Phase change on reflection

Intermediate

Fixed ends invert the pulse; free ends do not.

A pulse on a string reflects inverted from a fixed end and upright from a free end. For light, reflection from a denser medium gives a π phase shift.

Worked example

Waves on a rope tied to a wall come back upside down.

Common mistake

Phase changes matter for interference.

In more detail

When a wave reflects from a fixed end, its displacement is inverted, a phase change of π. From a free end, there is no inversion.

A rope tied to a wall reflects pulses upside down.
Anti-reflection coatings use phase changes in thin films.
A rope tied to a wall reflects a pulse upside down, while a loose end sends it back the same way up.

Why does a fixed end invert the wave?

The boundary cannot move, so the reflected wave must cancel the incident displacement there.

What happens at a free end?

The wave reflects with the same phase, because the end can move freely.

Why does a fixed end invert the pulse?

The wall pushes back against the pulse, creating an opposite displacement that travels back along the rope.