Notes on Resonance

Resonance occurs when two sources of excitation fall completely in sync, and reinforce one another endlessly. In this state, the sources convey an unbounded amount of energy over time.

Pictured below is a local signal (blue) and a signal received from a distant source (orange).

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The coupling between the two sources is represented by the product of their signals.

(Bringing signals into a context for multiplying is called “mixing”.)

Integrating this product over time yields the cumulative energy.

In most cases, including the example above, net energy remains small, because the wavelengths of the signals are not exactly matched.

However, if the sources happen to be on exactly the same wavelength, resonance occurs and energy grows without bound.

For perfectly-matched sources such as these, the rate of energy growth is determined by the phase difference between them.

If the signals are moved into an orthogonal phase relationship, the observed energy drops to zero, and the sources appear not to be interacting.

But once the sources are brought back into perfect phase alignment, energy growth resumes at the maximum possible rate.