Diving into ellipsoid swimming pool at one focus

[synch]

[ just a fun question :) ]
Thinking of the focussing properties of ellipses -
If a swimming pool was shaped liked a large half-ellipsoid...and someone dived in at a focus...would the splash then largely appear at the other focus ? In fact would a swimmer at the second focus then be projected up from the water ?

 

[DaveE]

Yes, I think so. Except for people being "projected up", we don't float that well. Most of the action is on the surface, most of us isn't.
https://www.falstad.com/ripple/
https://en.wikipedia.org/wiki/Whispering_gallery

 

[berkeman]

half-ellipsoid

Your thread says ellipsoid, but in your OP you mention half-ellipsoid. Well, which is it young feller? (What movie is that from?)

 

[DaveE]

Your thread says ellipsoid, but in your OP you mention half-ellipsoid. Well, which is it young feller? (What movie is that from?)

I don't think it matters because of symmetry. The only significant reflections from the cut would happen at the foci. Of course, you have to cut it on the major axis.

edit: OTOH, it would hurt diving into the foci of my half-ellipse.

 

[berkeman]

OTOH, it would hurt diving into the foci of my half-ellipse

Good point; owiee!

 

[Frabjous]

Most of the water displacement is occuring due to body movement at points away from the focus.

 

[DaveE]

I could play for hours* with that simulator. So much better than the real wave tank in high school!

https://www.falstad.com/ripple/Ripp...00+1+0 e+0+8+136+699+584+0 w+0+9+362+699+362

*OK, many minutes. LOL

 

[Baluncore]

In fact would a swimmer at the second focus then be projected up from the water ?

Only if people were small spheres. It would be close, but not efficient.
The problem is that people have different shapes, and are larger than the size of the point focus.
If there was no object at the second focus, the pressure waves would pass there, and reflect from the surface, to meet again at the primary focus. Could that injure the diver?

 

[A.T.]

In fact would a swimmer at the second focus then be projected up from the water ?

Maybe if it was a small kid on a floatation device, while a big adult makes a cannonball dive at the other focus.

 

[synch]

I have seen drops of coffee ejected back from cups when liquid is added.
It would be an easy experiment on the small scale, say make a half ellipsoid from plaster or somesuch in an old plastic drum, and see what happens if a baseball is dropped in at a focus. Maybe a bit messy though - I'll leave it to anyone else !! :)

 

[sophiecentaur]

say make a half ellipsoid from plaster or somesuch

Just bend a strip of aluminium sheet and make a wall in a tank of any shape - say a cement mixing spot which would be a good shallow depth. But why not go for the whole ellipse? A circular wall with string pulling two sides together would give a pretty good ellipse. A network of adjustable strings could improve the ellipse shape.
I almost feel a project coming on.

 

[jrmichler]

Since a circle is a limiting case of an ellipse, just cannonball into the center of a circular pool, and find if the waves come back and fling you up. Or drop something into the center of a round bucket of water.

 

[synch]

I was thinking more of half of the full 3-d ellipsoid, like half an egg shape. EG carve out an ellipsoid volume in foam then set the plaster around it. Now I remember , there was a image once, an ellipse of xenon atoms placed with an ATM. with a cobalt atom at a focus - there was a "ghost" signal at the other focus - weird as !

 

[sophiecentaur]

I was thinking more of half of the full 3-d ellipsoid, like half an egg shape. EG carve out an ellipsoid volume in foam then set the plaster around it. Now I remember , there was a image once, an ellipse of xenon atoms placed with an ATM. with a cobalt atom at a focus - there was a "ghost" signal at the other focus - weird as !

There are many demos of arrangements with pairs of foci. It's stunning with two paraboloids out in the open, focussed on each other. The sound 'amplification' is amazing between two talkers.

 

[DaveC426913]

Yes. I have had an elliptical swimming pool with an eccentricity of zero (some might call it circular).

I would stand at one of the foci and jump up and down rhythmically, and the waves would reflect off the walls and cause very high crests and troughs at the other focus (which, technically was co-incident with my location).

If I did this enough, I could cause enough wavage to drain half the pool.

 

[DaveC426913]

There are many demos of arrangements with pairs of foci. It's stunning with two paraboloids out in the open, focussed on each other. The sound 'amplification' is amazing between two talkers.

And in-the-wild examples too. The Oval Office is one. Grand Central Station in New York has another (partial). In certain places the arches overhead are parabolic; you can stand one one side of a hall an hear a whisper from the other.

 

[Baluncore]

Just bend a strip of aluminium sheet and make a wall in a tank of any shape - say a cement mixing spot which would be a good shallow depth. But why not go for the whole ellipse? A circular wall with string pulling two sides together would give a pretty good ellipse. A network of adjustable strings could improve the ellipse shape.
I almost feel a project coming on.

If you are going to make an ellipsoidal pool for the experiment, it might pay to check the acoustic impedance of the wall material, and compare it to that of water. It would be a pity to get only a little energy reflected from the ellipsoidal boundary.

