This shape rings for several seconds. Plates with slightly different geometry are quickly damped.	Sonagrams showing the sounds made by striking the plates shown with a rubber mallet. (Reproduced from our article in Acoustics Australia.)

What is surprising when you hit a bell plate is the loudness, clarity and sustain of the sound. Bell plates are polygonal metal plates that are played like handbells but are rather cheaper. However, only a limited class of shapes works for bell plates: in general, polygons with a handle at one corner just go “clunk”. The dependence on shape is critical.

This sensitivity to shape — which is quite astonishing when one holds two slightly different shapes in the hand — is explained by the modes of vibration and the requirements of supporting a percussion instrument. First, the handle must be at a node of vibration: a place where vibrational velocity is zero. Otherwise, translational energy is transmitted to the player’s hand and quickly lost. But this condition is insufficient: local rotation or torques at the handle are also effective at quickly damping the vibration.

The standard bell plate shape can be considered as a rectangular plate with two corners removed and a tang for the handle attached. The lowest vibrational mode of a rectangular plate has two nearly parallel nodes. Removing successively larger pieces from the corners gradually bends these nodes towards each other. In a family of shapes, which includes that used for commercial bell plates, these nodes fuse at the tang, providing an extended region with neither translational nor rotational motion.

The sonagrams below (amplitude in a logarithmic grey scale vs time and frequency) show the sounds made by striking the plates shown with a rubber mallet. A standard shaped bell plate (top) has several short transients, but its lowest mode rings for much longer than several seconds. After a 25 mm strip was cut from the low edge (bottom), the lowest mode is heavily damped.

Sound files and photos illustrating the effect are at http://www.phys.unsw.edu.au/music

Daniel Lavan, John Tann and Joe Wolfe