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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?

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  • $\begingroup$ I believe the resonant frequency has a lot to do with the speed of sound in the resonant medium (5.8km/s), if the size is a multiple of 1/4 of a wavelength then boom, resonance (although you want 1/2 a wavelength so it only vibrates in the middle). Based on the size of this old military 2kHz quartz crystal your amulet would probably be... amulet sized. The catch is that thicker resonators are stiffer, i.e. they move less when resonating, i.e. they're going to make less noise (more movement = louder noise) $\endgroup$ – Samwise Dec 21 '19 at 21:21
  • $\begingroup$ @Samwise -- what would the minimum thickness be for an amulet-sized quartz disc to be robust enough to withstand an adventurer's lifestyle? $\endgroup$ – Shalvenay Dec 21 '19 at 21:28
  • $\begingroup$ "Minimum thickness": very thin, supposing that the adventurer knows a good jeweller who can mount the crystal in a suitable frame. $\endgroup$ – AlexP Dec 21 '19 at 22:07
  • $\begingroup$ @AlexP ah, interesting point re: the frame. What would such a frame look like? I was originally thinking it'd be a frameless setup, but I don't think there'd be any objection to a frame being a thing $\endgroup$ – Shalvenay Dec 21 '19 at 22:10
  • $\begingroup$ Ideally, the frame would be in the shape of Euterpe, the muse of music. $\endgroup$ – AlexP Dec 21 '19 at 22:12
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A modern 20kHz tuning fork crystal, as used in electronics, is housed in a cylinder 6mm in length and 2mm in diameter. Assuming the frequency scales linearly with size, you would probably get something up to the size of a thumb depending on desired frequency.

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  • $\begingroup$ This answer fails to take into account that tuning-fork crystals are named such because they are physically cut in a fork-like shape, and vibrate accordingly as a result. This presentation from a crystal manufacturer is a good summary of how they work. $\endgroup$ – Shalvenay Mar 26 at 22:19

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