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Sound and supersonic motion -- a question from Feynman's lectures

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In chapter 51, volume 1 of the FLP, Feynman writes
Quote:

Incidentally,...it turns out, very interestingly, that once [an] object is moving faster than the speed of sound, it will make sound...Any object moving through a medium faster than the speed at which the medium carries waves will generate waves on each side, automatically, just from the motion itself.
Unfortunately he didn't give a justification for this claim. I was hoping someone in Physics Forums could fill this gap in.

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