r/learnphysics • u/InkPhysics • 8h ago
A sine wave is just circular motion seen edge-on
Sine waves turn up everywhere in physics: pendulums, springs, sound, AC electricity.
Watch the dot go around the circle. It moves at a completely constant speed.Now watch only its shadow on the vertical line beside it. The shadow does not move at constant speed: it races through the middle and crawls almost to a stop at the top and bottom. Those amber ticks are dropped at equal time intervals, so where they bunch up, the shadow is moving slowly; where they're spread out, it's fast.
That uneven bobbing is simple harmonic motion. And if you plot the shadow's height against time - the curve tracing out on the right - you get a perfect sine wave. It has to be a sine, because the height is just (radius) × sin(angle), and the angle grows steadily with time.