Skipping class

Even at UWC's students sometimes skip class but that's not what this post is about. I've been doing various different forms of standing waves demos and practicals for many years, like the one in the photo (waves in a string) where a string is made to oscillate by a vibration generator. Whilst doing this experiment I noticed that the string is sometimes vertically polarised but more often then not it spins round more like a skipping rope. The frequency of these two motions is pretty much the same, you can make the mode of vibration change by touching the string. So, what I was wondering was, is the equation for the skipping rope the same as that for a wave?

When thinking about this problem one thing didn't make sense. A vibrating string has a resonance at one frequency but a skipping rope can be spun at any frequency, how can that be? I reckoned that as the rope is spun more quickly the tension in the string increases causing the frequency of the 1st harmonic to change. I decided to measuring the tension as the rope was spun and discovered that this did seem to be the case. Furthermore it did seem that the frequency was indeed proportional to √Tension as would be expected for a vibrating string. I thought this would make a good DCP practical so I wrote a worksheet. Haven't tried it out with my students yet though.

Whilst on the subject of skipping, I have often wondered if it would be possible to get two people to skip in the two antinodes of the second harmonic of a skipping rope. From the video clip below it seems that it is. This I will have to try.