# Does rope in a standing wave expand and contract as it moves between being straight vs sine?

Images of standing waves often show two people using a jump rope. The shape of the rope goes from straight to waves to straight, then a sine wave the other way and then straight again as it repeats. During those straight moments, it seems the rope takes a shorter path then when it is extended into the crest and trough.

Theories:

1. the rope does not expand or contract but instead moves out from the drawing in 3d to fit its length. But that doesn't seem to be what I experience when I do these things in real life.

2. the rope secretly conspires to generate smaller and smaller peaks and trough along the rope during the transition. What seems a straight rope line is actually a series of very small waves, which continue to break down until they can flip.

3. The diagram is false. The people holding the rope must move their hands closer and farther apart at double the frequency of the standing wave.

These are contrived and probably wrong. Any ideas how the rope compresses to a straight line for standing waves?

Update:

If the wave must push the particles into a dimension orthogonal to any 2d perspective, the distance correcting waves could would be small in comparison to the overall wave being observed.

For now, I assume there are no completely defined 1 dimensional waves in a medium having fixed distances.

• I thin kit might be best to think of this as a standing wave where the nodes might move closer together when the waves are at trough/peak than when they are not. I don't know, though... Good question. Sep 27, 2022 at 2:24
• Thanks RukiyaMeria. I seems like you are saying that the rope is like a bunch of points the move closer sort of like a pressure within the rope. But what if the rope was a long bicycle chain with links locked in place at specific distance. What would it mean for the node when the points within it can not compress together? Sep 27, 2022 at 2:36