Chladni Patterns are formed when sand settles at the nodes of two dimensional standing waves, excited on a metallic plate which is driven at a resonant frequency. By considering a two-dimensional rectangular membrane with fixed boundary and constant density as an idealized model of the metal plate, a formula for predicting the Chladni Patterns that will form at certain frequencies can be found. In addition to mathematically exploring these mysterious patterns, I have created my own “Chladni Patterns” in the lab.
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Coughlin, A. M.
"Patterns in the Sand: Mathematical Exploration of Chladni Patterns,"
Journal of Mathematics and Science: Collaborative Explorations: Vol. 3
, Article 20.
Available at: https://scholarscompass.vcu.edu/jmsce_vamsc/vol3/iss1/20