Noise from basement through plumbing chase

There is a plumbing chase in my house that runs from the basement to the attic. The chase is located in a second floor wall right where a bed is set up and noise from the basement (ex. sump pump) travels up the chase and is annoying. I know for certain that there is NO insulation in this wall because of an IR energy audit done on the house. Should my contractor have insulated this wall or blocked any openings at the basement level or each floor level? I'm also concerned as the rest of this bedroom's walls were insulated for sound and this particular wall, being the bed wall, probably should have been insulated for sound proofing as well. Any recommendations? Unfortunately, the basement ceilings were sheetrocked and the second floor walls are plastered.

chase

You do not have a pipe chase, you have a potential fire chimney. EVERY VERTICAL shaft, or wall, is supposed to be "stopped off" or blocked every eight feet or less to prevent fire spread. Definitely seal that off or otherwise block it, if for no other immediate reason than sound proofing.

Even if the wall were insulated, the hollow cylinder of the chase conducts sound really well. You'd still get annoying sound. I agree with HJ. Cap that pipe in the basement. It'll muffle the sound AND it'll provide a fire stop.

Also, cap it in the attic. Otherwise, cold attic air will condense and collect in the pipe and fester.

As a side note, you'd be surprised how much hot air can escape from your basement through that chase. (I'm assuming it's 2-3" wide).