The Circular Membrane Modes model displays the analytical wave equation solution for an ideal circular membrane with a fixed boundary. The solution is described by two integers m and n where n is a positive integer that counts the number of radial nodes and m counts the number of azimuthal (angular) nodes.  The model shows a time-dependent animation of the membrane displacement and Chladni-like nodal pattern.

The  Circular Membrane Modes model is a supplemental simulation for the article "Chladni Patterns on Drumheads: A Physics of Music Experiment" by Randy Worland in The Physics Teacher 49(1), 24-27 (2011) and has been approved by the authors and The Physics Teacher editor.  The model was developed using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_mech_CircularMembraneModes.jar file will run the program if Java is installed.

Please note that this resource requires at least version 1.5 of Java.