A rope of length L and uniform linear density is hanging from the ceiling. A transverse wave pulse, generated close to the free end of the rope, travels upwards through the rope. Select the correct option.

Step-by-step solution

Tension at a section x distance from free end is T = m g = μ · x · g where, μ = mass per unit length of rope. Wave speed over the rope is given by v = T μ = μ · x · g μ = g · x ⇒ v 2 = g x Comparing above equation with v 2 - u 2 = 2 a s , we get ⇒ v 2 = 2 a x = g x ⇒ Acceleration, a = g 2 Now, if t = time for wave pulse to cover a distance x , then from s = u t + 1 2 a t 2 , we have x = 1 2 × g 2 × t 2 or t = 2 x g ⇒ t ∝ x or time to travel complete length of rope t ∝ L .