Classical Wave Equation

This applet calculates the classical wave behavior of a string 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 string 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 wave moving more clearly.
  3. Click on the "Clear" button to stop the string from vibrating.
  4. Directly below the string is a row of "dots" that represent the amplitudes of the other normal modes. Pick the second dot and drag it's amplitude up a bit. How many nodes are in the second normal mode (also called the first harmonic)? (Remember that a node is where the string crosses the y=0 line.) How many nodes are in the third normal mode?
  5. Try a combination of normal modes. Are any of your combinations "stationary"? I.e. are the nodes fixed in space, or do they move around?
  6. Click on "Stopped" and then change the Mouse menu to "Mouse = Shape string". Use your mouse to "shape" the string in a pattern of your choosing (try a gaussian shape or a sawtooth or triangle wave). What happens when you click on "Stopped" again and let the string resume it's oscillation?

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