A rope of total mass m and length L is suspended vertically. a pulse travels from the bottom to the top of the rope in an approximate time interval delta(t) =2sqrt(L/g) with a speed that varies with position x measured from the bottom of the rope as v = sqrt(gx). Assume the linear wave equation describes waves at all locations on the rope.
(a) Over what time interval does a pulse travel halfway up the rope?
(b) A pulse starts traveling up the rope. How far has it traveled after a time interval sqrt(L/g)?