I have two powered PA speakers plugged into my unpowered mixer. When the speakers are on and plugged into outlets they emit no hum. When one speaker Is on and plugged into the mixer with a quarter inch and the other speaker is on but not plugged into the mixer there is no buzz. As soon as both speakers are plugged into the mixer, There is a buzz. This is the only time the buzz is going on. I've tried different outlets and different cables and different power cords. Each speaker while on, when individually plugged into the mixer produces no buzz.
I plugged both speakers into the SAME outlet and stopped the ground loop. Ground loop averted. ground loop diverted. Ground loop no longer. Ground loop obliterated. Ground loop neutralized. Ground Loop destroyed. Ground loop beaten down. Ground Loop humiliated. Ground loop f in the a!
What type of cables are being used to transmit your output signal? If they're unbalanced jack connectors, they'll likely cause ground issues. Make sure you're using something balanced for this! (Balanced XLR or TRS is standard). This will, hopefully, prevent any issues in the future.