A rope of length l and mass m hangs from the ceiling. If a wave of frequency n propagates through the rope, find the phase difference between the top and the bottom of the rope.
Please Solve This.
Phase difference=(2pi/£)(path difference) where £=wavelength.
Put path difference=l.
£=v/n where v=(gl)^(1/2)
Put path difference=l.
£=v/n where v=(gl)^(1/2)
i think you havn't noticed that tension in rope wil vary due to weight. So the velocity of wave can't be considered constant and thus this doesn't work.
Sorry could not reply back earlier.
You are right,the tension will vary-I had just ignored the part about the rope being vertical,stupid of me!
So I guess you could take a small element dx at a distance x from the bottom of the rope. The tension on that element will depend on the weight of rope below it. Find the tension in terms of x, follow the same procedure as I had given in the previous post, and integrate the resulting expression for phase difference from 0 to L.
I hope this works!!
I used that method. Can u please give me just the answer you will get.
I want to match my answer.
Will this change depend on the length of the wire.
Yes, I suppose it will depend on the length . Also, according to my calculations, the phase difference will be the same irrespective of whether the rope is vertical or horizontal. Do you think so too?
No.
Mine result was just dependent on angular velocity and not length or mass.
And for horizontal wire wave velocity will be constant thru out but in vertical alignment the case is not the same.