Re: What is the resonant frequency of granite or quartz?

Hello...Mick!

Looks like you're a budding materials scientist or mechanical engineer!  And 
you had a number of questions for me, so we'll go through your letter part 
by part and I'll put in comments and answers as appropriate.

Mick notes:  "I have read about resonance as relates to a glass, or the   
              Tacoma narrows bridge, and I have also read that John Worrel 
              Keely was able to shatter Quartz veins using resonance.  I 
              know you can buy artificial quartz resonators for 
              electrical purposes, and that they have a specific resonance.

Mad Scientist:  These are both examples of mechanical resonances driven by 
                external forces. In the case of the bridge, it was the wind.
                For the manufactured quartz resonators, it is the imposed 
                electrical voltage that excites what is called the 
                piezoelectric effect (the crystal expands and contracts as 
                voltage is varied across it).

Mick asks:  "What is the resonant frequency of granite and quartz, and how 
is it calculated?"

Mad Scientist:  There is no one answer to this question. The resonant fre-
                of a mechanical system depends both on the properties of
                the material (its "stiffness") and the geometry of it. Take
                a common wooden ruler (plastic ones don't work as well for
                this demo, at least the ones I had didn't) and put it over
                the edge of a table. Now hold down, with one hand, all of   
                the ruler that is in contact with the table. Bend down the 
                free end and let it go. If only a short amount of ruler is 
                over the edge, you will get a different tone than if more of 
                it is over the edge (works best with between 7 cm and 22 cm
                over the edge for my ruler). All I have changed here is the 
                geometry (in this case the length of the resonating 
                portion). Or, consider the varying sizes of church bells, 
                all made of the same material, yet the larger bells have 
                deeper tones. 

                Changing the mechanical properties of a material can also 
                change resonance. Consider how a guitarist tunes his 
                instrument: he tightens or loosens it, varying the 
                tension in each string to modify the tone. A tight string 
                will act "stiffer" and have a higher frequency of resonance.

                With the quartz resonators you mention, thin slabs of quartz 
                are cut to a thickness that makes the resonance occur 
                at a specific frequency chosen by the manufacturer. There is
                no one "magic" frequency at which quartz will oscillate.

                Granite is even more difficult. All of what we call 
                "granite" does not have constant physical characteristics. 
                That is, not all granite has the same composition, and even 
                for samples with similar chemical composition, the sizes of
                the constituent mica, feldspar, and quartz crystals can vary
                quite a bit.

Mick:  "Also I believe the resonant frequency of water is somewhere around 
        2450  Megahertz, but how would you calculate the resonate frequency 
        of particular compounds, such as salt, or the resonant frequencies 
        of metal forms such as the drawbar on a semi-trailer?

Mad Scientist:  You have now switched away from a mechanical system to the
                modes of vibration of a chemical bond in a molecule. For 
                water, things are actually a little more complicated than
                you mention. Water has three resonances: a symmetric stretch
                (both hydrogens move toward or away from the oxygen in the
                same way at the same time), an asymmetric stretch, and one
                related to the amount of bending in the H--O--H structure.
                Here's a good website that discusses water molecular 
                vibrations in much more detail:

                    http://www.sbu.ac.uk/water/vibrat.html

                The calculations on bond "stiffness" (rate of change of 
                bond energy with distance, e.g. for simple linear motion)
                are very tough. This requires computations with differential
                equations in a quantum-mechanical system. It's probably 
                easier to excite the molecules with suitable microwaves and
                look for the effects of resonance (faster temperature rise, 
                e.g.).

Mick:   "Your time is much appreciated"

Mad Scientist:  We appreciate the questions!  Resonance and vibration are
                fascinating subjects. I don't know of a book devoted only to 
                it at an introductory level, but you might look up the book 
                "To Engineer is Human" by Henry Petroski. He devotes a 
                chapter to the problems with the Tacoma Narrows bridge. The 
                entire book is highly interesting reading if you are getting 
                interested in engineering and/or materials.