Metronomes generally keep their own beat -- that's why we love them -- but when several get together, a compromise is hammered out
This charming little video demonstrates the principle of resonant frequency using oscillating metronomes. The mechanical wind-up metronomes used worldwide during the dreaded Saturday piano lesson employ an inverted pendulum to keep even time intervals. The resonant frequency of the pendulum is adjusted by moving the mass up and down. Sliding the mass higher up the rod decreases the resonant frequency of the pendulum by increasing its rotational inertia.
In the demonstration, each metronome is set to the same frequency, but they are originally all out of phase with each other. This means that at any given moment they are each in different parts of their respective cycles — thus creating a rhythm too complicated for the average music student. When they’re sitting on the table they stay out of phase, because they are not affected by the others’ vibrations. However, when they’re placed on the piece of wood, although the metronomes are not in phase, they impart a net average vibration. Notice how the wood begins to oscillate back and forth as well. As the wood vibrates, it begins to force all of the metronomes into the same pattern. This is a condition called forced resonance. In this case, the forcing frequency of the wood is also the natural or resonant vibration frequency of each metronome, which results in maximum-amplitude vibrations. If you force an object to vibrate at a frequency other than its resonant frequency, its amplitude will decrease.
The idea of resonance is particularly relevant when constructing things like bridges and buildings. You don’t want these structures to have resonant frequencies similar to those of seismic waves from earthquakes. Ground shaking at the resonant frequency of a building can initiate vibrations in the building at a very large amplitude. This is obviously not a desirable situation, and modern engineers use a variety of techniques to avoid this when designing buildings in earthquake zones. However, as far as metronomes are concerned — let them oscillate!
Adam Weiner is the author of Don’t Try This at Home! The Physics of Hollywood Movies.