Chladni Pattern

Wence Xiao

Student thesis: Termpaper


The report aimed at mathematically describing the Chladni Pattern for a plate based on the equation of motion in two dimensions. It began with deriving the equation of motion of a single point from Newton’s laws, and later derived the equation of motion for the vibration in two dimension, and gave the normal modes through the method of separation of variables. The next was deriving the nodal pattern when the initial conditions and bound- ary conditions were given. At the same time, the wave pattern and nodal pattern of the vibrating plate was drawn by Matlab as a visual help. The equations of nodal patterns were found at last, and the patterns de- pended on the nodal numbers m and n which were related with the frequency of the driving force. Also in many situations the patterns were a mixture of some basic forms of patterns.

EducationsBasic - International Bachelor Study Program in Natural Sciences, (Bachelor Programme) Basic
Publication date18 Jun 2010
SupervisorsAnders J. Hede Madsen


  • nodal lines
  • wave equation
  • Chladni Pattern