2-d Classical Wave Equation

This applet calculates the classical wave behavior of a membrane under tension. We have been looking at the behavior of this system in class, and this applet will let you play with the behavior of this system (as well tweaking it to see how it vibrates under a number of other conditions)

Sorry, you need a Java-enabled browser to see the simulation.


  1. Move the slider controlling the "Damping" to the far left (this gives us the undamped behavior of the classical wave equation). At this point, your membrane should be vibrating in the lowest frequency normal mode. If it isn't, click on "Fundamental" to start the vibration.
  2. Move the slider controlling the "Simulation Speed" to the left so that you can see the membrane moving more clearly.
  3. Click on the "Clear" button to stop the membrane from vibrating.
  4. Directly below the membrane is an array of squares. These represent the normal modes of the membrane, with the x normal modes going up as you move left along the x axis, and the y normal modes going up as you move down along the y-axis. Click on one of the squares along the top or left edge to get the membrane moving in one of these one-directional modes.
  5. Try a diagonal combination of normal modes. Are the nodes single points like they were for the string, or are they lines? Are they aligned with one axis?
  6. Try the (2,1) mode in combination with the (1,2) mode. Where's the nodal line?
  7. Try the (3,1) mode in combination with (1,3) mode. What does the nodal line look like now? (Look closely!)
  8. Change the aspect ratio of the membrane so it isn't square. Try some of the same modes you just looked at.
  9. Change the Mouse menu to "Mouse = Adjust view angle". Look at the membrane from either edge. Can you make it look like the original string applet?

This wonderful applet and many others like it can be found at Paul Falstad's Math and Physics page: www.falstad.com/mathphysics.html We'll be referring to a number of these applets during the semester.