The sound of church bells: Tracking down the secret of a traditional arts and crafts trade

The sound of church bells is part of most people's everyday life and can easily be examined with smartphones. Similar to other experiments of this column, we use a suitable iOS app. The underlying physical theory of church bells proves to be difficult. A reliable prediction of their natural frequencies based on their exact dimensions is only possible using the finite element method. If you ask bell founders how they calculate the rib of a bell (half longitudinal section of a bell, which completely determines the acoustic properties, Fig. 1) in order to get a church bell with the desired frequency spectrum, you will certainly not get an answer: the art of bell casting is based on centuries of experience and knowledge of the rib structure is only shared with direct descendants. We want to have a closer look at these well-guarded secrets, knowing full well that we cannot fully unravel them. This article presents simple mathematical models and a comparison with a data set of almost 700 bells.