Surface waves in a liquid

[SuperSlim]

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, a radial pattern of standing waves was made. I could see little or no turbulence even at the perimeter of the liquid.

Everything looked nice and smooth, a really nice spatial derivative. A good way to prove water is an elastic fluid.

Edited February 13, 2022 by SuperSlim

[exchemist]

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, a radial pattern of standing waves was made. I could see little or no turbulence even at the perimeter of the liquid.

Everything looked nice and smooth, a really nice spatial derivative. A good way to prove water is an elastic fluid.

The normal meaning of elastic is to a material that returns to its shape when a distorting force is removed. So that would not apply to a liquid, surely?

What spatial derivative do you mean?  

[SuperSlim]

On 2/15/2022 at 2:55 AM, exchemist said:

The normal meaning of elastic is to a material that returns to its shape when a distorting force is removed.

And that's what I observed. The water in the bowl returned to its 'non-excited' state when I stopped rubbing the edge.

 

[Ken Fabian]

2 hours ago, SuperSlim said:

And that's what I observed. The water in the bowl returned to its 'non-excited' state when I stopped rubbing the edge.

Despite some outward similarities that is not elasticity. It isn't settling into that bowl because water is elastic, but because it is a fluid in a container, affected by gravity. The absence of other factors, like vibrations of the container allows the water to become still again.

Other factors will matter - any variations in temperature within the water will result in water movement by convection and if in open air, the surface likely will be cooled by evaporation, so there will be continuing movement. Water has surface tension as well, affecting it's shape in a container, but if the water were elastic the bowl wouldn't matter - the water would retain the bowl shape without the bowl. It doesn't.

[SuperSlim]

1 hour ago, Ken Fabian said:

Despite some outward similarities that is not elasticity. It isn't settling into that bowl because water is elastic, but because it is a fluid in a container, affected by gravity. The absence of other factors, like vibrations of the container allows the water to become still again.

I think you might be confusing long-range elasticity in solids, with the kind in fluids.

When you drop something into water, there is a response, not a long range one except that after the local one (a splash, maybe some plumes), waves spread out on the surface. But these waves must involve the same short-range elasticity the water just demonstrated with the response to an impulse. The object you dropped did not just slip into an inelastic medium, it would have just disappeared soundlessly under the water; there would be no "long-range" waves on the surface.

Edited February 17, 2022 by SuperSlim

[exchemist]

10 hours ago, SuperSlim said:

And that's what I observed. The water in the bowl returned to its 'non-excited' state when I stopped rubbing the edge.

 

A liquid, however, has no shape. It takes on the shape of its container.

 

@Ken Fabian's comments seem to be spot-on. An elastic substance resists deformation, by means of a restoring force generated by the material itself. It is rather perverse to maintain a liquid is elastic, when the only force restoring the surface to flatness is external to the material, viz. gravity.  

Edited February 17, 2022 by exchemist

[studiot]

The concept of elasticity has meaning in fluids.

 

Quote

Constant viscosity elastic liquids, also known as Boger fluids are elastic fluids with constant viscosity. This creates an effect in the fluid where it flows like a liquid, yet behaves like an elastic solid when stretched out.

 

Constant viscosity elastic fluid - Wikipedia

en.wikipedia.org › wiki › Constant_viscosity_elastic_fluid

Quote

 

Bulk Modulus and Fluid Elasticity - The Engineering ToolBox

www.engineeringtoolbox.com › bulk-modulus-elasticity-d_585

The Bulk Modulus Elasticity - or Volume Modulus - is a material property characterizing the compressibility of a fluid - how easy a unit volume of a fluid ...

 

[swansont]

I learned recently that these - nonlinear standing waves that appear on liquids enclosed by a vibrating receptacle - are known as Faraday waves

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

[exchemist]

1 hour ago, studiot said:

The concept of elasticity has meaning in fluids.

 

 

Sure, but that is not responsible for the restoring force in surface waves on a liquid, which is the the scenario under discussion. That restoring force is gravity, which is not intrinsic to the material. 

Edited February 17, 2022 by exchemist

[studiot]

17 minutes ago, exchemist said:

Sure, but that is not responsible for the restoring force in surface waves on a liquid, which is the the scenario under discussion. That restoring force is gravity, which is not intrinsic to the material. 

