I would venture to suggest the reason that the pasta-fragmentation process stops. Once the strand breaks, it becomes x number of new strands, each of which is still vibrating at some residual frequency and amplitude. The mass, diameter, and length of each resultant strand might determine the wavelength and amplitude necessary to break it. If a strand has gotten small enough that the amount of energy contained by the frequency and amplitude of the residual vibration are too low to cause enough stress on the strand, it doesn’t break. My wife has put me on notice that any further experimentation is strictly off limits in the kitchen, so I will leave the mystery to the experts.

Jim Longley
Allen, Texas