I'll start by saying, Audacity is not the best software for this type of sound design. It's an audio editor, but really, it's just used as a free recorder and very simple editor, mainly by novices. It doesn't have the dynamic features to create a complex, moving sound like this. You can, however, create simplified examples of some of the effects present in the audio clip you provided.
(I should also note, live sound isn't really my field)
So, what are we trying to replicate?
To recreate the effect, we need to know what's going on, on a basic, practical level. The audio clip contains microphone feedback ("Howlround" as known by some professionals with more live sound knowledge than me :)). You can easily create it by waving a mic in front of the output speaker, but I wouldn't recommend it. It's also known as "The Larsen Effect", named after the guy who first studied the effect.
But what is actually happening? Well, the input of the system is being fed by the output, and if the amplifier gain passes a critical level (>=1), we start to get a runaway reinforcement loop at some prominent frequency, where self-oscillation will begin to occur (That's kind of how electronic oscillators work). Fortunately, there are limiting factors in how large the signal can get, which can be physical limitations or an electronic limitation (Usually clipping or voltage limiting circuitry), but unfortunately, the signal voltage can pass the safe power rating of the system and so it can damage equipment, and it can also damage hearing.
But what causes the screeching? Due to resonant frequencies in the room, the microphone, the distance between speaker and mic, the system and the speaker, one frequency will always be positively reinforced more than others. This can sometimes be changed by waving the microphone around, causing different frequencies to be reinforced or cancelled, creating positive and negative feedback. This is also what causes the high-feedback phasing effect that can be heard as the mic is moved around.
How can we recreate this effect in a software environment?
Now we know what is actually happening, we can begin to build an effect capable of recreating these physical and electronic features of the process. I knocked up a quick model in Reaktor to show you the direction I would go.
I simply created a sampler to run an audio loop, then sent it through this feedback loop then took the output before it looped back:
- Filters (Speaker response model)
- Diffused delay module (space between speaker and mic)
- Filters (Mic response model)
- Signal multiplier (feedback control) (Amp Gain)
- Clipper/Shaper (To model amp power cutoff)
- Split signal to go back to 1 and also out to Reaktor output
I also added some compression, distortion and other subtle effects to get a more "live" feel.(again, I haven't fussed about, it took me longer to write this answer)
I recorded an example of changing the mic distance and also the feedback gain. These things should happen at the same time, but as this was a quick mock-up, I was just using one virtual knob at a time for each.
But your question is how to recreate it in Audacity. Well, you can't ...easily do that. Unless you use a third-party plugin, which you could do, these are out there.
The trouble with doing it yourself in Audacity is getting the different effects to react and change over time. You can apply the EQ modelling and then apply a high-feedback phaser to get some of the substance of it, and maybe even then apply a filter with high resonance to hopefully force self-oscillation, then limit it with a clipping effect, but it would be very static and very difficult to progress further than that with the built-in effects and without a dynamic aspect to effect control. I wouldn't even put the time in to try that.
Positive and Negative Feedback
Electronic Circuit Oscillation
Gain in Electronics