I've done some searching and can't find a solution to this.
I have speakers and headphones, which I connect to my computer using a small extension cable that came with the headphones. This sits on my desk, and I switch out the headphones and speakers depending on which I want to use.
I recently noticed that the speakers produce a low humming whenever they are UNPLUGGED from the computer. This goes away immediately when I plug them back in. Volume does appear to affect it. I have been solving the problem by turning down the volume to 0, and it goes away.
The speakers are on the other side of the room, where I keep a separate monitor for watching movies, etc, so there is a long cable connecting them. I have checked and moved the cable away from power sources, but that has had no effect.
That is normal hum. You have no input to the powered speakers. If you connect the tip of the audio plug to ground (short it to the sleeve of the plug) the hum will stop.
The amplifier inside the powered speaker is going to hum when it has no input, so will any amplifier.