Abstract:
In 1830, Chladni proposed an empirical law relating the modal frequencies of a flat circular plate to the number of nodal diameters m and the number of nodal circles n. This law leads to a mathematical relationship for the modal frequencies: f[inf m,n]=C(m+2n)[sup 2], where C is an empirical constant. An earlier analysis showed that a modified Chladni's law f[inf m,n]=C[inf n](m+2n)Pn could be fitted to modal frequencies in a wide variety of flat and nonflat plates, including cymbals. Using electronic holography, as well as scanning the near-field sound, some 300 modes have been observed in a 16-in.-diam cymbal. These data can be fitted to a modified Chladni's law f[inf m,n]=C[inf n](m+2n)Pn [T. D. Rossing, Am. J. Phys. 50, 271--274 (1982)] or to a similar equation with three parameters f[inf m,n]=C(m+bn)P [Perrin et al., J. Sound Vib. 102, 11--19 (1985)], where b is also an empirical constant. Both modifications of Chladni's law appear to have some advantages in understanding the acoustics of cymbals.