A rope hangs vertically from a connection made in the ceiling with a mass hangin

Question

A rope hangs vertically from a connection made in the ceiling with a mass hanging on the end of the rope. The velocity of a wave propagating through the rope is found to be 50 m/s with 1 kg hanging on the end of the rope.

a. What is the mass per length of the rope?

b. How much mass has to be hung from the end of the rope to double the wave velocity?

c. Which of the following answers explain why the wave velocity is not truly constant within the rope with a single mass hanging on it?

Check all answers that apply.



The rope will stretch causing the velocity to be different than it was with only 1 kg mass hanging on it.


Gravity causes the wave velocity to be faster on on the way down through the rope than on the way back up.



The wave velocity will be constant as the wave travels up and down within the rope. It is NOT be different at all.



The rope has some mass and, therefore, the tension within the rope will be different at the top and bottom of the rope causing the wave velocity to be different also.

Explanation / Answer

velocity of wave = sqrt(tension in rope/mass per unit length) a) sqrt(1 * 9.8 / Ml) 50*50 = 9.8/Ml Ml = mass per unit length Ml=9.8/(50*50) =0.00392 Kg/m2 b) for doubling the velocity 100*100 = T/0.00392 T=39.2 Newton mass = 39.2/9.8 =4 Kg. C) foruth option explains this principle correctly ie: The rope has some mass and, therefore, the tension within the rope will be different at the top and bottom of the rope causing the wave velocity to be different also.

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