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Consider the case where a pulse hits a fixed end. I want to know the physics behind the following two phenomena

1) Why does the pulse get reflected?

2) Why does the pulse get inverted?

I somewhat understand the answer to the second question. The pulse exerts an upward force on the fixed end and by Newton's Third Law the fixed end exerts an equal and opposite force. Consequently, the particles on the rope will have a negative displacement. Regarding the first answer I think that it has to do with Principle of Superposition, but I can't quite verbalize an explanation.

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In mechanical vibrations of a string, those phenomena are related to the phenomenon of the elasticity, that, in turn, consist in the conservation of the total momentum. In other words, if a piece of the string attached to the fixed end is stretched upward, the elastic force, according to the third Newton's law, tends to pull it downward.

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  • $\begingroup$ That explains the second question, but what about the first question? Why is there a reflection of the wave of a fixed end? $\endgroup$ – model_checker Mar 13 '16 at 9:09
  • $\begingroup$ There are three options: the wave keeps propagating in the same direction, the wave is reflected and the wave is decayed. Only the second case is consistent with the momentum conservation law when the end is fixed. $\endgroup$ – freude Mar 13 '16 at 9:25
  • $\begingroup$ The momentum of the wave points in the direction of its propagation. $\endgroup$ – freude Mar 13 '16 at 9:33
  • $\begingroup$ The wave is incident on the fixed end with some velocity value $u_1$. The initial momentum, therefore, is $P_i=m_1u_1$. After collision, with the fixed end, the final velocity of the fixed end is $0$ and the wave's final velocity is $v_1$. Thus, the final momentum is $P_f=m_1v_1$. Now according to Momentum conservation $P_i=P_f$, which implies that $v_1=u_1$. This does not prove that the final velocity is in the opposite direction of the initial velocity and therefore suggests that the wave must travel in the same direction. What mistake have I made? $\endgroup$ – model_checker Mar 13 '16 at 9:59
  • $\begingroup$ There is a good explanation in wiki how to compute velocities for elastic scattering en.wikipedia.org/wiki/Elastic_collision $\endgroup$ – freude Mar 13 '16 at 10:16

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