How does gravity affect a single pulse traveling through a medium?

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When a single pulse, like a crest, travels through a medium such as a rope or slinky, it maintains its height as it moves to the end. Gravity acts as a restoring force, but it does not alter the height or orientation of the pulse during its travel. The shape of the rope already incorporates gravity, resulting in only minor deviations from equilibrium. The key point is that gravity's influence is negligible for the dynamics of a single pulse, which focuses on deviations from equilibrium rather than the overall position. Thus, gravity does not significantly affect the propagation of a single pulse in this context.
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if you have a rope or slinky and send a single pulse through the medium (for example a crest), the crest travels all the way to the end of the rope basically at the same height. I know that for disturbances to be waves, the motion must be rhythmic and one component of a wave is a restoring force, and in the rope, gravity I think would be the assumed restoring force.

How come as the crest travels, gravity does not slowly push this crest down toward the equilibrium position and then to the trough position? Why is the force of gravity or any other restoring force in other waves not able to change the height and orientation of a single pulse?

Thanks!
 
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Gravity is already included in the shape of the rope (small deviation from a straight line). If you just look at deviations from this equilibrium position, gravity does not matter (much).
 

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