# Surface waves in a liquid

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11 minutes ago, Ken Fabian said:

Gravity holds it in the container but wouldn't make motions within the water stop. I would expect friction within the water will be what dampens any motions. Plus some dampening from internal friction within the container itself, which would have to flex to pass vibrations to the water and would be flexed in turn by water motions.

The disturbing force has nothing to do with gravity.

On 2/13/2022 at 10:07 AM, SuperSlim said:

The liquid was water and the surface waves appeared after I put some in a large brandy bowl.

Using the usual technique, rubbing around the edge of the glass,

Edited by studiot

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36 minutes ago, studiot said:

The disturbing force has nothing to do with gravity.

Neither the disturbing force nor the dampening requires or is a result of gravity, but I would expect the experiment to play out very differently without it.

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I think, when asking about the elastic properties and what the restoring forces are, one should consider what happens in gravity-free situations.

Does a bell vibrate if struck in space? Does water, when it forms blobs, wobble around because of gravity, when in space, and why do blobs of liquid stay blobs? GIven the ISS is in a gravity-free scenario and has an atmosphere, I think a gas in a container in space is covered.

From a physics textbook: "It is very important to understand what is propagated as a wave in a wave motion. . . . it is not matter that propagates, but the state of motion of matter.

I.e. wave motion is not a bulk flow of matter. Actually, Baez states it's the flow of momentum, parts of the medium transmit momentum to other parts, so that the matter moves the least distance to transmit the wave. Waves obey a principle of least action.

And here's something to think about: the waves I produced on the surface of a large brandy bowl had a small wavelength, the pattern was like rays of standing waves; near the center of this "wave motion" the wavelength was so small it effectively vanished. The wavelength near the middle could not have been gravitational, the wavelengths were too small.

So a blob of water in free fall; can you make capillary waves on the surface of the blob? How is gravity involved?

Edited by SuperSlim
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13 hours ago, SuperSlim said:

I.e. wave motion is not a bulk flow of matter. Actually, Baez states it's the flow of momentum, parts of the medium transmit momentum to other parts, so that the matter moves the least distance to transmit the wave. Waves obey a principle of least action.

I agree there is sometimes no bulk flow of matter.

But how much momentum flows in the case of a standing wave ?

17 hours ago, Ken Fabian said:

Neither the disturbing force nor the dampening requires or is a result of gravity, but I would expect the experiment to play out very differently without it.

On 2/17/2022 at 12:57 AM, Ken Fabian said:

but because it is a fluid in a container, affected by gravity.

18 hours ago, Ken Fabian said:

Gravity holds it in the container but wouldn't make motions within the water stop. I would expect friction within the water will be what dampens any motions. Plus some dampening from internal friction within the container itself, which would have to flex to pass vibrations to the water and would be flexed in turn by water motions.

This is not as I understand the mechanism

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1 hour ago, studiot said:

I agree there is sometimes no bulk flow of matter.

But how much momentum flows in the case of a standing wave ?

This is not as I understand the mechanism

Surely the processes that damp out waves involve energy conversion to heat, through fluid friction, and friction of the fluid against the walls of the containing vessel. If there were no such friction, and gravity were the only influence acting, the waves would continue to reverberate without diminution, wouldn't they? Just as a pendulum would continue to swing indefinitely if it were not for friction.

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2 hours ago, exchemist said:

Surely the processes that damp out waves involve energy conversion to heat, through fluid friction, and friction of the fluid against the walls of the containing vessel. If there were no such friction, and gravity were the only influence acting, the waves would continue to reverberate without diminution, wouldn't they? Just as a pendulum would continue to swing indefinitely if it were not for friction.

Yes this is a damped oscillation, as you say, but there is more going on that.

I'm not sure what part of my post you were responding to though.

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The combination of container and gravity makes the shape of that water in it's hypothetical undisturbed resting state. Other forces make waves and motions, like vibrating the container to create standing waves. Friction damps those motions. It isn't elasticity - that is a misleading misnaming of why, when external forces cease it reverts back over time to it's resting state.

