Not a physicist, but this might not work quite the same since light is both a particle and a wave, whereas sound is just a pressure wave on a given medium. Would happily be proven wrong though!

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...

The story is “Silence Please” (1).

(1) https://en.wikipedia.org/wiki/Silence_Please

Re-emits the opposite sound?

Like noise - canceling headphones, presumably.

Exactly like noise cancelling headphones. Also like any number of industrial noise cancelling systems.