Question

Two people, that are 10.4 m apart, stretch a rope (2.31 kg) with a tension of 74.4 N. If one person sends a pulse through the rope, how long will it take for the resulting disturbance to reach the other end? A. 0.5 sec B.0.585 sec C.0.54 sec D.0.568 sec

Answer 1

Option D. 0.568 s

Given:

Length of the rope, l = 10.4 m

mass of the rope, M = 2.31 kg

Tension, T = 74.4 N

Solution:

The velocity of the wave,
`v_(w)` is given as:

`v_(w) = \sqrt((T)/((M)/(l)))`

Putting the values in the above formula:

`v_(w) = \sqrt((74.4)/((2.31)/(10.4)))`

`v_(w) = \sqrt 334.96 = 18.30 m/s`

Time taken, t can be calculated as:

`t = (distance)/(speed or velocity)`

Since distance between two end is the length of the rope

Therefore, using the formula for time, t:

`t = (10.4)/(18.30)`

t = 0.568 s

therefore, time taken for the disturbance to travel from one end to the other is t = 0.568 s