How do I determine the physical size of a quartz crystal of a given shape and vibrational mode needed to approximate a specific resonant frequency?

So, one of my D&D characters has a cut/relief-carved quartz crystal amulet (medallion shaped) that's both an arcane focus (crystal) and a holy symbol (amulet), and I thought it would be a good idea for it to resonate within the audible range, given that quartz crystals can make good, pure-tone mechanical resonators. However, I can't find much on what size a quartz resonator needs to be for a given shape, vibrational mode, and frequency.

In my case, I'm thinking this would be a flexural mode resonator for practicality and probably audibility/volume as well, made in a cylindrical disk shape (with relief carvings on both sides and a hole in it for wearability) to serve as an amulet, and with a resonant frequency somewhere in the audible range (preferably somewhere from a few hundred Hz to 15kHz). Considering that a reasonable maximum size would be somewhere around 25mm in diameter and 5mm thick, what actual size would be needed to reach the audible frequency range?

posted almost 5 years ago

Shalvenay‭

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