How do Thermoacoustics work? How would a thermoacoustic refrigerator work?

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My friend is getting his PhD in the above field. He tried (and failed) to explain matters to me. Maybe one of you can help?

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I hope that the mods won’t take me down, but I have two great videos by a guy that does some great DIY stuff:

Basically, thermoacoustics is that air expands and contracts as it is heated and cooled, which can create air flow that in turn makes things resonate. A thermoacoustic refrigerator compresses air at a certain point in a tube. When air is compressed, it warms up, and this heat is then drawn away from it. When it expands again, it has less energy than before and is therefore cooler.