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8 minutes ago, Ken Fabian said:

Friction damps those motions.

Yes, that must be true for a blob of water in zero gravity.

8 minutes ago, Ken Fabian said:

It isn't elasticity - that is a misleading misnaming of why, when external forces cease it reverts back over time to it's resting state.

When you place sand on a glass plate, the sand doesn't bounce around "elastically", although the glass plate does vibrate when you bow it with a violin bow.

No wait, that's misleading. Of course particles of sand bounce around because they are elastic, solid particles. Frictionally damped liquids don't vibrate elastically, because friction damps the vibrations. No, wait . . .

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@SuperSlim -As long as you use the term "elastic" so broadly and wrongly you will mistake phenomena that have nothing to do with elasticity for phenomena that do.

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56 minutes ago, Ken Fabian said:

As long as you use the term "elastic" so broadly and wrongly you will mistake phenomena that have nothing to do with elasticity for phenomena that do.

Are you saying the surface waves that appear in a brandy bowl, are not an example of elastic waves?

Can you demonstrate why that's the case (if it's true)?

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5 hours ago, SuperSlim said:

Are you saying the surface waves that appear in a brandy bowl, are not an example of elastic waves?

Can you demonstrate why that's the case (if it's true)?

I've looked into this a bit more and it seems I was at least partly wrong to say gravity is responsible for the restoring force in the very fine ripples one sees on the surface of a liquid in a glass.

These ripples are, it seems, something called capillary waveshttps://asa.scitation.org/doi/10.1121/1.2019710

In capillary waves the dominant restoring force at very short wavelength is surface tension rather than gravity, though gravity plays an increasing role as the wavelength goes up: https://en.wikipedia.org/wiki/Capillary_wave

However I don't think surface tension will result in true elastic behaviour either, as the restoring force on a wave crest or trough will not increase linearly with deformation (i.e. stress is not proportional to strain).

Edited by exchemist
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Does anyone remember the long thread about the mechanism of the  'tin can telephone' (made of two tin cans and a taught lenght of string) we had not too long ago ?

Remember also that the mechanism is quite complicated.

Here also we have a complicated mechanism.

Firstly note the the OP did not say he was vibrating the glass or the glass wall.
He said

On 2/13/2022 at 10:07 AM, SuperSlim said:

Using the usual technique, rubbing around the edge of the glass, a radial pattern of standing waves was made. I could see little or no turbulence even at the perimeter of the liquid.

Now that finger introduces a point compressive load on the glass wall, which moves around the glass.
The the glass wall acts as a very slender strut under the moving compressive load.
On account of the curvature the wall bends slight inward where the finger acts and relaxes elastically again as it moves on.
The inward movement slightly decreases the total volume of the container so the water is squeezed slightly upwards locally.
Once the finger has moved on and the glass wall has relaxed back to its normal position, the water surface is (again locally) too high up the side of the glass to be in equilibrium under gravity.
So gravity pulls it back down again.
The falling water moves horizontally away from this point.

This produces a rising and falling of the water surface locally, which in turn results in periodic water movements horizontally against surface tension, (which acts horizontally).

So these pulse moves across the surface  reflecting off the opposite walls creating and maintaining the standing waves observed if the frequency of rotation around the glass is in phase with the resonant frequency of the water.

I remember our old A level Physics teacher demonstrating resonance using a 2kg hanging weight struck periodically with a knotted handkerchief.

So as you see the phenomenon is quite complicated, separate consideration being needed for all the different forces involved, both horizontal and vertical.

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Yeah, It is complicated. It is because the glass bowl is vibrating at a resonant frequency. The pattern seen on the surface of the water is a standing wave--it doesn't rise and fall as the finger moves around the glass. The entire surface is involved, as long as the glass is vibrating.

It's a physics problem where you want to know the impedance of the oscillating systems. There's a transfer function for a system in resonance.

