hmmm.... using a wall wart for power.....

Many "modern" wall warts now contain switching supplies instead of the traditional xformer/rectifier setup in order to meet minimum efficiency standards
that now apply in many areas.
That may well be the source of your noise. Like Mike said... an electrolytic cap of a few hundred uF, with 1 or more small (.01-.1uF) ceramic caps in parallel may help a lot.


steve