# Surface waves in a liquid

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So, after careful consideration, my opinion is that the Faraday standing wave pattern (with a smooth waveform at the boundary), is there because of the way sound propagates in different media

There are three phases of matter involved: the solid glass in which stress patterns appear that can be visualized with the right spectroscopy; the liquid water in which sound propagates more slowly, but not much. then the air transmitting sound out of the cavity. The surface of the "newtonian fluid" gets saturated wth sound and the Faraday waves emerge, at resonance and with a stable bulk fluid.

The reason the video I posted isn't a very good pattern, except at the edges, is because there is too much water; it's sloshing around so isn't a smooth sound transducer.

But you can see those radial waves appear as the system approaches resonance; the sloshing could be avoided if there was a sound generator with variable frequency and volume, aimed at the glass.

Edited by SuperSlim

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There are known formulas for waves on a surface, with two dimensions, which indicate to me that the radial pattern is a superposition of modes, a finite expansion.

The minimal surface is definitely acting just like an elastic membrane. It deforms minimally by finding the greatest number of available modes, and filling them. The pattern is an eigenvalue for a sum of (abstract) wave vectors on a 2-dimensional surface with a circular boundary.

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So if my analysis is to proceed, it will be based on the different velocities of sound in solid glass, in water and in air.

A vibrating wineglass or brandy bowl is definitely an acoustic chamber, because it's a bell made of glass. You could make some measurements and determine how good it is at amplifying sound waves. The vibrations in water, sitting inside the bowl of glass, are going to have internal reflections reinforcing the sound and amplifying it. The air inside the glass is a column, with pressure waves in it which are reflected and transmitted at the water surface.

It's going to be a pretty complicated formula. But I could just concentrate on the liquid phase, and treat the rest as an input. The input has contributions from the solid and the gas phase the sound is propagating in. The real input is either some kind of bowing of the glass or an external speaker.

Back to the question of inertia: does knowing the radius of gyration constitute a measurement?

It's pretty simple for a thin disk of rigid material, and if that thin disk of material then curls itself up in a minimal way--to conserve something--it doesn't change the radius of gyration, but what about the amount of mass? The surface area has to increase to accomodate the periodic function.

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I keep remembering, but not saying so much about it, that measurement isn't necessarily an output--it can be an input too.

If you want to, just call what the excitation of the glass is, a measurement. The guy rubbing the edge with his finger is measuring something physical (I don't know that you can measure anything else, but that's another story).

The glass is responding, there are sound waves traveling into his finger, a feedback mechanism. But is the idea of feedback--positive or negative--included in a measurement? To see the pattern--a surface response to sound--seems entirely passive, you don't do anything but look at it.

The measurement you "perform" by looking at a pattern (maybe an interference pattern) includes the memory you then have of it.  You have Shannon entropy.

I think an interesting thing to pursue in this is, what does determine the position and direction of the rays? Some experiments involving translation and rotation, using sensitive measuring equipment might turn up something curious. But just explaining why it happens when you leave the glass where it is, and each time you get it to resonate, the rays appear in the same place. That's curious because it implies the glass is fixing the pattern, and so rotating the glass should change it.  So does it? I can't say, I didn't really try to look at that.

But what does theory say about it? What theory is it?

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The kind of experiment I'd like to do, or see done, involves a pair of glass bowls and an external speaker large enough to make both vibrate at resonance. An overhead camera can record the patterns in some water in both the bowls. It should be different levels to investigate the frequency change, and both patterns will either line up or they won't.

The second result indicates its the inner glass surface and the fact it isn't an exact smooth one. Otherwise there's a bit of explaining to do. The next thing I would try is picking each bowl up and making the water in each one rotate in opposite directions. Then apply the sound input again to see what happens.

If the patterns in both bowls are fixed, what's fixing them? If it doesn't depend on rotation, then what does it depend on? I'd like to know.

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Another thing I thought about, was this is an example of a coherent output, a two dimensional surface bends regularly into a third dimension; well ok it's already curled up at the edges, but there's the measurement idea to consider, and if the coherent waveform is because the water underneath (a mostly cohesive liquid, with a gravitational potential gradient, i.e. inertia), is being pumped with sound waves, it's like laser coherence with light, except with sound you get something else.

What keeps it coherent is not, apparently dependent on whether the bulk is rotating, or even sloshing (pitching and yawing). It only depends on how sound waves "pile up" as they reflect back and forth in the water. It looks like a kind of waveguide, or wave-antenna, IOW.

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I haven't until now really thought about what it would take to investigate this properly. I've been in a lab or two so I imagine it would mean some kind of interferometry as a way to detect wavefronts.

You want to count them, and you want to know if the pattern rotates with the glass, or in any other way.

I've gathered some more visual evidence, and it seems the surface waves I'm focused on are quite different than the kind you get when the glass container is less efficient at resonance than a crystal (lead) glass one. With ordinary glass it's usually thicker and there are more lower frequency harmonics. In some images you see how the water gets driven to an 'inertial' solution, involving more of the bulk and a greater surface area to get to equilibrium.

In these first shots, there are evanescent type waves around the glass, spreading out on the surface.

The water's been dyed with green food dye. The contrast is better (I guess red wine should work, then).

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The above amateur experiment I think is a trick this person has done before.

After this initial demonstration, more water is added; not a lot, but it looks like the experimenter has some idea how to 'tune' the glass. It does look like it might be ordinary glass, but it's hard to tell. There is a well-known difference in the quality of sound between ordinary glass and crystal glass. Crystal or lead glass is tougher, it's been tempered by adding some metallic elements, in a well-understood process.

With the extra water the system now tries to move to a new equilibrium (a superposition of concentric waves and other modes).

I'd guess because of the elliptical vibrations, there's a superposition of 'horizontal + vertical' waveforms. You need a wave equation for an elliptically vibrating wineglass, it seems that it only needs to produce enough power to drive the inertial waves.

Edited by SuperSlim

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