Transverse waves mechanics in a rope

[Mårten]

This thread is a continuation of another thread where the mechanics of water waves were discussed - see: https://www.physicsforums.com/showthread.php?t=274210

I'm trying to understand the detailed mechanics of a transverse wave in a rope. I base my ideas here on Crowell's textbook (see http://www.lightandmatter.com/html_books/3vw/ch03/ch03.html#Subsection3.2.1" ), where you see the rope as a series of masses connected with springs. The parts on the rope which have a bend is exposed to a force, and therefore an acceleration occurs there.

Now I make a flick in the end of the rope, sending only one pulse through the rope. (Actually, it works better and you see better what happens if you use a scarf lying on the floor instead.) So why is the wave pulse propagating?

Let's look at this flick movement in slow motion: When my hand is in the top position of the flick, the rope (or the scarf) lies bended, almost in a e^-x shaped curve (maybe not exactly, but sort of); it's bended like that due to gravity and the loose tension in the rope. In this curve of the rope, I cannot see that any forces act upwards on the particles. So, when my hand goes down again in the flick, some parts of the rope some inches from my hand, don't manage to go down as fast as my hand does, so there is a crest and a sine-like curve from my hand to the crest (i.e. like that part of the sine-curve that lies between phi=0..Pi/2). This means that there are forces acting diagonally downwards on that part of the rope that lies in between my hand and that crest. But on the top of the crest, the force is just downwards, and further away on the rope, there cannot be any forces yet except for gravity.

So how come that the parts of the rope that is beyond this crest receives an upward force? Cause there must be this upward force, otherwise the wave wouldn't propagate.

 

[Mårten]

Anyone who can answer this? How could a wave propagate through a rope, i.e., what makes particles on a rope beyond the wave crest, go upwards?

 

[astrokreng]

I can provide an explanation for the mechanics of transverse waves in a rope. When you flick the end of the rope, you are giving it an initial displacement from its equilibrium position. This creates a disturbance in the rope, which travels along the length of the rope as a transverse wave.

The disturbance in the rope causes the particles of the rope to oscillate up and down, perpendicular to the direction of the wave. This oscillation creates a tension force in the rope, which is responsible for the propagation of the wave. As the wave travels along the rope, the particles are pulled in the direction of the wave and then pushed back to their equilibrium position. This process continues, causing the wave to propagate along the rope.

In terms of the specific scenario you described, the flick of your hand creates a bend in the rope, which is a form of potential energy. As the rope returns to its equilibrium position, this potential energy is converted into kinetic energy, causing the particles to oscillate and creating the tension force that propagates the wave.

The shape of the wave, in this case a sine-like curve, is a result of the tension force and the restoring force of gravity acting on the particles. As the wave travels, the tension force decreases due to the restoring force of gravity, causing the wave to gradually decrease in amplitude.

In summary, the mechanics of transverse waves in a rope involve the interplay between tension and restoring forces, which allows for the propagation of the wave along the length of the rope.