## 5pMU8. Vibrational modes of cymbals and Chladni's law.

### Session: Friday Afternoon, December 6

### Time: 4:00

**Author: Charles Wilbur**

**Location: Phys. Dept., Northern Illinois Univ., DeKalb, IL 60115**

**Author: Thomas D. Rossing**

**Location: Phys. Dept., Northern Illinois Univ., DeKalb, IL 60115**

**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.

ASA 132nd meeting - Hawaii, December 1996