# Chladni Figures and Vibrating Plates

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.

#### See lab work and a theoretical discussion of
Chladni Plates.

Applet Updated 1/26/99