Reflection and Transmission at a Boundary

A traveling pulse carries energy through a medium, like a rope, until it hits a place where the medium changes, like a knot connecting to a different rope, or a wall. At that boundary, the wave cannot just keep going unchanged, because the new medium responds differently. So the energy splits: some bounces back as a reflected wave, some keeps going as a transmitted wave. How much goes each way depends on how different the two sides are. A rope tied to a wall is as fixed as a boundary gets, so almost all the energy reflects, and the pulse flips upside down because the wall yanks the rope end back down as it reacts. A free end, like a ring sliding on a frictionless pole, barely resists at all, so the pulse reflects right side up, with the end overshooting before snapping back.

Between those extremes, a pulse crossing from a light rope into a heavy rope meets a partial mismatch. Part of the pulse reflects, inverted because the heavy rope acts more like a fixed end, and part transmits into the heavy rope, right side up but smaller, carrying less energy at a slower speed. The closer the two ropes are in mass, the more energy transmits and the less reflects, since a small mismatch barely disturbs the wave. This is why no boundary short of a perfectly rigid wall or a perfectly free end reflects all the energy back.

This idea connects directly to echoes and, later, to layered reflections in sound and light. An echo is just a reflected sound wave bouncing off a distant boundary, like a wall or cliff, and returning to the source. Since the wave's speed stays constant in a given medium, doubling the distance to the wall doubles the round-trip path, which doubles the delay time before the echo returns.