Hi-
This is a very common problem. It is usually referred to as
common mode interference (I think).
The cause is usually that your power cable to your radio is acting as an antenna and is picking up a
60 cycle hum from your AC wiring and other potential radiators. Radio forums discuss this a great deal.
One solution is to wind the power cable around a ferrite core (choke) made of
number 42 material. The choke should be as close to the radio as possible.
Radio Shack makes a nice core that they sell blister packed, in pairs for about $8 (?)
As you can see, it opens up to make it easier to wrap. I think that the card that they come in has wrapping instructions.
NEATNESS REALLY COUNTS HERE. These cores also may be snapped together for more effect.
Check out Google Groups with the terms (without quotes)
"ferrite ac interference radio"
for more. You may have to juggle these terms a bit.
Usually this happens with 'wall warts' and I'm a bit puzzled that it's happening on a Superradio as mine doesn't use a wart (Superradio III).
Another solution, as previously mentioned, is to run it on batteries. The Superradio III gets
400 hrs (!) on one feeding of alkalines and that's how I have always run the ones I've had.
Good luck