Every time someone flushes a toilet upstairs, I hear the water draining very loudly through the wall of my downstairs bedroom. Is there a way to fix that?"
You are not alone in your struggles with audible flushing. This is a common problem in newer homes -and commercial spaces for that matter. The sound you may all be hearing is the gurgling of water through the large drain pipe, or "soil line" in your home. Soil lines are much larger than your typical hot and cold water supply lines that run to sinks and appliances. This is line is a minimum 3" diameter (but more like 4" diameter) pipe.
It's not just you.
“ I feel like in the houses I grew up in, this wasn’t a problem, but now I notice it all of the time. Am I just more neurotic than I used to be? ”
Today most pipes are made of PVC, as opposed to cast iron as they were in the past. PVC pipes do little to muffle the sound inside of them.
What you can do.
There are a couple of things you can do to solve your gurgling problem. Unfortunately they all involve opening up your wall around the soil pipe.
1) Have a plumber cut out the PVC section of the pipe and replace it with a cast iron pipe.
2) Wrap a sound insulative product around the pipe. There are foam sleeves you or your plumber can purchase that adhere right to the pipe. A company called the Soundproof Cow makes a decent product for this. Check it out here.
3) Fill in the gaps between the pipe and the studs and drywall with acoustical batt insulation. Acoustical batt is not dense enough to solve your problem on its own, but it's a good additional layer of sounds absorption. You should probably do this step even if you do the two above because it is inexpensive and your wall will already be opened up.