Knots in the resonator: elegant math in humble physics

At the heart of every resonator - be it a cello, a gravitational wave detector, or the antenna in your cell phone - there is a beautiful bit of mathematics that has been heretofore unacknowledged. Yale physicists Jack Harris and Nicholas Read know this because they started finding knots in their data. In a new study in the journal Nature, Harris, Read, and their co-authors describe a previously unknown characteristic of resonators. A resonator is any object that vibrates only at a specific set of frequencies. They are ubiquitous in sensors, electronics, musical instruments, and other devices, where they are used to produce, amplify, or detect vibrations at specific frequencies. The new characteristic the Yale team found results from equations that any high school algebra student would recognize, but which physicists had not appreciated as a basic principle of resonators. It is this: If you make a graph of how the resonator's frequencies change while you -tune- the resonator - by varying its properties in almost any way - the graph will show braids and knots.