The Bell's Parish: Audibility Radius, Households Reached, and the Bell Mass at Which a Solar Horn Wins on Cost

A church or village bell is bought by weight, but what a parish actually receives is an area within which the bell can be heard. This paper models that area from stated assumptions: a source level at 1 m of 118 + 10 log10(M/100) dB for a bell of mass M kg, spherical divergence on the slant path from the tower, a ground-and-air excess attenuation of 0.08/h dB per metre for tower height h, a rural ambient of 35 dBA, and an audibility criterion of 45 dBA. At a settlement density of 12 households per km², a 100 kg bell in a 20 m tower is audible over a radius of 1879.6 m and reaches 133.2 households at an installed cost of USD 7000, or USD 52.56 per household reached — the most households per unit cost of any mass tabulated, at 19.03 households per USD 1000. Raising the same bell from a 10 m to a 30 m tower extends its radius from 1321.9 m to 2243.2 m. A single solar-powered horn (112 dB at 1 m, 60 degree sector, USD 650 complete) reaches only 4.5 households in total at this density, but at USD 144.67 per household; it passes the bell on households reached per unit cost only above a crossover bell mass of 2560 kg. Below that mass the bell is the cheaper way to be heard per household, though the horn is far cheaper to buy outright. SIMULATED, NOT MEASURED.