Why Larsen effect produces always high pitched sounds, never low pitched?
the Larsen effect occurs when there is positive feedback between the output and the input of the sound system.
This means that there is (at least) 360 degree phase shift between the output and the input of the amplifier, with a gain greater than 1. This phase shift is made up of two components: an electrical phase shift, and an audio phase shift.
The electrical phase shift tends to occur naturally with any amplifier, as it will be designed to "roll off" at higher frequencies (although this depends on how the equalizer is set up). The acoustic phase shift is a result of the path difference from the speaker back to the microphone.
For a good amplifier, the electrical phase shift will be very small - so we need an acoustic phase shift. This means that there needs to be at least one wavelength of sound between microphone and speaker - but also, there needs to be a gain greater than 1.
In principle, a speaker that is 3.4 meters from a microphone will produce "singing" at frequencies of 100 Hz, 200 Hz, ... (and the further away you are, the closer spaced these frequencies could be). But then you have to look at the over all gain of the feedback: both the speaker and the microphone have certain frequency response, and there are typically multiple paths for sound to get from A to B. Now the more multipath there is, the greater the chance that there is some high frequency for which constructive interference occurs between all signals - in other words, the chances of getting positive feedback are greater at high frequencies.
This is actually hinted at in the article you link:
The frequency of the resulting sound is determined by resonance frequencies in the microphone, amplifier, and loudspeaker, the acoustics of the room, the directional pick-up and emission patterns of the microphone and loudspeaker, and the distance between them.
The ringing occurs at the frequency where the over all gain is greatest (with a 360 degree phase shift, or a multiple thereof). In an audio system with "perfectly flat" response, it's the acoustics of the room that help determine where that resonance sits - and unless you specifically craft a situation where you can leverage a low frequency mode of the room, it's likely you are finding a higher frequency resonance.
Take the simple situation of a floor: there is one audio path from the speaker directly to the microphone, and a second path that reflects off the floor. The path difference is not very large; but at a sufficiently high frequency, the path length will be one wavelength, and you get signal amplification.