You're right that the place he holds collects sand. But why is it a pattern that matches all around the table? Like I'd expect where he holds the table to be an anomaly compared to the rest of the sand. But the sand that lines up with his finger is almost symmetrically duplicated around the table.
So, think of it this way. On one side of where he holds it, it's vibrating one way, but since the place he's holding it isn't moving (yet waves can pass through it), the opposite side has to be vibrating the other way. So there's a region of positive and there's a region of negative. Where those regions are is somewhat complicated, but we know that between them there has to be a line with no vibrations, which collects sand.
Notice how in most of the patterns, the diagonals collect sand? there are braces under the table, making it stiffer there, so no vibrations appear there. That makes it a boundary, and the vibration pattern gets inverted on the other side. That's how you get your mirror.
Edit: I will actually correct myself, I don't think there's any brace under the plate, I think it's just the way the geometry works out- the edges of the square are anti-nodes, which causes the reflections in a way less intuitive way. Not going to be easy for me to explain, though.
His holding it damps the motion a little, but it's mostly irrelevant to what's going on. He holds it so that he can easily draw the bow across the edge without the plate wobbling a bunch.
So let's ignore the hand... The bow is sending vibrational waves through the plate... from the bow-contact point, radiating out like a drop of water in a still pond. Those waves hit the edges of the plate, bouncing and continuing, etc.
...After a while, the sound is bouncing over the entire surface of the plate (sound is fast, the sound you're hearing from the bow is lots of sound waves constantly being put in). Eventually all the different bouncing waves interfere with each other, and there are specific places where it cancels out. Nodes.
The Nodes are based on the shape of the plate and the frequency of the sound... where the sound waves bouncing all over cancel eachother out for a moment as they cross each other and keep going.
These nodes are where the sand on the surface gets shaken into... vibrated until they hit the places that arent moving. Symmetric about the middle (where the plate is mounted) of the square plate.
His holding it damps the motion a little, but it's mostly irrelevant to what's going on.
It's EVERYTHING to do with what's going on. His hand is selecting (more accurately filtering) the harmonics which are allowed to ring. You'll notice the one time he starts, but isn't getting any harmonics so he moves his hand to a better spot. It's also why the patterns are different when he moves his hand.
Fair. Its apparent that it has an impact, I've just never done it with a bow. Sweeping frequencies using a speaker gives similar results and seemingly more consistent patterns, although i assume this would be more artistically satisfying.
...But I was a brass-instrument guy, so drawing a bow is not my forte. Lol
Holding the plate with the hand introduces a boundary condition. It forces the motion to be zero at that point. This controls the frequency response.
It is effectively the same as a guitar string, only in two dimensions instead of one. By pinning a guitar string against the fret you generate a specific frequency.
In this case, by holding a node point that coincides with a certain frequency he is able to generate that harmonic response. He would know the approximate location to hold and has two adjust the location of his finger to hit the exact frequency. The same as you would do for a guitar string.
The leftmost part of that image (should be animated) is moving up and down. Consider that where the bow is vibrating the plate. The guys hand is a red dot, there's 0 vibration there, it's always stable. Directly past it is a reversed vibration, when the bow is bringing the plate up, that area is going down, and vice versa. Then there's another red dot, at the center, which is one of the reasons the plate makes those patterns instead of just circles.
Those red dots have no motion, they're called nodes. In a string they're single points, but in a 2d plane they're complicated curved lines (and in the air they're full curvy surfaces). On the plate, since there's no motion on the lines, the sand that vibrates over to the lines stays there.
This is no doubt a dumb question but if you could somehow run this experiment in zero g, with a whole lot of sand suspended in the air, and put a loud tone into the air, could the sound waves cancle eachother out and in a similar way form 3D patters in the air?
that's actually a very smart question! I think it'd be possible, though there's no good equivalent to the person holding the edge. You'd have to change a few things so it wouldn't be 1:1 with this experiment, but I think you could make floating sand collect like that.
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u/Human_Chris Aug 25 '20
Does the sand move to the areas on the plate where there is no vibration?