How do I get rid of speaker static?
It sounds like you are getting interference from the AC->DC power supply.  This can happen if you have a poorly regulated power supply, so that some magnitude of the AC wall voltage (~120V) is coupled onto the DC output voltage (between 5V and 12V, probably).  This in turn gets transmitted through the circuit and shows up at the output as a hum at the AC wall frequency (60Hz) or its harmonics (120Hz, 180Hz, 240Hz...etc).

mains-hum-wiki

You could try powering from a battery; if this fixes the problem you know for sure that you need to improve the power supply.  Alternatively, listen to the sounds in the wiki link.  If it sounds similar, it's probably due to AC interference.

In this case, you could use a band-stop filter.  However, I consider this the tail wagging the dog and it would be a lot easier and provide better quality audio if you just fix the power supply or replace it.