Estudo da vibração de placas através dos padrões estacionários de Chladni

Abstract

In physical systems out of equilibrium, oscillations occur when a restoring force acts on them. These oscillations create different types of waves that propagates with speeds governed by the characteristics of the propagation medium. The wave equation shows how the deformation of the medium occurs as time goes by. In the study of wave physics, the textbook emphasizes one-dimensional waves. In this work, the study of two-dimensional standing waves is presented in a proposal to solve the investigative problem of the vibration of Chladni plates within the perspectives of the teaching methodology by investigation in conjunction with Vygotsky’s Sociocultural Theory. A low-cost experimental apparatus was developed to generate the standing wave patterns. In addition, GeoGebra was used to create an interactive mathematical graphical interface to builds these Chladni patterns from the solutions of the wave equation on square plates. Several Chladni figures were experimentally created through grains deposited on metal plates subjected to vibration. It was graphically observed at the resonance on square plates with free ends, the proportional relationship between the frequency of the standing wave patterns on a plate versus inverse square of side. From the comparison of experimental results and those obtained by computer modeling, all groups were able to explain the formation of Chladni Figures.