Resonances of a plate: Chladni patterns
For this experiment we use a small circular plate; a CD that we have painted black so the Chladni patterns will show up better when filmed.
This plate is quite stiff, and would be difficult to attach directly to a loudspeaker. In the earlier experiments the sinusoidal motion of the cone of the loudspeaker occurred because a sinusoidal current flowed through the loudspeaker’s ‘voice coil’, which is immersed in a steady magnetic field and attached to the loudspeaker cone. This produced a sinusoidal force on the loudspeaker cone.
In this experiment we will drive the plate directly. The sinusoidal current is passed through a small inductor (a coil of wire with no magnetic core) and produces a sinusoidal magnetic field. This is then placed close to a small magnet attached to the plate, and so produces a sinusoidal force on the magnet.
We used a 3 mH inductor from a loudspeaker crossover network – see figure 10. The exact value doesn’t matter, any reasonably sized inductor should be OK.
For this demonstration the plate as supported at its centre by means of a nut and bolt, the end of which was pushed in some reversible adhesive in a hole in some Perspex – see figure 9. However any rigid means of support that allows the plate to be horizontal would be OK.
The experiment was then assembled in a plastic tray – this is important as otherwise sand gets everywhere. Two small magnets are placed on the edge of the plate. The inductor is placed so its centre is directly beneath the magnets and as close as possible to the plate without touching it – see figure 8. (If you get a buzzing sound during experiments, it probably means the magnet is too close and touching the vibrating plate.)
Now sprinkle some dry sand over the plate and increase the frequency (we used 1 Hz steps for this clip).
You can hear sound because the plate is vibrating and acting like a speaker cone.
The mode shown here is the (3,0) mode, although the Chladni pattern is slightly distorted by the mass of the two magnets.
Several other modes are possible for this configuration.
There are several possible extension sto this experiment.
You can move the magnets about the plate and investigate different driving points, either near to or far from the regions where the sand accumulates.
You can investigate how the way the plate is supported affects the patterns.
You can investigate how additional masses affect the shape of the Chladni pattern by adding extra magnets.
You can also try plates of different shapes and materials.