Sounds like a ground loop problem.

I assume you're talking about a home computer speaker set...

First, triple check all connections to make sure you don't have a loose plug.

Next, I would start unplugging everything that the PC is connected to except for the bare minimum. For instance, leave the monitor plugged in, leave the kbd and mouse plugged in, leave the speakers plugged in. But unplug absolutely everything else including phone and network connections.

If the buzz is gone, start plugging things back in one at a time until the buzz re-appears. When the buzz re-appears, there's your ground loop. Change the way that object is grounded, for instance, move it to a different plug.