What mathematical factors influence the shapes produced in cymatics experiments?

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prepond
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Hi all,

just I made my own Chladni Plate or CymaScope and have played a little bit with it:



I was curious and I made some tests with guitar:



but my question is: does enyone know why this is happening?
 
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When you mechanically excite a plate you will get standing waves in the plate. The dust will tend to collect in the nodes of the standing wave.
 
do you know some mathematical relation? I know frequency, what do I need more to "predict" this shapes?