a rope hangs vertically from the ceiling. a pulse is sent down up the rope. does

ID: 2298907 • Letter: A

Question

a rope hangs vertically from the ceiling. a pulse is sent down up the rope. does the pulse travel faster, slower or at a constant speed as it moves toward the ceiling?

(a) What is the tension (T ) in a hanging rope as a function of the distance ( x ),
as measured down from the top hang point for a rope of uniform linear density
? ? Answer this simply by calculating the mass of the rope from point x down
to the bottom at x ? L. This should be easy for you since the rope has uniform
density.

(b) Now apply the "waves on a string" velocity result. (You do not have to
derive it here, but you should know how to do it.) Is the wave speed the largest
or the smallest at the top of the rope? Why can you answer this question
without any math? Does your math check this intuitive result?

(c) Not required (for this write-up), but it will help your understanding: Apply
your result to a real rope. Make a decent estimate as to the linear density of
run-of-the mill rope (if nothing else, go find a rope and weigh it). How much
does a 50 foot long rope weigh?