If a microphone gets too close to a speaker, the microphone picks up any sound coming out the speaker, sends it back through the amp for more amplification, where it is then picked up again by the mic, and sent back to make even louder, etc.
Why is this sound always high-pitched and ear piercing? Why not a low rumble, a pleasant A 220 Hz, or something like that? Why does it always feel like an ice pick hitting your eardrum?
The frequency of feedback howl is determined mainly by resonances in the mic, speaker and amp. Unfortunately for your ears, these tend toward the high side.
Former semi-pro audio engineer here. Feedback is a resonance of the audio system in question, and its frequency depends on a number of factors, including the characteristics of the speakers and mike, the distance between them, and the resonant frequencies of the room.
I would guess that the reason feedback is usually in the high midrange is that speakers and mikes are more sensitive to that range (and components between them are usually set to emphasize it), because that’s where the human voice is in the audio spectrum.
Although audio components are said to have a range of 20 Hz to 20,000 Hz, few are flat across that range, and most total systems have a peak between about 400 and 4,000, the range critical to voice intelligibility.
But if you filter out the high frequencies you can get LF feedback.
Think of it like this, feedback only grows when the crest of a soundwave has traveled from speaker to mic and unloaded its energy. For a given time period, a high frequency wave will crest more often than a low frequency wave… thus high frequency feedback grows at a greater rate than low frequency feedback.
It’s not that low frequency feedback doesn’t occur, it’s just that you can’t hear it over the already-much-louder high frequency squeal.
If you have a space with acoustics that interfere with certain sound frequencies based on shape or material composition, you can get whatever tone you want.
A typical vocal mike like the Shure SM58 has a peak sensitivity at about 4kHz and the PA speakers (most likely 1 or 2 inch horn-drivers) are more efficient than lower frequency speakers. Result when the gain is turned up is squeal at the very frequency your ears are most sensitve to, ouch. I’d expand but I’ve got work to do.
Testing, tessssting, one two, one two. . .
[SDMB Qualifier ]Also the speed of sound in whatever medium the room is filled with!
Slight hijack…
You see performers on B stages all the time now where the mic is more or less directly in front of the PA but there’s no feedback. I’ve seen ads in music mags for feedback suppressors which I guess are the reason why - how do they work?
You can put a mike in front of a speaker provided there isn’t enough gain in the system to cause positive feedback.
I don’t know how well feedback suppressors work (we didn’t have them back in my PA-guy days) but they won’t let you just stick a mike in front of a PA and wang everything up to 11. The ones suitable for music use notch filters which will work fine for squashing squeal-like feedback, but when the gain is high across the whole spectrum it will basically feedback at any/all frequencies at once and you’re back to turning the overall volume down.
Missed the edit window.
I’m behind the times 
On a bit more Googling I found this. Wow! Maybe these days you can just wang everything up to 11.
Good point! Feedback is much worse when you’re working underwater because the speed of sound is five times faster. I forgot about the problems we used to have when mixing sound at the bottom of swimming pools. And in the ocean, the fish used to swim into the speaker cabinets. What a pain!
Oh my yes! I was once running camera cables in an auditorium where they were simultaneously trying to tame a resonance peak at something around 90 Hz. I’m not exactly sure how it happened - I think someone just grabbed the wrong faders and opened some mikes. It was like a big engine trying to catch and run - the hum started loping in loud pulses then the feedback loop closed in on itself. The sound pressure was so intense as to be disorienting until someone could hit the master gain.