H. John Sathoff
Phys. Dept., Bradley Univ., Peoria, IL 61635
Thomas D. Rossing
Northern Illinois Univ., DeKalb, IL 60115
The fundamental frequency of a bell has roughly the same dependence on thickness and diameter as flexural vibrations in a circular plate, and thus in designing a bell chime or ensemble of bells, it would be possible, in principle, to scale all dimensions proportional to 1/f. Tonal considerations often dictate otherwise, however, and in practice different scaling laws are found in ensembles of large and small carillon bells, church bells, handbells, and ancient Chinese bells that have been studied.