Chladni Figures

Inspired by the formation and applications of Chladni figures on violin plates, this paper aims to further my understanding of how Chladni figures form by constructing a mathematical and physical model myself. Armed only with the book “Elementary Differential Equations and Boundary Value Problems (W. Boyce and R. DiPrima, 1986)”, from which the vast majority of my knowledge on this subject stems, my father's workshop as well as the school's science lab, I set out on the mission to explore and solve the two-dimensional partial differential wave equation on my own. The methods in this paper are not necessarily conventional, since they were largely obtained through hours of trial and error. When comparing my theoretical results to the experiments I did to test my mathematical predictions, I found that my formulas were able to successfully describe the formation of certain Chladni figures and the frequencies at which they occur.