Chladni Plates
standing waves - two dimensional oscillators - harmonics
What it shows:
The excitation of various modes of vibration in two dimensional oscillators with free edges called Chladni Plates.
How it works:
A Chladni plate consist 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 set up form a
complex but symmetrical pattern 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. We
have four brass plates
1
mounted in a row on the same wooden platform, two circular (diameters 20cm and 25cm, and
two square 20cm and 25cm of side). Each is attached to a wooden base by a 10cm brass rod.
The plates are driven using a cello bow. Hold the plate with finger or thumb at a point on the
edge (this point will automatically become a node) and draw the bow down across the edge.
The plate will ring loudly (if you manage to excite a mode of vibration!) and repeating the strokes
of the bow will drive that mode (practice makes perfect!) The sand will start gathering at the
nodes and a pattern will appear. Where the bow strokes in relation to your finger will dictate
which mode of vibration you excite. For simplicity, maybe start by holding a corner of the square
plate, stroking the middle of a side, or stroke the circular plate 45° around from your finger.
Setting it up:
The plates can be made visible by mounting a mirror behind the row of plates, angled so that the
top of the plates are visible to the audience (same idea as in Polarization by Scattering). Create
the optimum angle for the front rows, as the back rows will be looking down on the plates anyway.
Make sure the cello bow is nice and tactile by treating it with rosin before the performance.
Sprinkle the sand on the plates so that it forms an even cover. Don't overdo the amount.
Comments:
Good demo to show how complicated modes of vibration can get by increasing the number
of dimensions. Reference 3 uses paper scrapers instead of Chladni plates. Rating****
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)