I was studying mechanical waves today and have questions regarding how a pulse is propagated on a string and its reflection and transmission at a boundary and I hope I can find help here.
First, regarding the propagation of a pulse. Let us assume we have a taut rope and I introduce a pulse in it by whipping one end. When I whip the rope at an end, I apply some force and displace the particles at that end which generates some kinetic energy which must propagate along the rope. I am to understand that each energized particle provides a force for its neighboring particle to displace along the $y$-axis (which is how the energy propagates). What is the force that restores these energized particles back to their initial position? Is it the reaction force according to Newton's third law) from the neighboring particles they just displaced or is it a component of the tension of the string? If it is due to the tension of the string (as I believe it is), what about the reaction force which the neighboring particle should exert? What effect does this reaction force have on the rope? Please give me a clear idea of how this full propagation takes place.
The blue arrows depicts the restoring force. Now if I have clamped the other end of the rope, the pulse is reflected back inverted. Can you provide an intuitive explanation on how this inversion takes place? I read that the reaction force from the rigid particle causes this inversion, but since the last clamped particle of the rope can not even move, how is the energy due to this force even propagated back and transferred to the adjacent particle which can move? The usual explanation for how a wave is propagated is that when one particle is disturbed (say, moved up), it exerts a pull on another, which in turn exerts a pull on the next one, and so on. In other words, to exert a pull or push on the next particle there must be some movement/disturbance of the previous one. But the particle is clamped.