Time it takes for a wave to travel up and down a rope?

AI Thread Summary
The discussion focuses on calculating the time it takes for a wave pulse to travel up and down a rope, using the length of the rope (l) and its mass (m). The solution involves applying Newton's Second Law to determine the wave velocity, which is derived from the tension in the rope. The time is then calculated using the formula time = distance/velocity, with the total distance being twice the length of the rope. There is mention of alternative methods involving sine and cosine, but the straightforward approach seems sufficient. The key question raised is whether the wave velocity remains constant along the rope.
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Homework Statement



A man brushes the end of a rope that sends a pulse up the rope to the fixed end of the rope and back down to the bottom. How long does it take the pulse to make the trip from the bottom of the rope, to the top, and back? Let the length of the rope be l and its mass m.

Homework Equations



Newton's Second Law of Motion (where velocity is equal to the square root of the force of tension times mass divided by the length of the rope) and time = distance/velocity.

The Attempt at a Solution



We took Newton's Second Law of Motion and basically isolated velocity. From there, we simply plugged velocity into time=distance/velocity. We would then multiply that by two to get the time for it to travel up and down the rope. Is this reasoning right? Our professor was talking to another group about the same problem and they started talking about sine and cosine and it was terribly complicated, but it seems like working it out like this would work as well.
 
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Hint: Is the wave velocity constant along the rope?
 

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