Good stuff, yes the constraining math of quartz acoustics. We are blessed by its unique properties and having lots of quartz material. It's the scarcity of manufacturing.?
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Similar acoustic behavior lurks inside our smart phones. Not just for frequency stability but fitting all these waveforms into it. Not many know this, but bulk acoustic filters are its key. Not quartz so much but materials that are piezoelectric that can be deposited onto semiconductor wafers. Two such materials are known, ZnO and AlN. The latter is largely favored due to its better temperature stability. And those same formulas, along with AlN acoustic and electrical properties determines the bandwidth of these filters. They operate at GHz frequencies and are very tiny. I was blessed to work with 2 pioneer researchers who knew both the math and physics to make them. Meanwhile, I testify much more fun to work with quartz in our home labs (otherwise I might still be working (-:
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73 Curt wb8yyy?
Former EE etc.
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