| I am assuming that this is a two-speaker setup in a large room. Are both speakers on the same channel of the amplifier or are they on separate channels? If the channels are separate, you could probably "balance" everything out by turning down the volume on the speaker closest to the "ringing" side.
Unless your room is perfectly symmetrical in every way, you are going to get some degree of variances in the amount of feedback that you get through the mic.
To give you a layman's perspective of how feedback works, basically when sound comes out of the speakers, some of it goes back into the microphone and back out through the speakers again. In a desireable situation, the sound dissapates with every recurring cycle. In an undesireable situations (e.g. when you hear a loud squeal) the sound is being amplified and re-amplified with every cycle. The "ringing" that you hear indicates that you are teetering right on the threshold of both examples. (the sound is over amplified and then it quickly dissapates)
There are a few things that can cause one side of the room to have more feedback than the other:
1. Odd shaped room - Your surfaces on that side of the room could have a shorter distance between the wall, microphone, and the speaker.
2. Varying surfaces - You could very well have one wall surface that is more sound reflective than the other.
3. Mismatched number of speakers - Some room setups have two speakers or two stacks/arrays of speakers that cover the entire area while others might have 2 sets of main speakers and then another pair to facilitate a seating section that is not directly in line with the main FOH.
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