Wave Propagation in a Hanging Rope: Speed at Top vs Bottom

[forsberg21]

Homework Statement

If a wave is started up a long rope hanging from the ceiling, it will not climb at constant velocity. Why? Will the wave be traveling faster or slower at the top than the bottom? (Hint: Is the tension of the rope a factor?)

Homework Equations

v=square root (F/u) (tension over mass per unit length) ?

The Attempt at a Solution

I don't know how to do this.

 

[lzkelley]

"I don't know how to do this" is not an attempt.
We can't help you unless you try something, or put some thoughts out there.

 

[forsberg21]

Ok...well I considered that the tension in the rope may be greater at the top because of the weight of the rope below it, but it would have to be a very large rope for that to make much difference. I also considered that if the rope is connected to the ceiling that may reduce the ability of the rope to carry a wave which would slow the wave down.

 

[forsberg21]

Is it possible for a wave to lose energy as it moves up?

 

[lzkelley]

Awesome, you've got it all right there.

The rope is connected to the ceiling, but oddly enough, it does NOT slow the wave down.. even though it seems like it should. The ceiling connection will "dampen" the wave (decrease its amplitude/strength) but not slow it down.

You're also very correct about the tension... and although the effects of that tension change seem small, think about this:
How much tension is there at the very very bottom of the rope, like the very last 1/10,000th of an inch (where there is essentially nothing below it)?
How does that compare to the top of the rope?

You've totally got the answer.

 

[lzkelley]

Is it possible for a wave to lose energy as it moves up?

In an ideal situation, no it cannot lose energy.
In actuality it will always lose some energy.

When i said that it loses amplitude as it goes up - its still conserving energy, it just takes more energy (more work) to create smaller amplitude changes as you get closer to where its fixed to the ceiling.

 

[forsberg21]

sweet thank you