The hum goes away when I plug the amp into the second receptacle of the wall outlet, or when I use a cheater plug to connect it to the Shunyata.This is caused by something called a ’ground loop’. Its generally a sign that some part of the system is inappropriately grounded. I’m not talking about the power cord and its ground connection nor the use of a grounding post (which I think you’ll find won’t help).
I’m talking about the way a component is internally grounded. How it should work is if there is a metal chassis, it should be grounded thru the power cord. But if the audio circuit inside is directly grounded to the chassis it leaves the circuit open to ground loops. To avoid this, none of the audio circuit should be tied to chassis, instead an impedance of some sort (a resistor perhaps) should go between the two, allowing the audio circuit to float at ground potential (this is the reason why RCA connectors have insulating shoulder washers to insulate them from the chassis, even though the barrel connection is 'ground'). The resistor should be high enough resistance (if a resistor is used) to prevent the ground loop.
I’ve really boiled this down; grounding can be a very complex issue!
If you own a component that has a poor internal grounding scheme (IOW its use causes a ground loop in your system) you can get around the problem by use of an isolation transformer between the AC outlet and the component. Its not the best solution (you have to get a big enough transformer) but it does work. I prefer to have the grounding of the components set up properly to begin with...