Modes of vibration and decay times in cymbals

Abstract

The principal modes of vibration of a cymbal, which dominate at low frequency, have m radial nodes extending outward from the cup to the rim. Their modal frequencies can be fitted to an equation of the form f = cmk, where parameters c and k take on one set of values for small m and another for large m [R. W. Peterson and T. D. Rossing, J. Acoust. Soc. Am. Suppl. 1 66, S18 (1979)]. We have studied modes of vibration in over 60 cymbals having diameters from 8 to 24 in. and thicknesses from 0.02 to 0.09 in. Although c varies with diameter and thickness, as expected, values of k are surprisingly similar in large and small cymbals. Average values are k1 = 1.73 and k2 = 1.60. Decay times have been measured when the individual modes are excited at small amplitude in the steady state, and also when the cymbal is struck in various ways. Modal decay times decrease with increasing frequency, whereas decay of the percussive sound depends upon the manner of striking. [Work supported in part by the Avedis Ziidjian Comp...