Of course gravity is involved; when you stop moving your finger, the water relaxes because of gravity (mostly).

Edited by SuperSlim
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19 hours ago, SuperSlim said:

Are you saying the surface waves that appear in a brandy bowl, are not an example of elastic waves?

I think we are arguing over terminology. The first post claimed it is an example of an Elastic Fluid, but I'm not convinced that it is what the phenomena described is. That may have led me astray.

"Elastic fluid" seems to refer to compressability -

Quote
 those which have the property of expanding in all directions on the removal of external pressure, as the air, steam, and other gases and vapors. - Rankine.

Elastic waves -

Quote

When elastic waves propagate, the energy associated with elastic deformation gets transferred in the absence of a flow of matter,

Surface waves that appear in a brandy bowl may indeed be examples of "elastic waves" in a fluid; something I wasn't aware of - I stand corrected.

I had been thinking there was flow of matter involved - but I may have been misunderstanding "flows", ie where a container wall moves back and forth and displaces water without compressing it. It will involve wave propagation by compression and release (elastic fluid) but most of what we see in that bowl will be water physically moving rather than being compressed and uncompressed.

Introducing the topic with reference to elastic waves rather than elastic fluids may have avoided confusion.

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I would say the phenomenon is in the same class as a vibrating string, fixed at both ends.

Except it's the vibrating surface of a glass bowl, transferring this vibrational mode to the surface of the water.

How deep a layer is needed to see a regular pattern? I didn't look in to that, and I didn't look at different liquids, like say kerosene or light machine oil. I didn't try a thin layer of oil on top of the water, to investigate damping, say

Nonetheless I know it's an example of a boundary value problem. with a unique solution. For water, that is. But I can't really see why other liquids wouldn't have unique solutions. How viscous does the liquid need to be to damp the response? Do more viscous liquids have the same number of rays as water (in the bowl I estimated about 50, the bowl was about 12 cm diameter at the liquid surface).

The problem sort of demands that you see the surface of liquid water as having a boundary, it's "trapped in a cavity" and responds to forced oscillations.

The pattern is fixed (I didn't see it rotate or oscillate at all). This is a repeatable experiment (!).

Each ray will have an amplitude which increases from the centre towards the glass boundary, where it's a maximum. You know what the normal direction to the surface is, and you know the gradient of the amplitude of each ray; that's a boundary condition. No part of any ray (apart from the centre itself where all rays vanish), is tangent to a characteristic.

Edited by SuperSlim
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I guess you need to look at the fact a brandy bowl with some water in it is an acoustical chamber--you can change the pitch by changing the volume of water.

Sound waves that exit the chamber dissipate; the water surface is reacting to the air vibrating inside the chamber + the vibration in the glass, these are in phase.

So that determines what the forcing is--the acoustic chamber is an amplifier. It's like an upside down glass bell with water in it. And, the standing pattern doesn't change with time, but does it change with frequency? I tried this a few times on different days and I didn't see any real difference, I just used about the same amount, enough to get a sound and some waves.

Edited by SuperSlim
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The problem is one of those B.v.p's that is independent of time; there is a fixed waveform, at the boundary there is an integral number of sine or cosine periods.

Another thing I recall is, the location of the rays was the same if I repeated the rubbing, after stopping. I don't know, is that inertia or something?

I'm guessing it's also independent of frequency, it's a passive response which seems capacitive and depends only on the amplification of sound in a chamber, it's got that nice linear behaviour in the summation of a set of standing rays.

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8 hours ago, SuperSlim said:

I would say the phenomenon is in the same class as a vibrating string, fixed at both ends.

Except it's the vibrating surface of a glass bowl, transferring this vibrational mode to the surface of the water.

