My tube amp causes isolation transformer to buzz

So I have an ARC Classic 60 tube amp that was causing a hum/buzz on my speakers regardless of volume.  In an effort to eliminate variables I plugged the amp into a Variac Transformer.  The sound from the speakers was almost completely eliminated, however once the power was turned on at the amp the transformer, which was otherwise silent, started to buzz.  Not super loud but audibly.  My amp draws 350 watts at idle. My Variac can handle up to 800 watts. 
So my question is, does applying a load to a transformer cause it to buzz, or can the amp cause the transformer to buzz?