# A question about vibrations and water

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Ok, if i put say a spherical mass (one where i can control how it vibrates) in pure or almost pure water and if i hit a certain frequency or intensity would a space be created between the sphere and the water?

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Ok, if i put say a spherical mass (one where i can control how it vibrates) in pure or almost pure water and if i hit a certain frequency or intensity would a space be created between the sphere and the water?

OK let us look at some figures.

At room temperatures the average speed of water molecules is about 600 metres/second.

Say the surface of your sphere pulses in and out at some frequency, f.

As the surface moves out it pushes the water back and as it moves in the water molecules will move in to occupy the void at an average speed of 600m/s.

So if the surface is moving faster than this it will leave a void behind as the water molecules cannot catch it up.

For an object vibrating in simple harmonic motion the maximum speed is given by

$Maxspeed = 2\pi fA$
Where A is the amplitude and f the frequency as already noted.
The maximum speed occurs as the surfaces passes through the undisplaced position so for a total displacement of 1mm (0.5mm outwards and 0.5mm inwards)
A = 0.5 x 10-5 metres.
Substituting values
$600 \le 2\pi f(0.5*{10^{ - 3}})$
$600 \le 10\pi f*{10^{ - 4}}$
$\frac{{6*{{10}^5}}}{\pi } \le f$
$f \ge 200,000$
So a frequency above 200 kilohertz will just begin to create such a void, but two things
600 is the average speed of the water molecules.
Some will be moving quite a bit faster.
The frequency calculated is for the maximum speed of the vibrating surface.
The surface speed will actually slow down to zero over the 0.5mm so the water molecules will soon catch it up.
Both of these effects serve to raise the necessary frequency, probably into the Mhz range, the exact value will depend upon just how much water you are prepared to let into your empty space and just how thick you want it to be.

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As the surface moves out it pushes the water back and as it moves in the water molecules will move in to occupy the void at an average speed of 600m/s.

So if the surface is moving faster than this it will leave a void behind as the water molecules cannot catch it up.

I hear what you say, or rather I read what you write, and I cannot fault your argument. But I am surprised that the speed of water molecules which you quote is not somehow dependent on the air pressure above the water.

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I hear what you say, or rather I read what you write, and I cannot fault your argument. But I am surprised that the speed of water molecules which you quote is not somehow dependent on the air pressure above the water.

Yes of course the temperature and pressure will affect the water molecule speed.

Don't forget this is back of the envelope stuff.

I simply googled average water speed at 20o C and came up with 590m/s

Also dividing 6 by pi does not exactly equal 2.

But I thought it provides a feel for the question.

Also note that the waves have to be transverse to push the water away. Longitudinal (surface) waves will not do.

@connor

Was this for some sort of spaceship/submarine story?

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@studiot thanks for the answer, and no i was using this as a stepping stone for a bigger theory/question but thinking about it now it may not link together as i wished. A better question might have been, how do vibrations effect the fabric of space?

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@studiot thanks for the answer, and no i was using this as a stepping stone for a bigger theory/question but thinking about it now it may not link together as i wished. A better question might have been, how do vibrations effect the fabric of space?

You would need to consider gravitational waves for that.

https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=gravitational+waqves&gbv=2&oq=gravitational+waqves&gs_l=heirloom-hp.3...1056.6657.0.6858.20.11.0.9.6.0.189.1060.9j2.11.0....0...1ac.1.34.heirloom-hp..4.16.1007.TGnqpm8s9GY

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Just so your aware water waves follow a dipole transverse waveform. However gravity waves are transverse quadrupole due to spin 2 statistics. So while their is simularities, their is also a significant difference in how the two cause strain.

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OK let us look at some figures.

At room temperatures the average speed of water molecules is about 600 metres/second.

I'm having trouble understanding why this is relevant. Sure water molecules move quickly, but they also collide with other water molecules in a very short distance. What you care about is the bulk behavior of the water. Later you ask if this is about a submarine story, so are likely aware of the phenomenon called cavitation: forming a low enough pressure region that water vapor or dissolved gas pockets form. The object doesn't need to be moving at the molecular speed of water, it just needs to be moving fast enough that the pressure drops to where a void can form and water can't fill in the void quickly.

Such effects occur at well bellow 200 kHz. Marine animals can experience cavitation.

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I'm having trouble understanding why this is relevant. Sure water molecules move quickly, but they also collide with other water molecules in a very short distance. What you care about is the bulk behavior of the water. Later you ask if this is about a submarine story, so are likely aware of the phenomenon called cavitation: forming a low enough pressure region that water vapor or dissolved gas pockets form. The object doesn't need to be moving at the molecular speed of water, it just needs to be moving fast enough that the pressure drops to where a void can form and water can't fill in the void quickly.

Such effects occur at well bellow 200 kHz. Marine animals can experience cavitation.

Thank you yes I'm aware of cavitation effects and was planning to introduce it into the discussion if it proved to be about submarines.

I was also pleasantly surprised to find that my envelope calc produced a frequency employed in modern sonar.

http://hypertextbook.com/facts/2001/EmranYusufov.shtml

Two points about cavitation.

Firstly it is a local effect - Could you envisage a sphere surrounding itself with a void by cavitation?

Secondly as the pressure in the cavitation bubble is lowered, water boils into the low pressure within the bubble, so the bubble is not a true void.

Edited by studiot

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Does it matter what kind of vibrations you're referring to?

You could have:

• linear vibration of a fixed volume sphere. - simply put a metal ball moving side to side, along a line through its origin. 1 linear frequency.
• planar vibration of a fixed volume sphere - a metal ball moving side to side and up and down (or plane-rotational vibration). 1 radial frequency dimension.
• tri-planar vibration - hard to imagine, but this might need 3 linear frequency values to fully describe, or 1 radial and 1 linear.
• volumetric vibration - like a balloon expanding and contracting at some frequency. 1 linear
• volumetric tri-planar vibration - 1 radial, 2 linear.
• rotational vibration - Assuming there is some frictional value between the surface of the sphere and water to enable rotational vibrations. 1 radial, 1 linear
• Then the sphere could moving (not just vibrating around the origin point of the sphere) around a fixed point in the water medium. Lets say for simplicity its movement is circular on a plane. Then if the angular speed is significant relative to the vibration frequency and amplitude, that would be interesting. 1 radial, 1 linear
• A 3-plane frictional rotational oscillations about origin, 3-plane linear oscillations about origin, 3-plane movement about fixed point, volumetric vibration system would need 3 radial and 4 linear dimensions to describe!
• Also all oscillation frequencies could themselves be oscillating!

I think you could make lots of patterns, in a standing unbounded water medium, where spaces might occur, especially at high frequencies

Edited by AbstractDreamer

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My instinct is that the speed of sound in water is the proper metric. If something is vibrating faster than that, it's moving faster than the bulk water can move, and you would end up with a void

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Perhaps any gap, or void that has been mentioned would be in the form of water vapour. This seems closely allied to cavitation on ship's propellers.

https://www.iims.org.uk/introduction-propeller-cavitation/

Edited by Joatmon

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