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I've recently been conducting experiments on the Chladni Plates, testing out how the length of a square Chladni plate (and consequently its area) affects the frequency at which each respective chladni pattern is formed.

The result shows that as the area of the plate decreases, the frequency at which each respective pattern is formed increases exponentially. However, after doing some research. Besides Chladni's law:

$$f=C(m+2n)^{p}$$

No other equation, I've found really relates properties of the plates to the frequency at which certain patterns are formed. Furthermore, since both C and P are unknown except for objects such as bells, I am unable to use the Chladni Law.

My question is if anyone knows of a formula that can relate of them the frequency and dimensions of the chladni plate together, or if there even is one.

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