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Reflection of Waves
All waves can be reflected.

A wave is reflected at the boundary of the medium through which it is travelling or at any point where there is a change in the velocity of propagation of the wave.

Some aspects of reflection of waves can be studied by observing waves on springs.
Hold a long spring vertically, as shown below, and give it a short sharp shake, horizontally.
A transverse pulse will travel down the spring and be reflected from the other end.

What happens during the process of reflection depends on the nature of the boundary.
Notice that, if the end of the spring is fixed in place, the pulse "flips over" to the other side.
We say that there has been a change of phase.
The reflected pulse is said to be in anti-phase with the incident pulse or, by comparison with sine waves, 180° or pradians out of phase.

When the end is free to move, the pulse goes back up on the same side, so we say no phase change has occurred.

Reflection at a Point where the Wave Velocity Changes
In the above examples, the change is rather dramatic... we go abruptly from wave to no wave (by definition, you can't have a wave on a spring where there's no spring!)
A slightly less dramatic, though equally important case, is one in which some property of the medium through which the wave is traveling changes, resulting in a change of the velocity of propagation of the wave.
For example, if a wave goes from a spring having a certain mass per unit length to another of different mass per unit length, we find that a certain proportion of the energy of the wave is reflected back from the point where the velocity of propagation of the wave changed.
Some of the energy continues past the change in medium: this forms what we call the transmitted wave.

In the examples below, imagine that the blue spring has a greater mass per unit length than the red spring, so the wave velocity is lower in the blue spring.

Wave slows down at the change of medium, v2 < v1

Before Reflection

After Reflection

 Reflected wave, phase change Transmitted wave, no phase change

The phase change of the reflected wave should be no surprise, having seen that it occurs when the end of the spring is fixed.
Imagine an extreme example with a (blue) spring of ginormous mass per unit length (I mean, like, really really massive...)
In this case the end of the red spring would be more or less fixed in place by the much more massive spring so the two situations would be very similar.

Wave moves faster after the change of medium, v2 > v1

Before Reflection

After Reflection

 Reflected wave, no phase change. Transmitted wave, no phase change.

Again, this should be no surprise after the non-phase-change from a free end.
Again, to convince yourself, consider a very very low mass spring (I mean, like, really really low mass), you get the idea...
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