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

Answer:

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:

$v_{w} = \sqrt(\frac{T}{\frac{M}{l}})$

Putting the values in the above formula:

$v_{w} = \sqrt(\frac{74.4}{\frac{2.31}{10.4}})$

$v_{w} = \sqrt 334.96 = 18.30 m/s$

Time taken, t can be calculated as:

$t = \frac{distance}{speed or velocity}$

Since distance between two end is the length of the rope

Therefore, using the formula for time, t:

$t = \frac{10.4}{18.30}$

t = 0.568 s

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