The usual hum source is nonbypassed diodes in the wall wart, which
provide a nice RF ground when they conduct and none when they don't,
thus changing the antenna system 120 times a second when there's an
instant that they're all not conducting at once.
Even if you ground the radio yourself, they still change the antenna
system, though usually it matters less the more grounded the radio is.
One test is whether the hum changes if you hold a hand on the radio,
improving its RF ground a bit.
The fix is a wall wart with bypassed diodes, or NiMH batteries, which
are good enough these days so you don't really need the wall wart.
Just swap a battery set when needed.
--
Ron Hardin
On the internet, nobody knows you're a jerk.