I have installation where a person makes a sound in a microphone and they hear the sound manipulated back 2 seconds later. The issue is that the mic also hears the delayed sound coming from the speaker so the sound gets stuck in a 2 second feedback loop. I'm considering workarounds involving cutting the mic gain but the ideal solution in my mind would be to cancel the sound coming from the speaker to the microphone while simultaneously continuing to actively capture sounds from people.

I played with delaying the sound using Zexy's [z~] instead of [delay~] and then subtracting the delayed sound from what the mic heard. With this method I tried to tweak the delay, considering the time it takes for the sound to travel from the speaker to the mic, but couldn't get any meaningful results. I also tried playing with this patch:
https://github.com/JosephEoff/PureData_NoiseFilter

and that did a great job removing feedback when no 2 second delay was present but it doesn't seem to be the appropriate tool for my problem.

Any thoughts or suggestions would be appreciated.

@whyameye Not an easy task.
The subtraction method needs the delay to be sample perfect to avoid artefacts and to be finely equalised for the microphone and the speaker so that the subtracted signal matches the returning signal.

The simple solution is not to use Pd and use an analogue preamplifier between the microphone and the speaker amplifier and keep the speaker fairly close to the microphone (1970's rock and roll).

The expensive solution is to use a professional sound card with asio (windows) or core audio (mac) so that the delay is not perceptible as an echo.... more like a chorus if it is perceptible at all.... but you still need the speaker close to the microphone because of the speed of sound, and there is always a limit to volume before feedback.

Ah! I just read your post again.
You are introducing the 2 second delay on purpose within Pd using [delay~]?
A sound booth, or putting the microphone in another room would be a solution.... or would that ruin your installation...?
David.

Hi. Thanks for the response. Yes I'm introducing a 2 second delay on purpose within Pd. I tried using |delay~| and also Zexy's |z~| hoping for more control. Unfortunately we can't put the microphone away from the speaker. It's an outdoor installation with the intention that kids run up to it, make their crazy noises, and hear more crazy noises come back to them.

All I've come up with so far is to use |bonk~| or |sigmund~| (I'm trying both to compare results) to see when the kid starts talking into the mic. I make the mic live for 2 seconds then cut the mic for 2 seconds when I see that. I'm thinking to add some LEDs to give the kid an indication of when the mic is live. That's the best I got so far.

@whyameye Then you need a microphone that is very directional...super cardioid (shotgun)... or at least cardioid.
The Shure SM58 is still one of the affordable best cardioid with good rejection, but will still pick up some surrounding sound.
Sports presenters used to use a microphone that covered their mouth but there are a few good reasons not to use that here.
David.

Directional mic is a good idea. Thanks for that!