Proving Transverse Wave Travel Time in Suspended Rope: A Case Study in Physics

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In summary, a rope with a total mass M and length L suspended vertically can have a transverse wave pulse travel along its length in a time t=2(L/g)^0.5. This can be determined by taking the distance of any point A on the rope from the lower end to be X, with a linear density of M/L and a tension of MgX/L. The velocity of the wave can be calculated using the formula v=(T/linear mass density)^0.5=(L^2/Xg)^0.5, but this does not match the desired result. To find the correct time, the integration of dx/v must be performed, taking into account that the speed of the wave diminishes as it gets closer
  • #1
Wen
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A rope of total mass M and length L is suspended vertically.Show that a transverse wave pulse travel in the length of the rope in a time t=2(L/g)^0.5

If i take the distance of any point on the rope ,A, from the lower end to be X.
linear density is M/L
Tension due to the segment of rope below A is MgX/L
velocity =(T/linear mass density)^0.5
=(L^2/Xg)^0.5
if X=L
V= (L/g)^0.5

which is not what is needed to be shown. So where am i wrong?
 
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  • #2
Wen said:

velocity =(T/linear mass density)^0.5
=(L^2/Xg)^0.5


Check your calculations ! and write [tex] v = dx / dt [/tex]
 
  • #3
The speed of the wave is not constant. It diminishes as the wave gets closer to the lower end. So to find the time, you have to integrate dx/v.

(And yes, check your calculations :tongue2:)
 

1. What is a wave?

A wave is a disturbance or variation that travels through a medium, such as air or water, transferring energy from one point to another without causing any actual movement of the medium itself.

2. How do waves work?

Waves work by transferring energy from one point to another through a series of oscillations or vibrations. These oscillations can be caused by a variety of factors, such as wind, earthquakes, or even sound.

3. What are the different types of waves?

There are two main types of waves: mechanical and electromagnetic. Mechanical waves require a medium to travel through, while electromagnetic waves can travel through a vacuum.

4. How do waves interact with each other?

When two or more waves encounter each other, they can either reinforce each other (constructive interference) or cancel each other out (destructive interference). This interaction is known as wave interference.

5. How are waves measured?

Waves are typically measured by their frequency, wavelength, and amplitude. Frequency is the number of waves that pass a point in a given time, wavelength is the distance between two consecutive points on a wave, and amplitude is the height of a wave.

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