Reflection of a wave by a rigid boundary

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Summary:

Why does it invert?
I found this on the internet.

The inversion of the reflected pulse can be explained by returning to our conceptions of the nature of a mechanical wave. When a crest reaches the end of a medium ("medium A"), the last particle of the medium A receives an upward displacement. This particle is attached to the first particle of the other medium ("medium B") on the other side of the boundary. As the last particle of medium A pulls upwards on the first particle of medium B, the first particle of medium B pulls downwards on the last particle of medium A. This is merely Newton's third law of action-reaction. For every action, there is an equal and opposite reaction.
Source

How does the crest reach the end of the medium? As the other end is fixed there is no way the crest can reach the interface. Isn't it?

My book gave an alternative explanation. It stated that as there is no net displacement at the interface, we can use the principle of superposition to find the phase of the reflected wave (The reflected phase should be 180 more than the incident phase). But my question isn't both the same wave? We use the principle of superposition when there are two different waves. Here, the same wave is just being reflected.

Please correct me
 

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