Question-

1. A uniform rope of mass m and length L hangs from a ceiling.

a) Show that the speed of a transverse wave in the rope is a function of y, the distance from the lower end, and is given by v = Sqrt(gy).

b) Show that the time it takes a transverse wave to travel the length of the rope is given by t = 2sqrt(L/g). (Hint: calculate the length of time to travel a length dy at distance y on the rope first).

c) Does the actual mass of the rope affect the results of (a) and (b)?