Could this be used for making something perfectly black or something like that? There was an A.C.Clarke story about a silence machine that reemits the sound with a delay to cancel it.
Seems like the cancelation happening in your scenario would likely be from a delay of half the period of the sound waves, effectively making them roughly "complementary" or "inverse". Can't say I'm familiar with the research, though.
On a sillier note, have you heard of the Speech Jammer? [0]
It's a device to disrupt a person's speech by playing it back to them with a delay of a few milliseconds. Hilarious results. Also easily reproducible at home if you're bored.
[0] https://phys.org/news/2012-09-speech-jammer-ig-nobel-winners...