water resonance in a sphere

[Paul-R]

It is kind of like tuning a guitar or a piano.  The sphere (filled with water) will "ring" at a resonant freq. 

What you need to do is plot a graph of frequency versus amplititude, getting the amplitude
of vibration from a strain gauge, possibly.

It should be the architypal upside down pudding basin, with resonance at the top.
Paul.

[TinselKoala]

The problem is that there are several (many) resonance "modes" for a sphere.

You could try
f = v / (2*pi*r)
where f will be the characteristic resonance
v is the velocity of the wave in the medium (i.e. the speed of sound in water)
r is the radius of the sphere

Also f = v / 2*r   is supposed to be the frequency of resonance of the "first quadrupolar mode" of the hollow sphere. I don't know what happened to the "pi" factor here.

One ambuguity, as I'm sure you have found by now, is whether you are talking about the container, which would be a hollow sphere, or the water in it, which would be a solid (liquid!) sphere.

Since the theoretical situation is somewhat murky, I'd proceed empirically. Use Piezos and a known sphere size to determine a resonance frequency. Then generalize that finding to spheres of arbitrary dimension.

[Hydro-Cell]

hi tinsel koala

cheers for the info, however im not too sure how to use the formula, i worked it out for a 20cm diameter sphere and my answer was less than 1, it wa 0.0**** cant remember the exact figure.

could someone post an example for me please

[Pirate88179]

@ Tinsel Koala:

You always have a lot of good information.

I do have one question....it seems to me that anyone attempting to calculate this would have to know more about the sphere, such as the wall thickness, density of the exact type of steel used in the construction, etc.  Also, depending on the method used to create the sphere, the wall thickness and density may vary throughout the structure.  It would seem to me that unless someone knew all of these factors, the results would be sort of a WAG.  (wild ass guess)  Of course, I believe you said as much anyway.  I was just throwing this out there.

Bill

[TinselKoala]

thanks
Yes, that's right, and it also depends on whether there's a hole and/or a neck in the sphere, and whether the fluid being resonated is inside, outside, or both.

But, as a general rule, it's easier to think (for me) about resonance wavelengths, rather than frequencies. (Wavelength is the inverse of frequency, right? But it also captures the characteristic velocity of propagation in the medium concerned.) So, just like with electrical resonances in a transmission line or on an antenna, there is a characteristic length that corresponds to a particular resonance in a mechanical system, and integral multiples of that length will relate to resonances.
I think.

Wavelength = v / f

where v is the characteristic velocity (or phase speed) in the medium. This will be c for EM waves, and it will be the speed of sound in water or air, and it could even be the speed of sloshing in a basin or tub, or the speed the breakers roll in at your favorite surf beach.
and f is frequency.

To aid the math, wavelength has the unit: length
v has the units: length/time
and f has the units: counts/time or cycles/time, with Hz (Hertz) meaning specifically cycles per second.

So let's say you have a sphere, no hole, diameter 10 cm. So you could start with using 10 cm as the wavelength, and with water inside use 1500 m/sec or 150000 cm/sec.

wavelength = v / f
So f = v / wavelength
So f = 150000 / 10
So f = 15 kHz
Check the units: F is in cycles/time or 1/time, v is in length/time, wavelength is a length. SO units check.

And I would look at 1/4 wavelength so f=(150000 / 2.5)
and then integral multiples of the above

Now that's assuming what might be called a "transverse mode" of oscillation: the diameter of the sphere "houses" a sinusoidal pressure oscillation. But it is possible to imagine many other modes of oscillation, so the diameter might not be the appropriate length to try for those modes. I can imagine a circumferential oscillation that would include a "pi" term in calculating a characteristic wavelength from the sphere's radius.
I don't really know how a sphere of water can oscillate, but I'll bet it isn't simple and there will be multiple resonances.

So, yeah, pretty much WAG, but with a little guidance from the sphere's dimensions.

Resonating spheres with holes in them are called Helmholtz resonators and are extensively analyzed.

Someone in one of the threads asked if I had a source for high-power piezo transducers. Sorry, I don't really. I get most of my experimental materials from several local surplus outlets. The small transducer in the video cost 50 cents at Active Surplus. I also got some heavier duty ones there for a couple bucks each. And every once in a while I see some really high-power ex-military stuff at another local junker. SO I would recommend looking in places like that first.