Pulverize with sonic energy or when the fat lady sings.

The best way to determine the resonant frequency is by experiment. Hit the object and measure the vibration response. The frequency it vibrates at is its natural frequency.. When you then apply energy at that same frequency you will have a resonance condition.

I assume your question is actually, Can one use sonic energy to pulverise a material that is frozen? The answer is yes. Hook up a speaker to a function generator, start to vary the output frequency of the function generator, and when you get a strong sympathetic vibration in the material you have found the natural frequency. Then it is just a matter of generating sufficient sound intensity... Which may be easier said than done depending on what the object is..

(BTW this is not the thread on demolishing a bathtub resurrected is it??)

The resonant frequency is less about the material, more about the shape. You can make a bell out of brass to ring at just about any (audio) frequency you want.
You can make a quartz crstal resonate at different frequencies depending on how it is cut.

Right, and I would add the size. You can make a quartz resonate at lower frequencies (under 100 KHZ) but to get some measurable signal, THE SIZE MATTERS!

BTW, a lead bell has a very "dull" sound, at 273 K, but at 180 K things change...On the other hand, at 277 K, my favorite Cabernet has the lowest viscosity (the fastest flow)...rrr...what was I talking about?

can one pulverize a material with sonic energy...

this is off the track of "resonant frequency" of the material, but there are medical technologies using ultrasound to 'pulverize' ? stuff:

If you search PubMed for "HIFU" that is high intensity focused ultrasound, you'll find a literature on it. The term "cavitation" is also used.

Here's an abstract about acoustic cavitation in HIFU for example.

Don't know if something like this would be powerful enough to pulverize the material you're thinking of. From what I've read, the therapeutic use of HIFU takes time because the physical effects are small (search confocal re: efforts to make it more efficient, using dual frequencies). There's also something called HESW high energy shockwave, and shockwave therapy used to break up kidney stones.

Every winter the weather forecasters in Fargo, North Dakota, USA step outside with a cup of liquid and throw the liquid into the air and the liquid turns into snow, freezing in mid-flight.

The science shows also demonstrate freezing something with liquid nitrogen or sometimes CO2, and then tapping the material and watching it shatter.

So this relates to your super-cooling/freezing a material and then trying to determine the resonant frequency, probably just won't happen. A Twinkie has a completely different hardness coefficient at 25C, -10C, -273C which will yield very different sounds, which sound are you searching for ?

Corona Man,

We are looking for the sound or resonant frequency that we can excite with a matching frequency from a sonic device. This matching frequency will be so powerful that it will pulverize the target material. (The fat lady sings and breaks the wine glass) In our case the target material is smaller than a wine glass but it is not a crystal but it is hard. Therefore to make it harder we freeze it in liquid N. Sorry I can't tell you what the material is, still working on the patent application.

Scout02

Starting from the basics, at resonance a serial circuit (L,C) will draw the maximum power while a parallel circuit (L,C) will draw no power at all (ideally). See the way you excite your stone or whatever you freeze, and try to get a the resonance frequency from the consummated power.