## Sand Patterns on Circular Chladni Plates

Our research was an examination of the rings formed by sand on a circular Chladni plate of radius 12 cm when it was driven at frequencies between 50 and 1050 Hz. We tried to find a relationship between driving frequency and number of rings, based on the formula for finding resonant frequencies in an open-ended pipe. This was a good fit because both edges are antinodes (points that vibrate the most rapidly and at the highest amplitudes), just like in open-ended pipes. Our procedure was to slowly increase the frequency until we found a resonant frequency (one at which the sand formed a clear pattern on the plate), then adjust the frequency slightly until we find the most stable shape within 15 Hz of the frequency. Once we had this shape, we measured the distance between the plate's center and the outer edge of the sand ring along a predetermined line. We found that we were able to predict very accurately the number of rings that a given frequency would produce on the plate.

### Research Done By:

Richard Gibson*Center Line*

Brendan Roney*South Lake *