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I am a high school student doing an IB Extended Essay investigation concerning the resonant frequencies of Chladni plates of differing materials and sizes. Would someone please explain the definition of radial and diametric nodes ($n$ and $m$), and how to determine them? In addition, would someone be willing to provide a derivation of Chladni's equation $$f \sim (m + 2n)^2?$$

Here is a link with related mathematical resources: http://www.nhn.ou.edu/~johnson/Education/Juniorlab/Chladni/2001-ChladniPlates-CurtisParry.pdf

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