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Circular Membrane Modes Model
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.

Please note that this resource requires at least version 1.5 of Java.
1 source code document is available
Subjects Levels Resource Types
Oscillations & Waves
- Oscillations
= Coupled Oscillations
= Normal Modes
= Springs and Oscillators
- Upper Undergraduate
- Lower Undergraduate
- Instructional Material
= Interactive Simulation
Intended Users Formats Ratings
- Learners
- Educators
- application/java
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Access Rights:
Free access
This material is released under a GNU General Public License Version 3 license. Additional information is available.
Rights Holder:
Wolfgang Christian
Oscillations, Waves
Record Cloner:
Metadata instance created October 10, 2010 by Wolfgang Christian
Record Updated:
June 3, 2014 by Andreu Glasmann
Last Update
when Cataloged:
October 10, 2010
Other Collections:

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Record Link
AIP Format
W. Christian, Computer Program CIRCULAR MEMBRANE MODES MODEL, Version 1.0 (2010), WWW Document, (
W. Christian, Computer Program CIRCULAR MEMBRANE MODES MODEL, Version 1.0 (2010), <>.
APA Format
Christian, W. (2010). Circular Membrane Modes Model (Version 1.0) [Computer software]. Retrieved July 13, 2024, from
Chicago Format
Christian, Wolfgang. "Circular Membrane Modes Model." Version 1.0. (accessed 13 July 2024).
MLA Format
Christian, Wolfgang. Circular Membrane Modes Model. Vers. 1.0. Computer software. 2010. Java 1.5. 13 July 2024 <>.
BibTeX Export Format
@misc{ Author = "Wolfgang Christian", Title = {Circular Membrane Modes Model}, Month = {October}, Year = {2010} }
Refer Export Format

%A Wolfgang Christian %T Circular Membrane Modes Model %D October 10, 2010 %U %O 1.0 %O application/java

EndNote Export Format

%0 Computer Program %A Christian, Wolfgang %D October 10, 2010 %T Circular Membrane Modes Model %7 1.0 %8 October 10, 2010 %U

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Citation Source Information

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Circular Membrane Modes Model:

Is Based On Easy Java Simulations Modeling and Authoring Tool

The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Circular Membrane Modes Model.

relation by Wolfgang Christian

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