What do avoided crossings sound like?

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2022-07-02 07:00:06

One interesting mathematical phenomenon I encounter regularly in my research1 is that of avoided crossings. These emerge when, over the course of the evolution of a dynamical system, any two of its normal-mode frequencies become near-degenerate. If the two normal modes should be weakly coupled to each other in some fashion, then rather than actually becoming degenerate (and having their eigenfrequencies cross), the system responds in such a way that the actual normal modes exchange character smoothly between the two uncoupled modes; during this process the actual mode frequencies also interpolate smoothly between their uncoupled values.

I've made some sonifications of seismic data before for outreach purposes (and it sounds quite messy to the untrained ear), but I've been wondering lately what an idealised avoided crossing would sound like instead. In particular, would the human ear be able to distinguish between different strengths of coupling between the isolated components? I also haven't written a technical blog post in quite a while, and I thought this would be an interesting exercise. Here we go!

For this blog post I will be producing CD-quality PCM WAV files at a standard sampling rate of 44.1 kHz with 16 bits of dynamic range.

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