Transverse Wave
Each circle stays fixed in place — only the particle orbits, and its up-and-down motion is exactly the transverse oscillation that generates the wave. This matches real physics: the wave pattern travels, but each particle only moves vertically, never sideways.
Circular Motion → Sound Wave
The particle spinning on the circle (left) drives a piston that moves back and forth in a straight line — exactly how one air particle moves in a longitudinal sound wave. Traced over time (right), that same back-and-forth motion draws a sine curve, even though the real motion never left a straight line.
Longitudinal Wave
This is the same back-and-forth motion, repeated across many particles with a slight delay between neighbors — that delay is what makes the wave travel.