Accumulation of sand at nodes of vibrating plate reveals resonance patterns.

What It Shows

A Chladni plate consists of a flat sheet of metal, usually circular or square, mounted on a central stalk to a sturdy base. When the plate is oscillating in a particular mode of vibration, the nodes and antinodes that are set up form complex but symmetrical patterns over its surface. The positions of these nodes and antinodes can be seen by sprinkling sand upon the plates; the sand will vibrate away from the antinodes and gather at the nodes.

How It Works

We have four brass plates ¹ mounted on a common wooden platform: two circular (diameters 8in and 10in), one square (10in), and one "stadium" (a 8in square with an 8in diameter semicircle at each end); all plates are roughly 1/16in thick, and each is bolted through the center to the wooden base by a 10cm brass rod.

The plates are driven using a cello or violin bow (for best results use plenty of rosin). Hold the plate with finger or thumb nail at a point on the edge—this point will automatically become a node—and draw the bow straight down across the edge. The plate will ring loudly if you manage to excite a mode of vibration, and sand will start gathering at the nodes to form a pattern. The distance between the bow and your finger will dictate which mode of vibration you excite.

Setting It Up

Firmly clamp the wooden base to the lecture bench. Use a video camera with a wide lens mounted to a benchtop stand. Sprinkle the sand on the plates so that it forms an even cover.

Comments

Good demo to show how complicated modes of vibration can get when we increase the number of dimensions.

References

1. E. H. Barton, Textbook on Sound (Macmillan, 1923)
2. E. F. F. Chladni, Acoustics: Historical and Philosophical Development, ed. R. B. Lindsay p.156 (Dowden, Hutchinson & Ross, 1972)
3. G. R. Graham, Physics Education 24 (1989) pp25-29
4. J. W. Strutt (Lord Rayleigh), Theory of Sound (Dover, 1945)

1 The origin of our plates is unknown, but similar examples are available from Cenco (70706) and Sargent-Welch (3314)