AC adapter and audio interference
One way that I've used to defeat hum is throw an ferrite inductor or a toroid choke around the wire connected to your device. The noise might not be conducting through that wire, maybe another wire, so it might take some effort to find which one it is. 

If you have a toroid wide enough you can coil the wire around the inside with a few turns (if the connector will fit through) 

You can buy clip on inductors from many sources. They clip onto the outside of the wire and increase its inductance. 

By increasing the inductance you create impedance (or an equivalent is resistance) for high frequency signals, which are usually the ones that create interference. 

I've used this for a clock radio (I had a powerline adaptor that sends high frequency signals to transmit network information) and for audio cables in my car (to block high frequency signals from DC to DC converters from 12V devices from getting into my car radio)