Don't use the shower. Sorry I shouldn't try and be funny.
Anyway the steel or cast iron drains normally were quieter the newer PVC pipes. The water in the pipe will make noise. The only things that can be done is to relocate this noise or easiest is to muffle it. If you can open up one side of the wall and pack insulation around the pipe it should help a lot. When remolding I insulated all my interior walls for sound.
Dave, I agree with the other reply about using cast iron pipes for such a drain, pack the area with insulation, and you may consider "RC channel" in case you re sheet rock your whole downstairs room, the channel holds the rock off the wall just a bit so sound will not travel through the wall. Easiest solution replace plastic pipe with cast iron and cover with black foam pipe insulation if there is room.Suzanne