Chladni patterns are a classic undergraduate demonstration. You can visualize the nodal lines of a vibrating elastic plate by sprinkling sand on it: the sand is thrown off the moving regions and piles up at the nodes. Normally, the plate is set vibrating by bowing it like a violin. It helps to put your fingers on the edge to select the mode you want, much like fingering the strings of a violin. This takes some practice.

You can make a nice modernized version of this demonstration using an electromagentic shaker (essentially a powerful speaker).

With this you can vibrate much larger plates to much higher and purer modes. The shape of the plate is important. The usual demonstrations are round and square plates. Here are some sample patterns: all the plates were 0.125 inch thick Aluminum, painted black.

• Round plate (70cm across, held at centre, bowed)
  10 spoke pattern, 14 spoke pattern

• Square plate (70cm on a side, driven from centre with shaker, frequencies in Hz)
  142.2 , 1225.0, 1450.2, 3139.7, 3678.1, 5875.5 .

A more interesting shape is a stadium: a square with rounded endcaps.

• Stadium plate ( 70cm across, driven from centre with shaker, frequencies in Hz)
  387.8 , 519.1 , 649.6 , 2667.3 , 2845.0 ("superscar") , 3215.0 , 4583.0 , 6005.3 , 7770.0 ("bow tie mode").

Finally, getting back to our musical roots, we built a plate in the shape of a large violin. Here are some patterns:

• Violin shaped plate (120cm long, driven from centre with shaker, frequencies in Hz)
  145.2 , 268.0 , 762.4 , 954.1 , 1452.3 , 1743.5 , 2238.6 .

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The Experimental Nonlinear Physics Group, Dept. of Physics, University of Toronto,
60 St. George St. Toronto, Ontario, Canada, M5S 1A7. Phone (416) 978 - 6810.