Exploring the Origin of Maximum Entropy States Relevant to Resonant Modes in Modern Chladni Plates

Yu Hsin Shu, Yu Chen Tseng, Yu Hsiang Lai, Yan Ting Yu, Kai Feng Huang, Yung Fu Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The resonant modes generated from the modern Chladni experiment are systematically confirmed to intimately correspond to the maximum entropy states obtained from the inhomogeneous Helmholtz equation for the square and equilateral triangle plates. To investigate the origin of maximum entropy states, the inhomogeneous Helmholtz equation is modified to consider the point interaction coming from the driving oscillator. The coupling strength associated with the point interaction is characterized by a dimensionless factor α. The δ potential of the point interaction is numerically modelled by a truncated basis with an upper index N. The asymptotic behavior for the upper index N is thoroughly explored to verify that the coupling strength of α = 1.0 can make the theoretical resonant modes agree excellently with the maximum entropy states as N→∞. It is further authenticated that nearly the same resonant modes can be obtained by using a larger coupling strength α when a smaller upper index N is exploited in the calculation.

Original languageEnglish
Article number215
Issue number2
StatePublished - Feb 2022


  • Maximum entropy
  • Modern Chladni plates
  • Pattern formation
  • Point interaction


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