I very carefully didn't say gravity was acting in this case, because some of what was offered was correct.

In fact gravity is (also) responsible for the ordinary surface waves in water that we see in the ocean.

However two members seemed to be suggesting rather strongly, that fluids cannot be elastic or support elastic waves.

How would you describe a sound wave in a fluid, if not as an elastic wave ?

[swansont]

3 hours ago, exchemist said:

A liquid, however, has no shape. It takes on the shape of its container.

 

@Ken Fabian's comments seem to be spot-on. An elastic substance resists deformation, by means of a restoring force generated by the material itself. It is rather perverse to maintain a liquid is elastic, when the only force restoring the surface to flatness is external to the material, viz. gravity.  

Does water have a preferred shape when gravity can be ignored (e.g. in freefall)? Yes, it does. It forms a sphere.

[exchemist]

7 minutes ago, swansont said:

Does water have a preferred shape when gravity can be ignored (e.g. in freefall)? Yes, it does. It forms a sphere.

Yes under those conditions surface tension provided a (very small) force that seeks to minimise the surface. 

1 hour ago, studiot said:

I very carefully didn't say gravity was acting in this case, because some of what was offered was correct.

In fact gravity is (also) responsible for the ordinary surface waves in water that we see in the ocean.

However two members seemed to be suggesting rather strongly, that fluids cannot be elastic or support elastic waves.

How would you describe a sound wave in a fluid, if not as an elastic wave ?

OK, I should have said "behaves elastically" rather than "is elastic". Is that better? 

[SuperSlim]

Another thing about fluiids like water; when you drop an object into it, it doesn't respond "gravitationally". 

The response is very much a property of liquids, the reaction with high speed photography seems more elastic than gravitational.

It suggests that liquids respond to a sudden increase in pressure much the way gases do, except for the compressibility.

That gases are elastic is supported by the existence of wind instruments, and my old physics textbook.

It seems that elastic properties are not confined to the solid state.

 

p.s. thanks to swansont I now know about Faraday waves; I thought my little experiment might be an example of Chladni waves.

Edited February 17, 2022 by SuperSlim

[Ken Fabian]

@SuperSlim- The actual water molecules are constantly moving and do not returned to where they were. Irrespective of examples of "elasticity" in fluids (interesting, thanks studiot) water returning to the shape of a container after being disturbed - what is described in the original example - is not demonstrating elasticity.

[SuperSlim]

On 2/18/2022 at 10:18 AM, Ken Fabian said:

@SuperSlim- The actual water molecules are constantly moving and do not returned to where they were. Irrespective of examples of "elasticity" in fluids (interesting, thanks studiot) water returning to the shape of a container after being disturbed - what is described in the original example - is not demonstrating elasticity.

So when an organist stops pressing a key and the air relaxes in some pipes, that isn't an example of elasticity either?

What about when a pipe organ key is pressed, or when I was making a liquid 'vibrate' with standing waves? Is either of those an example? If it isn't, please give a definitive example and explain why my examples aren't examples of elastic waves in a medium?

Please bear in mind a bloke named Chladni investigated glass plates covered with sand, and used a violin bow. Patterns--standing waves--appeared; when he stopped bowing the side of the glass, the sand stopped responding. A layer of sand doing nothing on a sheet of glass is what kind of example?

Wait, I know what kind of example: it's an example of small bits of solid matter acting like the disconnected particles of lquid or gas do when they are subjected to elastic waves.

Let me put it this way.

Although elastic waves are common, in sound, in liquids, and of course solids, people who have a physics background assume that elasticity is restricted to solids, and is a long-range phenomenon; it happens because solids have connected particles, they stay where they are.

But it isn't just solids with their long-range version, liquids and gases have it as well. In fluids, elasticity and surface tension aren't restricted to surfaces, the whole medium has surfaces in it, right? When an organ pipe vibrates, elastic standing waves are set up, there are density variations along the pipe so the air gets squeezed and stretched; the forcing means the air has to rearrange itself, 'elastically'. Ok?

