Consider a rope hanging from the ceiling (massive / massless irrelevant, I suppose). A wave pulse is set up on the rope. Just as the wave pulse starts propagating on this rope, the top of the rope is cut off and the rope is allowed to fall freely.
What happens to the wave pulse?
I posed this question as a homework problem for a sophomores' class on Waves, but then I realized that this was probably not as simple as the naïve answer I had.
My naïve answer was, since there is no tension in the rope once in free fall (no gravity), the velocity for transverse waves on the rope is 0, therefore the pulse will freeze relative to the rope and fall.
My colleagues pointed out to energy and momentum conservation. One of my friends concluded that the rope should do some weird sort of spiraling to conserve momentum and angular momentum about the center of the pulse.
I'd appreciate if someone could shed some light on this problem.