Simple demonstration of 2D normal modes 
of a circular elastic membrane

Presented at the 158th meeting of the Acoustical Society of America
in the Project Listen Up session (October 2009)

The goals of this project are to

• Develop a simple and inexpensive apparatus to demostrate 2D resonances in an elastic membrane with circular geometry
• Create a an engaging physical manifestation of of the mathematical solutions to the 2D wave equation in polar coordinates.

The slides illustrating the construction demo and various activities can be downloaded here. [pdf]

I refer to several computer simulations developed by others.  Here are the links:

• Wolfram Demostration Project: Normal Modes of a Circular Elastic Membrane [link]
  A Mathematica script which plots various normal modes and animates them.  It produces high quality graphics.
•  Paul Falstad  [link]
  A very nice Java based simulation with the options of visualizing (and hearing) multiple excited modes, as well as spectral components of an impulsive strike to the membrane.  This one is very good and runs on about any browser!

Movies:

• High speed video of the fundamental mode (0,1) [avi]
• High speed video of the next higher mode (1,1) [avi]
• Realtime video of the effect of changing the boundary conditions on mode (0,1)
  by placing a hand close to the vibrating surface.   [mpeg]
• Realtime video of the same thing for mode (1,1) which shows evidence of nonlinearity. [mpeg]