both side by side.
Every particle in the medium repeats the same up-and-down (or back-and-forth) motion as its neighbour, just slightly delayed in time. That delay — the phase difference — is what makes the pattern appear to travel, even though no particle actually moves along with it.
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