We find experimentally and theoretically that thin plates or membranes resonate at certain "modes." This means due to initial conditions imposed upon the plate (i.e. fixed edges) the plate can vibrate only at certain allowable frequencies and will demonstrate predictable "node" patterns. Nodes are points on the plate that vibrate with zero amplitude, while other surrounding points have non-zero amplitude. This concept can be seen with a vibrating string: tie one end of a string to a fixed object and smoothly vibrate the other end of the string. If vibrated fast enough, there will be a point or points in the middle that seem to be still while the rest of the string vibrates wildly. These points are the nodes. On a two dimmensional vibrating plate, the nodes are not points, but curves. With the circular plate, we most commonly observe concentric circular nodes and diametric modes, while with the rectangular plate, we commonly observe nodes parallel with the boundaries. To see some labortory work and a more technical discussion of node patterns click here.
This applet demonstrates the mode patterns of vibrating circular and rectangular plates, usually called "Chaladni Plates" in honor of 18th century scientist Ernest Chladni. Chladni conducted extensive work on fixed circular plates and developed Chladni's Law which states that modal frequencies of fixed circular plates varies according to f~(m+2n)^2, where n is the number of circular nodes and m is the number of diametric nodes.
The above applet allows the user to change values of "m" and "n" in both the fixed circular and fixed rectangular plates. Colors represent relative amplitudes of the waves, bright red being the highest. At the right, the frequency box displays a relative modal frequency value. If you right mouse-click on the plot, a copy of the canvas will appear, allowing you to compare several modes.
Applet Updated 1/26/99