More sound of church bells: Authors' correction

Abstract

In the recently published article “The Sound of Church Bells: Tracking Down the Secret of a Traditional Arts and Crafts Trade,” the bell frequencies have been erroneously oversimplified. The problem affects Eqs. (2) and (3), which were derived from the elementary “coffee mug model” and in which we used the speed of sound in air. However, this does not make sense from a physical point of view, since air only acts as a sound carrier, not as a sound source in the case of bells. Due to the excellent fit of the theoretical model with the empirical data, we unfortunately failed to notice this error before publication. However, all other equations, e.g., the introduction of the correction factor in Eq. (4) and the estimation of the mass in Eqs. (5) and (6) are not affected by this error, since they represent empirical models. However, it is unfortunate to introduce the speed of sound in air as a constant in Eqs. (4) and (6). Instead, we suggest the following simple rule of thumb for relating the radius of a church bell R to its humming frequency fhum: R≈100 ms−1fhum.(1)