Just that, well, consider the expansion, and what's causing it. So, you run current through the inductor, which magnetizes the core, and it expands. Turn it off, and it un-expands (despands..?!).
If the current were a +/- square wave, it would expand, contract then quickly expand again (as it crosses through zero), and so on; the contract-expand action only occurs for a split second, while it remains expanded for most of the time; the amount of acoustic power is small (though rich in harmonics, because it's a very spiky waveform).
Now, if current remains one sided (positive or zero, never negative), there's no reason for it to re-expand, so it should indeed be audible at the burst frequency, and not some multiple thereof (harmonics aside).
Tim