Chladni patterns show the geometry of the different types
of vibration of violin plates. This site has an introductory
explanation of modes of vibration and a library of photographs
of the Chladni patterns of the bellies and backplates of two
different violins (one mass-produced
and one hand-made). It also has
photographs of plates with regular
geometries which assist in understanding the violin modes.
For some related history, see Chladni's
law. For some Chladni patterns on metal plates, with sound
files, see Acoustics of bell plates.
To make your own Chladni patters, try this site.
(See also the explanations of How
a violin works, Bows and strings
and Strings, harmonics and standing
waves.) A mode of vibration is just a way of vibration.
Think what happens when you strike a xylophone bar in the middle
and set it vibrating. The bar is supported at two points towards
the ends. The simplest mode of vibration is this: when the middle
of the bar goes up (as shown by the solid lines in the figure)
the ends of the bar go down. When the middle goes down (dashed
lines), the ends go up. The two points that do not move are
called nodes and are marked N in the diagram. (If "modes"
and "nodes" sound confusing, remember that the node has
no motion.)
Here is a sketch of a simple mode of vibration of a bar. Think
of it as a xylophone bar, which would be supported at the
nodes, and you would excite this mode by striking it in the
middle. This first mode of the bar is rather similar to one
of the modes of vibration of a simple rectangular plate, one
that is called the (0,2) mode (the naming convention is explained
below.)
Now let's look at photographs of the Chladni patterns of
(left) mode (0,2) of a uniform rectangular aluminium plate
and (right) mode 2 of a violin back plate.
. .
In these pictures, the lines are formed from sand that has collected
at the nodes, but has been shaken off the moving regions. The violin
back is more complicated in shape, and so the nodes also have a more
complicated shape. White sand was used for the black-painted aluminium
plate, and black sand for the violin back.
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Here is a sketch of a simple mode of vibration of a bar. Think
of it as a xylophone bar, which would be supported at the
nodes, and you would excite this mode by striking it in the
middle. This first mode of the bar is rather similar to one
of the modes of vibration of a simple rectangular plate, one
that is called the (0,2) mode (the naming convention is explained
below.)
. . 
This sketch represents (with exaggerated amplitude) an instant in the
motion of the mode for the rectangular plate which is shown in the second
photo above.
