Question

A long rope of total mass m is hanging down from the rafters in the gym

a) Does the speed of a wave pulse increase, decrease, or remain the same as it ascends the rope. Explain your answer.

b) Now that we know what to expect calculate the time a pulse needs to travel up that rope as a function of the mass, and the length of the rope and any other parameters that might be necessary.

Answer 1

a)

As the rope ascends , the tension force in the rope decreases . we know that

speed = sqrt(tension/mass density)

so as the tension force decreases , the speed also decrease

b)

L = length of rope

= mass per unit length

T = tension force = mg

speed is given as

v = sqrt(T/)

time taken is given as

t = L/v = L/sqrt(T/) = L sqrt()/sqrt(T)