Question

A heavy but uniform rope of length L is suspended from a ceiling. (a) Write the velocity of a transverse wave travelling on the string as a function of the distance from the lower end. (b) If the rope is given a sudden sideways jerk at the bottom, how long will it take for the pulse to reach the ceiling ? (c) A particle is dropped from the ceiling at the instant the bottom end is given the jerk. Where will the particle meet the pulse ?

Answer 1

a) m ---> mass per unit of length of string
consider an element at distance ‘x’ from lower end.
Here wt acting down ward = (mx)g = Tension in the string of upper part

The velocity of transverse vibration

c) Suppose after time ‘t’ from start the pulse meet the particle at distance y from lower end.

Distance travelled by the particle in this time is (L – y)