Faraday crispations
It’s about time I gave an update on my non-linear physics class.
We spent the last few weeks building a framework to analyze partial differential equations with non-linear terms. After the pedagogical material, we went on to our first real example: Faraday waves.
Faraday waves were first described in an appendix to a paper published in the Philosophical Transactions of the Royal Society of London in 1831. These are standing non-linear waves that are generated when an open container with fluid is subject to vertical oscillations. When the oscillations reach a certain threshold, we begin to see an instability on the surface of the fluid. Our professor did a demo for us with two fluids: canola and water. I had posted a video to Faraday waves with corn starch some time back.
A bunch of people had previously observed this phenomena, but Faraday was the one who had described that the oscillation frequency of the waves is half that of the driving frequency. I’ve read this original paper, and he goes into excruciating detail about his experiments. Surprisingly for a physics paper, there wasn’t a single equation.
I’d like to draw attention to the point that we get a frequency that is half that of the driving frequency. This is impossible in a linear system, whose transfer functions have complex exponentials as eigenfunctions. The mixing of the modes of the system is not arbitrary, in fact we determined them after a ton of math.
To finish off, I’m posting a video to Chladni patterns formed with different frequencies. For the sake of saving some brain cells, don’t read the comments on that video.
Pictures courtesy of Jerry Gollub.
[...] physical phenomena is similar to Faraday waves seen in liquids almost a hundred and thirty years ago. The key difference is that while liquid [...]