Chladni’s law for vibrating plates

Abstract

The normal vibrational modes of free circular plates can be classified according to the number of nodal diameters m and the number of nodal circles n. Chladni observed that the addition of one nodal circle raised the frequency f about the same amount as adding two nodal diameters, and Rayleigh pointed out that f is proportional to (m+2n)2 for large f. Waller, however, concluded that the number of nodal diameters necessary to raise the frequency as much as a nodal circle varies from two to five. We have examined data on the vibrations of flat and non-flat circular plates and fitted their vibration frequencies to the relationship f = c(m+bn)k. By proper choice of c it is possible to satisfy Chladni’s law (b = 2, k = 2) over quite a wide range of frequency in flat plates. Non-flat plates such as cymbals and bells, require different choices of b and k. A brief history of Chladni patterns, and suggestions for observing and demonstrating the vibrational modes of plates are included (AIP).