Wave Velocity On Vertical Rope

Hey guys, just a quick question thats been bugging me for a couple of days. If you take a long rope with mass, suspended vertically and you produce a wave pulse in the lower end of the rope (so that the wave travells upwards), would the speed of the wave change as it moved upwards?
I have a feeling that it would, something to do with tension maybe, but i really don't know why i think this. If anyone could help, i would greatly appreciate it.

Reply 1

teachercol

yes - the wave speed depends on the square root of the tension. As T increases for a 'heavy' rope, v will increase.

Reply 2

Theorist

So the wave speed will be greatest at the top of the rope?

I think so

Ok.

this is a good problem (and i feel like there is something wrong in this...)
I'm not sure of what I'm gonna tell you, so i'll ask my teacher, then i'll post my remark.
(too much respect for teachercol :wink:

)
Good luck.

Reply 6

teachercol

You can demonstrate this by forming a standing wave on a vertical chain. The wavelength is least at the bottom because v is least there.

Reply 7

Jasmine*

My first idea was to say that velocity of waves is a constant of the environment of propagation.
So it was a reflex : something seemed wrong.
i'll work on it tomorrow, and i'll try to see how T decreases with altitude
Excuse my scepticism...

Reply 8

teachercol

Its because the tension in a vertically hanging chain varies as yu go up the chain - each bit has to 'hold' the weight of the chain below.

That makes it different to the usual horizontal waves on strings.

Gotta love PDFs...

Thank you very much, i see the problem clearly now.
Have nice evening.>>

Reply 11

9031olivia

Would the change in wavelength have anything to do with a change in frequency? Or is it just dependent on the change in velocity due to the force of gravity increasing as we move up the rope? (Which is due to the increase in mass below our moving point of interest.)