Study of Chladni’s stationary patterns

Wave physics describes physical systems in which a restoring force governs the oscillatory motion of the system around an equilibrium point. These oscillations manifest themselves in different types of waves and propagate at speeds associated with the different characteristics of the propagation medium. One of the phenomena that impresses by their symmetry and elegance are the Chladni patterns, which are even used as an indicator of quality in the manufacture of musical instruments. In this paper, a simple experimental apparatus and an interactive mathematical graphical interface, which was createad at the GeoGebra platform by equations solutions from the wave equation in square plates, were developed to study two dimensional Waves of the Chladni plates. Several Chladni figures were experimentally created from grains deposited on different metal plates under vibration. Square plates of different sizes with free edges were used to observe the ratio relationship between the resonance frequency of the stationary wave patterns and the inverse of the square of the side. It was found that the association between the experimental results and those obtained by computer modeling in the formation of Chladni figures allows for a better understanding of the principles that control the formation of these patterns.

Keywords:
Chladni figures; experimentation; computational modeling; standing waves