I could hear the avoided crossing even at 9 Hz once I knew what to listen for. At the middle of the crossing (exactly 2.5s in), the two tones are both rising in parallel, essentially forming a continuously rising chord, which sounds very different from the combination of a rising tone and a constant tone.
Before I clicked, I thought the answer would be "like the sound of very busy traffic"... Instead, it turns out to be theoretical physics.
Wav files don't load in Chrome, but an intriguing review of an interesting phenomenon.