Edited February 19, 2022 by SuperSlim

[joigus]

Quote

§1. The strain tensor
The mechanics of solid bodies, regarded as continuous media, forms the content of the theory of elasticity,* 

*The basic equations of elasticity theory were established in the 1820's by Cauchy and by Poisson 

Landau-Lifshitz. Theory of Elasticity. Chapter 1, page 1.

(My emphasis.)

When solids are subject to strains and stresses, and shear tensions, they tend to recover their original configuration in a directional way. This justifies the introduction of directional vector fields that implement this behaviour.

When fluids are subject to forces, they tend to recover their original configuration in a non-directional way. This, IMO, is what's led to the separation into two different disciplines.

Fluids are also characterised by velocity fields (particles making up a fluid move about quite freely; while in a solid, that's not the case: there's no convection, etc.).

Of course, nothing ever's quite that simple, is it? So @studiot's caveat is probably very relevant.

There are strange things that fall outside these classical (19th-century) categories, like liquid crystals, which are both fluid and non-isotropic, but that's another matter.

Edited February 19, 2022 by joigus
minor addition

[exchemist]

3 hours ago, SuperSlim said:

So when an organist stops pressing a key and the air relaxes in some pipes, that isn't an example of elasticity either?

What about when a pipe organ key is pressed, or when I was making a liquid 'vibrate' with standing waves? Is either of those an example? If it isn't, please give a definitive example and explain why my examples aren't examples of elastic waves in a medium?

Please bear in mind a bloke named Chladni investigated glass plates covered with sand, and used a violin bow. Patterns--standing waves--appeared; when he stopped bowing the side of the glass, the sand stopped responding. A layer of sand doing nothing on a sheet of glass is what kind of example?

Wait, I know what kind of example: it's an example of small bits of solid matter acting like the disconnected particles of lquid or gas do when they are subjected to elastic waves.

Let me put it this way.

Although elastic waves are common, in sound, in liquids, and of course solids, people who have a physics background assume that elasticity is restricted to solids, and is a long-range phenomenon; it happens because solids have connected particles, they stay where they are.

But it isn't just solids with their long-range version, liquids and gases have it as well. In fluids, elasticity and surface tension aren't restricted to surfaces, the whole medium has surfaces in it, right? When an organ pipe vibrates, elastic standing waves are set up, there are density variations along the pipe so the air gets squeezed and stretched; the forcing means the air has to rearrange itself, 'elastically'. Ok?

Why are you muddling up sound (i.e. pressure) waves in an easily compressible medium, like air, with surface waves on the surface of a liquid? The restoring forces in these two cases are due to quite different things. 

[SuperSlim]

6 hours ago, exchemist said:

Why are you muddling up sound (i.e. pressure) waves in an easily compressible medium, like air, with surface waves on the surface of a liquid? The restoring forces in these two cases are due to quite different things. 

And these quite different things are . . . ?

Why don't you just point out what the problem is, with whatever it is you think you've spotted? Why not just quote something from a recognized source?

Elastic waves in a compressible fluid should not be muddled with the elastic waves in an incompressible fluid, because . . .

Restoring forces in compressible fluids are different to those in incompressible fluids, because . . .

p.s. does it have anything to do with momentum?

[studiot]

2 hours ago, SuperSlim said:

p.s. does it have anything to do with momentum?

Good question as you are considering the fundamentals of the question "what is a wave" ?

I has been posited here that in order to have a wave a 'restoring force' is required.

Surely this force is only required if mass is involved.

If you are going to stick to the original example, mass is involved so it is worth investigating disturbing and restoring forces.

So thank you for starting off a worthwhile discussion, but please try to offer more focus at the outset.

[exchemist]

3 hours ago, SuperSlim said:

And these quite different things are . . . ?

Why don't you just point out what the problem is, with whatever it is you think you've spotted? Why not just quote something from a recognized source?

Elastic waves in a compressible fluid should not be muddled with the elastic waves in an incompressible fluid, because . . .

Restoring forces in compressible fluids are different to those in incompressible fluids, because . . .

p.s. does it have anything to do with momentum?

