What mathematical factors influence the shapes produced in cymatics experiments?

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Cymatics experiments, such as those conducted with a Chladni Plate or CymaScope, reveal that mechanical excitation of a plate generates standing waves, causing dust to accumulate at the nodes. Understanding the shapes produced involves mathematical relationships related to frequency and wave patterns. Key factors include the plate's dimensions, material properties, and the frequency of the excitation. Additional parameters like mode shapes and harmonics also play a crucial role in predicting the resulting patterns. Exploring these mathematical relations can enhance the ability to anticipate the shapes formed in cymatics experiments.
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?
 

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