How deep a layer is needed to see a regular pattern? I didn't look in to that, and I didn't look at different liquids, like say kerosene or light machine oil. I didn't try a thin layer of oil on top of the water, to investigate damping, say

Nonetheless I know it's an example of a boundary value problem. with a unique solution. For water, that is. But I can't really see why other liquids wouldn't have unique solutions. How viscous does the liquid need to be to damp the response? Do more viscous liquids have the same number of rays as water (in the bowl I estimated about 50, the bowl was about 12 cm diameter at the liquid surface).

The problem sort of demands that you see the surface of liquid water as having a boundary, it's "trapped in a cavity" and responds to forced oscillations.

The pattern is fixed (I didn't see it rotate or oscillate at all). This is a repeatable experiment (!).

Each ray will have an amplitude which increases from the centre towards the glass boundary, where it's a maximum. You know what the normal direction to the surface is, and you know the gradient of the amplitude of each ray; that's a boundary condition. No part of any ray (apart from the centre itself where all rays vanish), is tangent to a characteristic.

Whilst there are a lot of good points in this and your other recent  posts around it,

This first sentence is exactly what is isn't.

8 hours ago, SuperSlim said:

I would say the phenomenon is in the same class as a vibrating string, fixed at both ends.

That string is by definition fixed at the ends and so can only excited in between the ends.

The glass walls are not fixed but provided the excitment at the extremes.

It is also worth realising that there are two orthogonal forces acting - gravity and surface tension - so they can't directly influence each other

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16 minutes ago, studiot said:

That string is by definition fixed at the ends and so can only excited in between the ends.

The surface of the fluid is fixed at a boundary too. It is a boundary value problem. Certain boundary conditions for waves have to be met.

16 minutes ago, studiot said:

The glass walls are not fixed but provided the excitment at the extremes.

The glass bowl is a fixed, rigid container. It and the air in it are the reason it makes a sound you can tune with some water.

16 minutes ago, studiot said:

It is also worth realising that there are two orthogonal forces acting - gravity and surface tension - so they can't directly influence each other

And the idea, in analysis is to choose two parameters which may be interdependent. But this problem is about a waveform at a boundary and why it's there.

What are the dependencies, apart from the surface tension and the inertia? You have to energise the surface with sound, it has to be loud enough and the surface big enough that a radial pattern appears. My guess is getting a pattern like the one I saw was a coincidence of a large enough surface area that the surface tension could contribute to the physics, and the right kind of resonant chamber. I would guess that smaller glass bowls--wineglasses--would be harder to make waves in.

Edited by SuperSlim
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28 minutes ago, SuperSlim said:

The surface of the fluid is fixed at a boundary too. It is a boundary value problem. Certain boundary conditions for waves have to be met.

The glass bowl is a fixed, rigid container. It and the air in it are the reason it makes a sound you can tune with some water.

And the idea, in analysis is to choose two parameters which may be interdependent. But this problem is about a waveform at a boundary and why it's there.

What are the dependencies, apart from the surface tension and the inertia? You have to energise the surface with sound, it has to be loud enough and the surface big enough that a radial pattern appears. My guess is getting a pattern like the one I saw was a coincidence of a large enough surface area that the surface tension could contribute to the physics, and the right kind of resonant chamber. I would guess that smaller glass bowls--wineglasses--would be harder to make waves in.

The glass bowl is not truly rigid.

In fact there are no waves in a truly rigid object.

The glass bowl is a 3 dimensional version of the two dimensional tuning fork.

Yes, I agree that it is even more complicated than I made out since there are actually 2 fluid phases in the glass.
That is a very good point.
Yes you can excite the air a glass or bottle by the same mechanism that produces the ocean waves  -  variation in the passage of air across the inteface with the liquid leading to pressure variations that can allow the original lifting of bpdy of water above the equilibrium line.

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Thanks to certain mathematicians, like Laplace, Fourier, Euler and Lagrange, it is known that solutions exist for generalised wave equations.

The surface of the water is initially just a region with a boundary, it's mathematically the real plane with a boundary, C; on the boundary you know the direction normal to this plane. You have certain boundary conditions apart from knowing the normal direction, you also know what the waveform looks like at the boundary, and you know the amplitude and how it changes from the boundary towards the centre. Because of the symmetry you only need to consider a single ray, you know the wavelength and that the number of wavelengths is a whole number. It's a problem that solves itself, except for the analysis.