It has already been pointed out on this thread, though possibly not explicitly enough. A wave involves displacement of part of a medium from its equilibrium state, creating a restoring influence (a force, in the case of material media) that tends to return the displaced portion to equilibrium. In the case of a surface wave on a liquid (at least on the earth, as in the wine glass), that force is due to gravity. They are transverse gravity waves: https://en.wikipedia.org/wiki/Gravity_wave. The restoring force is thus not due to any elastic property of the liquid.  

Sound waves in an organ pipe are due to compression and rarefaction of air, which creates restoring forces due to the pressure differences created. These are longitudinal compression waves: https://en.wikipedia.org/wiki/Longitudinal_wave  in which it is the elastic behaviour of the medium that causes the restoring force.

  

Edited February 19, 2022 by exchemist

[studiot]

It is worth, as I suggested, considering the mechanism of disturbing and the restoring forces of the original example.

10 minutes ago, exchemist said:

Sound waves in an organ pipe are due to compression and rarefaction of air, which creates restoring forces due to the pressure differences created. These are longitudinal compression waves: https://en.wikipedia.org/wiki/Longitudinal_wave  in which it is the elastic behaviour of the medium that causes the restoring force.

I agree

 

11 minutes ago, exchemist said:

It has already been pointed out on this thread, though possibly not explicitly enough. A wave involves displacement of part of a medium from its equilibrium state, creating a restoring influence (a force, in the case of material media) that tends to return the displaced portion to equilibrium. In the case of a surface wave on a liquid (at least on the earth, as in the wine glass), that force is due to gravity. They are transverse gravity waves: https://en.wikipedia.org/wiki/Gravity_wave. The restoring force is thus not due to any elastic property of the liquid.  

 

How do you think this applies to the disturbing and restoring forces in the glass of water ?

Another similar wave, but with differences, is the wave that is called 'the equilibrium tide' for the Earth-Moon system.

 

[Ken Fabian]

I suspect the issue is the use of the word "elastic" is a bit elastic. Like The Greenhouse Effect doesn't actually work like a greenhouse, compression and release of fluids - Bulk Modulus Elasticity - isn't the same as "elastic" as used with respect to solids. Enough similarity that borrowing "elastic" seemed appropriate to whoever named it despite being very different phenomena.

[exchemist]

2 hours ago, studiot said:

It is worth, as I suggested, considering the mechanism of disturbing and the restoring forces of the original example.

I agree

 

 

How do you think this applies to the disturbing and restoring forces in the glass of water ?

Another similar wave, but with differences, is the wave that is called 'the equilibrium tide' for the Earth-Moon system.

 

The same as it applies to any other transverse gravity wave on a water surface. The side of the glass moves inward and outward, alternately displacing the edge of the water surface up and down, and then gravity makes the raised surface fall back, or the depressed surface rise back (due to the water displaced upward elsewhere), creating a wave. This behaviour is described in the link I provided.

No elastic property of the medium itself is involved, any more than it is in waves on the sea.     

[studiot]

50 minutes ago, exchemist said:

The same as it applies to any other transverse gravity wave on a water surface. The side of the glass moves inward and outward, alternately displacing the edge of the water surface up and down, and then gravity makes the raised surface fall back, or the depressed surface rise back (due to the water displaced upward elsewhere), creating a wave. This behaviour is described in the link I provided.

No elastic property of the medium itself is involved, any more than it is in waves on the sea.     

Thank you. +1

Yes was beginning to wonder if anyone else knew how the original effect was generated.

But, @Ken Fabian the distrubing force is not of the same type as the restoring force in the original effect.

In fact disturbing force is generated by elastic flexing of the wall of the glass. This results in a direct ( and local) contact force on water.
The waves are generated by the rotating finger on the glass, in contrast to the equilibrium tide in the Earth's oceans I referred to.
Again the rotation of the Moon around the Earth provides the required periodicity.

You are correct in saying that the restoring forces is gravity in both cases.

Incidentally probably the best definition of an elastic system is "A system in which the displacement is directly proportional to the applied disturbing force."

This would include both the volumetric compression of gases and the distortion of solids and the displacement of liquids.

 

[Ken Fabian]

1 hour ago, studiot said:

the distrubing force is not of the same type as the restoring force in the original effect.

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.