The Visual Patterns of Audio Frequencies Seen through Vibrating Sand | Hacker News Reader

The Visual Patterns of Audio Frequencies Seen through Vibrating Sand

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105 pointsvilda37 comments

It is interesting, but it's a standard way of demonstrating normal modes, or the applications of eigenvectors. I would think most physics and engineering undergraduates have studied this.

That's not to say you shouldn't watch it, but just to put it in perspective - this is a topic studied in the 1st/2nd year of university, not a poorly-understood topic for research.

https://en.wikipedia.org/wiki/Normal_mode

Is this essentially the same as a standing wave, except 2-dimensional?

Yes, the sand settles into the nodal lines of the pattern of vibration on the plate; those are the places where the plate is not moving. The same frequencies on a circular plate will produce different patterns.

I'm a cs person and never encountered this in school. Is this taught in engineering? Typical course names?

As a math person, I look at this and think "Fourier series".

I encountered the ideas in both Classical Mechanics 1 (third year physics course where I took it) and Differential Equations (third year math course where I took it).

It is still a nice visualization.

It's very close to Fourier series, but since the "solutions" (the equilibria) are not integer multiples of a fundamental, but solutions to a 3-dimensional wave equation, it's more like "wave equation."

From a mathematician's point of view it is a Fourier series. You have the property that any starting state can be divided into the sum of orthogonal components. No matter how complex the components are, that's still a Fourier series.

A physicist would disagree, I am sure. But to a mathematician, an orthonormal wavelet basis is also a Fourier series.

"Physics".

System Analysis and/or Control System.

Forgive my ignorance, but I don't have a physics or engineering background. Given it's a well understood phenomenon, is there some way of generating mathematically what the patterns will be for a given plate shape and frequency?

You solve the wave equation, a differential equation for the small-amplitude motion of the surface. The solutions depend strongly on the shape of the boundary, as is usually the case. For some shapes the patterns can be found analytically. For more complicated boundaries it's not too hard to solve this equation numerically - it's linear. Orders of magnitude easier than, say, calculating the flow of water down a pipe.

Yes, the shapes can be predicted by numerical solution of the governing PDE. I don't think that's what you had in mind, however. For an arbitrary plate shape, the solutions do not generally have what you might think of as a nice closed-form expression.

For certain specific cases (like a square plate), these modes do have reasonably tidy descriptions.

"The study of the patterns produced by vibrating bodies has a venerable history. One of the earliest to record that an oscillating body displayed regular patterns was Galileo Galilei. In Dialogue Concerning the Two Chief World Systems (1632), he wrote:

As I was scraping a brass plate with a sharp iron chisel in order to remove some spots from it and was running the chisel rather rapidly over it, I once or twice, during many strokes, heard the plate emit a rather strong and clear whistling sound: on looking at the plate more carefully, I noticed a long row of fine streaks parallel and equidistant from one another. Scraping with the chisel over and over again, I noticed that it was only when the plate emitted this hissing noise that any marks were left upon it; when the scraping was not accompanied by this sibilant note there was not the least trace of such marks. "

http://en.wikipedia.org/wiki/Cymatics

These patterns are also drawn on tiles in the Rosslyn Chapel and are thought to be displaying music:

http://en.wikinews.org/wiki/Rosslyn_Chapel_music_score_'deco...

Why is it sometimes asymmetrical vertically? Is it just a slight variation where the plate isn't perfectly square or the bolt not in the exact center?

It appears to be simply a lack of sufficient sand to show all of the lines- some of them become symmetrical when more sand is sprinkled on.

Here's a Science Friday video of the same thing but without the music on top, so you can actually hear the frequencies.

http://www.npr.org/player/v2/mediaPlayer.html?action=1&t=1&i...

Here's a not very good example using hair and a car stereo (http://youtu.be/4s_lpBkdoNc)

I wonder if that could be done at scale with a massive art installation and marbles.

Now that would be mind blowing to watch.

I'd love to see an enormous version of this harmonic motion demonstration.

(http://sciencedemonstrations.fas.harvard.edu/icb/icb.do?keyw...)

Interesting, but for a similar experiment that's rather higher on the "cool" spectrum, check some of the videos with "oobleck" (non-newtonian fluid, like cornstarch and water) on an amp.

Here's the first one I saw, a couple of years ago:

http://www.youtube.com/watch?v=Yp1wUodQgqQ

Linking it here because I just went searching for new examples, and none of what I found was quite as good at fooling my brain that living creatures were crawling out of the muck...

I wonder what would happen if you designed a helmet that vibrated your brain like that?

Maybe some frequency could tweak pleasure centers, etc?

Wondering if this actually happens when we are listening to music? ;)

I don't think small deformations of the brain do much, because they don't change the connectivity or electrical activity of the neurons. However, there are devices that induce currents inside the brain by applying magnetic fields, and this has profound effects.

Has this been attempted in a zero-gravity environment (or even water)? Would that completely obliterate the results of the test, as the sand wouldn't be on a solid surface? I'm curious what the results would be.

There's a really fun exhibit at the Exploratorium in SF that demonstrates this. Not quite so fancy, but if you can shove some kids out of the way it's still pretty cool to play with!

They have this at the Exploratorium! Definitely cool to play with.

Bold title for WWDC day.

Because some shiny new gadget will impress you more than a beautiful visualization of the mathematical structure of nature?

That was tongue-in-cheek (mostly...you never know with WWDC).

This video reminds me a bit of A New Kind of Science (http://en.wikipedia.org/wiki/A_New_Kind_of_Science): some of the phenomena Wolfram discusses gave me the same "holy! how does this happen in nature" kind of reaction.

Sorry for coming on so strong. And for being that guy who misses the tone.

No worries, we're all that guy sometimes.

+1 for emoji support in HN comments. (Also ironic...mostly.)

The mods have changed the title, so your comment makes less sense now. For those who are confused, the original title was something like "This is the best video you'll ever see!" or similar.

Couldn't you use something like this on a small scale to implement a better random number generator for computers?

Looks like all it would take is a tiny speaker, a thin metal plate, and something that reads that metal plate like a QR code. The tone could then be randomized by a psuedo-random number generator, and even though the shapes generated are similar, they are never quite identical.

if you want to see many other examples, search for "chladni plate"

Actually, this is salt.

No.

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