But you still need to determine what the initial conditions are, and how the system moves from one equilibrium state to another. It seems the excited state has only one solution, not dependent on the input frequency, but some fixed properties of the liquid.

Edited by SuperSlim
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I found a video that demonstrates what I've been talking about. The result in the video isn't as stable as the one I got, which I put down to using less water and a crystal glass bowl with a better shape, to trap and direct the sound pressure-waves onto the water surface.

If you stop the video when the pattern appears, you can see the boundary and a circle of individual rays. I think I've understimated the number which looks like it's over 100. Also notice how the radial pattern keeps appearing in the same position--but what fixes that? I'd say the video maker is using too much water and so there's turbulence, which tends to spread the fixed pattern out and distort it. I can vouch that this experiment, done properly, yields a nice, fixed, stable pattern. I wish I'd been able to take photos, but 'sigh', I didn't. With the example in the video the most stable pattern appears around 20s in.

Otherwise it's a turbulent system with too much instability.

Ok, so I pencil in things like a unit volume V of water. It has mass and a density [rho] in kg.m-3 (I don't know how to insert Tex here).

Then a differential volume dV, which inherits the physical units. So the mass is inertial and gravity is a downward force F = mg; the water is in a relaxed state inside a container which is a potential surface; the potential up the sides is gravitational potential and is parallel to the normal at the liquid surface.

Usually in a 'stationary, relaxed' state we have forces in equilibrium so mg = kx, for x parallel to the normal direction. x has units of distance so dx exists, and k must have units kg.s-2

Edited by SuperSlim
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1 hour ago, SuperSlim said:

I found a video that demonstrates what I've been talking about.

Alternatively here is a pdf of an MIT thesis on the mathematics of the phenomenon, plus a full modern laboratory investigation

Note the glass deflects, just as I said.

Quote

Singing wine glass rim undergoes elliptical deformations (top view of wine glass). There
are four antinodal points indicated;  their displacement Δ and frequency f of deformation can be derived.

I don't seem to have a reply to my comment on Hess's law yet.

Edited by studiot
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41 minutes ago, studiot said:

Singing wine glass rim undergoes elliptical deformations (top view of wine glass).

Yes, but I want to look into what the inertial fluid is doing inside the wine glass. The sound is driving some kind of inertial reaction, there's a surface layer of fluid interacting with sound waves, and it has a boundary where the fluid interacts with the vibrating glass. The fluid is responding to sound in a way that says something about inertia.

I think I know what it is, but not exactly why it is what it is, if you see what I mean. Inertia is something you can relate to mass through the radius of gyration, it doesn't have to have angular momentum, but it has to be able to conserve it. If it did have some.

What I'm leaning toward is getting my mate, if I can find him, to explain if Mach's principle applies, in an Einsteinian sense. This has to be a purely local effect.

Edited by SuperSlim
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I think this example of Faraday waves on the surface of water might be entirely electrostatic. The fluid and its inertia contribute minimally, only the smallest part of the surface layer is responding. The restriction is the strength of hydrogen bonding at the surface. Another restriction for the overall system Hamiltonian--if we assume the pattern constitutes a measurement of something physical, i.e. information.

Another way I look at it is an example of a periodic function, which is a smooth deformation of a manifold such that the surface area increases minimally, as a catenary "solution" to the input of sound. I think the water conducts sound waves so they reflect internally and build up to a feedback mechanism that contributes to overall resonance--and power output in the sound spectrum.

It's an example of Baez' morphisms, that take surfaces to surfaces. We can easily construct such a 2-dimensional morphism from the boundary to the boundary, at--the boundary. A time independent function of two parameters, but which two? The morphism introduces a kind of system of coordinates on the surface.

Edited by SuperSlim

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