Bigwheeledwagon: I am having the same problem as you... I do not have the problem when I plug my Strat directly into my blues Junior. When I add an effect between the guitar and the amp, I can faintly hear a radio station. The louder I turn up the gain on the amp the louder the radio station gets. Also, the radio staion level goes down when I stop touching the strings or metal parts of the guitar- leaving it floating. It seems to be a combination of things brings this out. Do these symptoms sound familiar to you?
