If a long rope is hung from the ceiling and a transverse wave pulse is sent up t

Question

If a long rope is hung from the ceiling and a transverse wave pulse is sent up the rope from its lower end, the speed of the pulse changes as it ascends. A common, incorrect line of reasoning for this scenario is as follows: Student: I think the speed of the pulse will decrease as it rises because it is moving up against gravity. It's like when you throw a ball straight up. As the ball rises, the downward force of gravity acts on the ball causing the ball to decrease in speed. The above explanation is incorrect. Why does the student's reasoning not work? Why is the rising ball not a valid analogy for thinking about the wave pulse moving up the rope?

Explanation / Answer

The speed of a wave pulse travelling along the rope is a function of te tension in the rope. As we move up, the tension in rope increases. Since the speed of wave in the rope is directly proportinal to the square root of tension in it, the wave velocity will increase as the wave ascends up the rope.

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