written by Wolfgang Christian

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.

• Download ejs_mech_CircularMembraneModes.jar - 1813kb Java Archive File

Last Modified June 3, 2014

This file has previous versions.

The source code zip archive contains an XML representation of the Circular Membrane Modes Source model.   Unzip this archive in your EJS workspace to compile and run this model using EJS.

• Download ejs_mech_CircularMembraneModes.zip - 22kb Compressed File

Last Modified October 10, 2010