 

[sophiecentaur]

It would be a pity to get only a little energy reflected from the ellipsoidal boundary.

Could be a problem with very thin strip but I was thinking in terms of thick / strong enough to present a good reflection. With a flexible dam, you could adjust for best performance in situ. The strip could be used for another job after all the fun.

 

[sophiecentaur]

compare it to that of water

This would be the impedance of surface (gravity) waves; pretty low. Not the acoustic impedance (pretty high). The wave speed is only in the order of 1m/s.

 

[Baluncore]

This would be the impedance of surface (gravity) waves; pretty low. Not the acoustic impedance (pretty high). The wave speed is only in the order of 1m/s.

The surface waves are irrelevant to this experiment. I am considering the acoustic impedance of the pressure wave in the fluid, not the sloshing of the secondary surface waves.

This brings up the question of the acoustic impedance of the body that dives into the water. Would the shape of the 3D response image be that of the skeleton of the diver, as would be seen with an ultrasound scan?

 

[sophiecentaur]

@Baluncore : The waves you see on the surface of a pool are gravity waves. At and near the surface, the displacement is transverse and longitudinal. Acoustic impedance refers to longitudinal waves. There is very low pressure when the surface can move up and down freely.
You seem to be imagining a piston in a rigid cylinder.

 

[A.T.]

The surface waves are irrelevant to this experiment. I am considering the acoustic impedance of the pressure wave in the fluid, not the sloshing of the secondary surface waves.

Which type of wave is more relevant for producing a splash at the other focus could potentially be tested experimentally, since they propagate at very different speeds.

 

[Baluncore]

Which type of wave is more relevant for producing a splash at the other focus could potentially be tested experimentally, since they propagate at very different speeds.

Gravity waves on the surface are irrelevant in a 3D ellipsoidal pool. Surface waves could be investigated in a 2D pool with vertical sides and a flat floor. It is the fast pressure wave that will be reflected from the 3D ellipsoid.

Acoustic impedance refers to longitudinal waves.

I don't know where you got the gravity wave from, but I see no value here in that discussion. Acoustic impedance determines the transmission and reflection coefficients of P waves at interfaces. The water-air boundary is a significant reflector, it is not so certain that the bottom of the pool will make a good reflector.

The flesh and skeletal body of a fish, is well-matched to the acoustic impedance of water. It is the gas filled swim bladder that provides the best echos to an acoustic fish-finder. Likewise, as a diver enters the water at focus 1, I would be interested to see if the presence of their lungs provided a significant change in the acoustic response at focus 2.

 

[sophiecentaur]

since they propagate at very different speeds.

You can actually see the progress of a wave on a swimming pool. Pressure waves travel a lot faster than sound in air. If we were dealing with pressure wave effects then we would hurt ourselves when we jump into the pool. We displace the water with very little force.

 

[sophiecentaur]

The flesh and skeletal body of a fish, is well-matched to the acoustic impedance of water.

Fishes are under the water and stay there mostly - at depth. P waves could be relevant in their case. I really can't see how the OP involves anything other than surface waves. It describes 'diving' into the water and presumes that the water is in liquid form so it can be displaced easily. Without jumping into the surface, I can't think of a way of introducing a human body into the pool fast (and still surviving).
Are P waves very relevant to the design of boats? I'm sure you don't need a link to help you with reflections of surface water waves at a wall.

 

[jbriggs444]

I was thinking more of half of the full 3-d ellipsoid,

Why an ellipsoid rather than an ellipse? Shallow water waves propagate in two dimensions, not three. You have to use shallow water waves because deep water waves do not have a fixed propagation speed. Compression waves are ridiculous for this purpose.

 

[sophiecentaur]

Why an ellipsoid rather than an ellipse?

Absolutely. For the best effect, you would want the wave speed to be the same over the whole path. An ellipsoid would give dispersion so a flat bottom would be best.

Compression waves would be great for cracking bottles etc but not for divers.

 

[Hornbein]

The OP means one half of a 3D ellipsoid. The foci would be on the surface of the water. That would be pretty cool.

Though maybe everyone knew that and I'm late to the party.

 

[A.T.]

Gravity waves on the surface are irrelevant in a 3D ellipsoidal pool. Surface waves could be investigated in a 2D pool with vertical sides and a flat floor. It is the fast pressure wave that will be reflected from the 3D ellipsoid.

In a 3D (half) ellipsoidal pool both types of waves will be created and reflected towards the other focus. Since they will arrive there at different times, you can compare the effect they have.

 

[Baluncore]

Since they will arrive there at different times, you can compare the effect they have.

Don't forget that the velocity of the gravity wave is depth dependent.

 

[A.T.]

Don't forget that the velocity of the gravity wave is depth dependent.

Yes. but if the wave period is short enough, such that the wavelength is much smaller than the average depth, this effect could be made small. At the boundary the slopes are very steep so it would not be like a shallow water wave.

It would be cool, if one could show both types of waves cause an effect at the other focus with the same impact.