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It seems like there should be a mathematical relationship between the two - is there?

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  • $\begingroup$ Define a material’s ‘natural frequency’? But, yes, mechanical properties are readily measured with sound waves. $\endgroup$ – Jon Custer Aug 16 '19 at 0:03
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Yes, there is. From a materials science standpoint, the density of the material and its elastic modulus determine both its natural frequency of vibration (of a plank of given size) and the propagation speed of sound through that plank.

(Note that for a slender rectangular plank (like a long marimba bar), the resonance condition occurs when one end of the plank is driven with a signal and the length of the plank and the propagation speed of the drive signal are such that after propagating down the length of the plank, bouncing off its end, and returning to the driven end the returning wave is in phase with the driving signal.)

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  • $\begingroup$ You're right that the density and elastic modulus determines the sound propagation speed, but the natural vibration frequency is determined by that speed and the shape of the material. :) $\endgroup$ – Erlend Magnus Viggen Aug 16 '19 at 7:39
  • $\begingroup$ I'm assuming a simple shape- that of the marimba bar I mentioned. $\endgroup$ – niels nielsen Aug 16 '19 at 18:42
  • $\begingroup$ Is there a formula for natural frequency in terms of the speed of sound? $\endgroup$ – Ryan Aug 17 '19 at 14:07
  • $\begingroup$ You can derive it- I'm sorry I cannot, it's been too long since I was active in the field! $\endgroup$ – niels nielsen Aug 17 '19 at 17:32

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