Transverse bending waves and the breaking broomstick demonstration

When a broomstick is supported at both ends by two wine glasses, a strong downward blow to the center will break the stick, leaving the wine glasses undisturbed, provided care is taken to cushion the wine glasses against an initial and brief downward motion of the ends of the broomstick. This downward motion is analyzed and estimated to be about 1 mm in magnitude. Qualitative experimental evidence of this motion is easily obtained using a force probe to monitor a light and nondestructive tap to a 2-m measuring stick. The method of analysis developed here leads to a simple derivation of the dispersion relation for transverse bending waves on a long rod.