Why are bells, well, bell-shaped? At first glance this seems a simple question, but there is a surprising amount of depth and beauty to the logic behind a bell.
The bottom is usually round for three reasons. One, the circle is a much structurally stronger shape than, for example. a rectangle, preventing the bell from cracking when rung.
Two, the rounded shape allows sound waves to bounce and travel along the perimeter. The standing waves that result from this are what produce the resonance associated with bells.
Three, the wide bottom allows sound to pour out downward, loudly. Useful to hear a bell placed at the top of a church from anywhere in town!
The reason for the bell’s diameter decreasing as you go from bottom to the top is so that, when rung, the bell will resonate at different frequencies. In larger bells, this can allow them to produce entire chords, all by themselves, making music from shapes.
As you can see, the bell is one of the simplest and most elegant examples of mathematics as an art.
