The sound of accoustic feedback

When acoustic feedback occurs between loudspeaker and microphone it always seems to generate a signal of similar frequency despite vast differences in the components involved from one system to an other. I recently heard feedback between 2 mobile phones and this must include substantial propagation delays yet the frequency is not dissimilar to that obtained by putting a mic in front of a loudspeaker. My question is what physical properties determine the frequency of oscillation in such systems.
COnsidering that the speed of light takes a signal around the world over seven times in a second, there is not a lot of propagation delay - in terms of audio and our listening perceptions - in wireless communication. Not enough to affect the audio. If you are talking around the world with several satellite hops in between, you can encounter that brief delay, but locally not.

Feedback occurs when the output of a circuit goes back into its input. In the case of mics and speakers on stage or walkie talkies, the freq that will ring out first is the one the system is mopst sensitive too, the one it responds to most strongly. No system is utterly flat. There will always be peaks in the response curves, especially when transducers are involved - mics and speakers.

In professional sound systems when we start to turn it up, the system may start to ring, and if increased further will break out into oscillation. We use equalizers to eliminate this. If the system is ringing at 800Hz, then we reduce the gain at 800Hz on the equalizer. Ultimately the response on the graphic equalizer is sort of an inverted view of the system response.

Each element has its own response peaks. In a mic it has to do with the dimensions, yes, but also the situation it is in. Even the angles between things matters. If you hold your wireless phones together they will feed back, but you should note that as you move them around there will actually be several freqs they squeal at as you move them, not just one steady freq that comes or goes.

Look at the response curves published for some mics. As you move off axis there are often lobes of response, and they vary with freq as well as angle. SO the angle between mic and speaker makes a difference which freq will be emphasized.

As to what physically makes a mic peaky, I cannot speak to that beyond noting the diapragm size, composition, mounting and suspension arrangement, acoustic environment, and so on all contribute.

Mics for live sound often have a upper mids "presence peak" that makes it more likely it will feed back at 2000Hz than 200.
always seems to generate a signal of similar frequency
Not in my experience.
In fact the frequency varies considerably with slight changes in orientation of the transducers. In general, I suspect that the greater the distance between them the more likely it is that LF modes will be excited, but many other factors such as are room resonances will have a major influence.
Certainly, a mic / speaker system with a flat response will put up with more gain before howlround than a peaky one, just as you'd expect.
Though I agree that there is a large variation in frequency I have never heard it cover the entire audio range or even what you would think was the entire range of even cheap microphones or speakers as found in mobile phones. Perhaps I should rephrase the Question as "Why do you not get feedback at very low or very high frequencies" I have never heard feedback at 12 KHz or 200Hz for example and why does the propagation delay inherent in the mobile phone system note make a big difference

As Enzo has pointed out, feedback can and does occur pretty much anywhere in the audio spectrum.
I suspect that LF feedback is less common in 'domestic' situations though, as the mic would have to be situated in the region of a wavefront peak or trough for maximum gain (I think...), which implies increasingly greater separation of the transducers as the frequency falls. Of course, I'm considering a direct path here, without all the complications introduced by reflected wavefronts.
Certainly some experts speak of acoustic feedback as being a phase phenomenon rather than in the frequency domain - but that water can become very muddy at times;)
Unless I need something else specifically, I use 100Hz in the shop for a general purpose test tone. Main reason being that I can listen to 100Hz fairly loud for a period of time, whereas the more common 1000Hz is piercing and hard to listen to for more than a moment.

In my head I know the telephone has a response that goes down to maybe 300Hz and up to maybe 3000Hz. But it never ceases to amaze me that I can have 100Hz blaring in here, and someone on the other end of the phone hears nothing. Emotionally I want to think, geez it is so loud SOMETHING ought to come through, but it doesn't.

So with the mobile phone at least, that is why there is never feedback out of that 300-3000Hz range.

"In fact the frequency varies considerably with slight changes in orientation of the transducers."

That is what I was trying to say, but you put it much better.

In guitar amps we often have reverb pans feeding back acoustically and that happens under 20Hz.
There are different approaches to feedback abatement. In sound reinforcement, we use graphic equalizers to tune the system, but there are also units that watch for individual frequencies to peak and remain, and they will then respond with a reduction in gain at that freq. A notch filter. Good units will have several of these dynamic filters so more than one sensitive freq can be controlled. The Peavey Feedback Ferret is a good example of this. SOme units will have several fixed freq filters - you set them up ahead of time - and then a few roving filtets as well.

Another approach is the freq shift. Feedback happens when a signal is sent through a system over and over so it builds. Certain antifeedback units will shift the freq of a signal coming through ever so slightly so the next time through it is not at the same freq so it cannot build. They can be very effective, to the point that you can aim your mic right into the speaker and it just WON"T. I can't think of a specific model name at the moment for these types.