Subharmonics, bifurcations. chaos and all that jazz
I. Rudnick, Robert M. Keolian · The Journal of the Acoustical Society of America · 1981
In this, the sesquicentennial of the publication of Faraday's landmark experimental observation [M. Faraday, Philos. Trans. R. Soc. (London) 299 (1831), Sec. 103; Lord Rayleigh, The Theory of Sound (Dover, New York, 1945), Sec.68b] of the subharmonic, f/2, in the crispations generated on a flat horizontal plate wet with water when it is oscillated vertically at a frequency f, we report on the results of a version of this experiment where we observe subharmonics of frequency f/m where m, at this writing, has been observed to have the values 2, 4, 12, 14, 16, 18, 20, 24, 28, 30, 32, 34, 35. Moreover harmonics of these subharmonics occur in profusion so that the frequencies which appear in an FFT graph are given by pf/m, where p is an integer which can reach values as high and higher than 2 m. The transition to a chaotic [Physics Today 34, 17 (March 1981)] or turbulent state is observed.