ooblick magick

[nibot]

We all know that cornstarch + water (otherwise known as ooblick) is amazing stuff. However, these guys in texas at the center for nonlinear dynamics have taken it to a new level. If nothing else, you should check out the paper and definitely the movie. I wonder if this could be repeated just using a loudspeaker and function generator? Yet another reason to procrastinate on studying for finals!

[edit: you're too late! I guess the movie was "slashdotted," as it's no longer available from their web page. )-: edit2: nevermind, they fixed it.]

[edit3: here's an experiment with solitons that you can do on the surface of a pool: Falaco Solitons. Check out the paper gr-qc/0101098 in arXiv. "String theorists take note, for the structure consists of a pair of topological 2-dimensional rotational defects in a surface of discontinuity, globally connected and stabilized by a 1 dimensional topological defect or string."]

On another note, I'm curious how much of antenna theory can be co-opted to make antennas for sound. A yagi for sound seems a bit unlikely, but parabolic reflectors certainly work, and it seems that there ought to be some magic with cavity resonators.

Comments

[nibot.livejournal.com]

I don't think the acceleration is important.

Suppose the equation for the driven vibrations is sinusoidal, with amplitude A:

  x(t) = A sin ω t

Then we can calculate the velocity and acceleration:

  v(t) = x'(t) = A ω cos ω t
  a(t) = x''(t) = - A ω2 sin ω t

The relationship between angular frequency ω and standard frequency f is ω = 2π f, so 120 Hz is an angular frequency of 754 radians per second. The maximum acceleration is amax = Aω2, acceleration due to gravity is g = 9.8 m/s/s, so 25 g's is about 250 m/s². I compute A = a_max/ω^2 = 0.44 mm. So the amplitude of the vibration is only half a milimeter. I'd say that a loud speaker could do that. (-:

You probably have a better feel for the frequencies than I do, but 60 Hz is the frequency of household AC current, so any time you hear a transformer or power line buzzing, it's most likely at 60 Hz — pretty low. In any case, the audio is probably over-dubbed. Regarding the camera, there are some aliasing effects, since a standard video signal is only 30 frames/second. They said they also used a 2000 frames/second camera for some of the video, but who knows how they transferred that to Windows Media. The fading effect is due to the aliasing, and I'm sure we could figure out exactly what's going on in that respect with a little thought and a re-viewing.

[nibot.livejournal.com]

I don't think the acceleration is important.

whoops -- I mean that the exact value is probably not important. But there are critical values of the acceleration.. the whole thing here is that the fluid is nonlinear, so acc is important.

[easwaran.livejournal.com]

You'd most likely have to put the thing directly on the speaker cone to get that magnitude of vibration. I suppose that was always your plan though :-) That makes sense about the audio being overdubbed, explaining why we wouldn't hear anything. But I still have a feeling that would be pretty loud at 120 Hz. (The lowest note I can sing comfortably is somewhere around 95 Hz.)

My wonder about the camera was that if the thing was vibrating, why didn't we see the dish moving? I guess if the vibrations are really small amplitude and the camera wasn't very high resolution, then that vibration wouldn't show up. But I thought the camera might have been vibrating in unison with the dish.

As for the aliasing, let's assume that the dish was vibrating at exactly 120 Hz and the aliasing took 1 second per fade in and out of the waves. This would mean that if the camera recorded at x Hz, then it takes x full cycles of the camera and 120 full cycles of the dish before they are lined up again. So the gcd of x and 120 is 1. This would suggest that the camera is recording actually at 29 or 31 Hz. Or possibly that the camera is exactly 30 Hz and the dish is at 119 or 121, but I suspect they have finer control over their vibrator than their camera. And the aliasing actually seems to be taking a couple seconds, so it's even closer to 30 Hz. Also, the fact that it fades in and out gradually suggests that it's as close to a divisor of 120 as possible, which would suggest 31 or 29 as opposed to 37 or 23.