I remodeled a single family two story home that had a problem with footfall noise from the upper level. On the lower level ceiling I put an extra layer of 5/8 drywall with Green Glue acoustic caulk. I thought about wood floors in the upper level, with possibly a layer of ply & Green Glue, or Sound Sense acoustic mats. In the end I put carpet with a dense pad. It's now very quiet.

Hi. I'm not sure if this is a valid answer, but I have the same issue SINCE about 1 year ago when I turned the MAIN water valve off to the house. I had to do a bit of repair work to the shut-off valve going to the commode, and my main valve to the house hadn't been turned off in about 10 years since I bought the house. (It actually wouldn't shut the water off all the way, and I've since had to have it replaced.) When I turned it back on, 'junk/small pieces' came out of several of the faucets, and in the bathroom (which is right behind the laundry room and main valve/water meter), I noticed this tapping you're talking about. At first I was nervous as I thought it was dripping behind the wall. I usually only notice it when the washer is filling up though, but like you said, its speed depends on the water speed. It is constant, but if I turn the sink on while the washer is filling, the tapping speed increases, and then decreases when I shut the sink off. I did notice that if I put my hand on the main valve (which is just inches before the water meter) when I hear the tapping, I can feel the tapping in the valve, and in all honesty, it sounds like it's coming from the water meter to me. A plumber recently listened and said it is not unusual for the meter to make that sound, and it basically reverberates throughout the pipes. Whether that's true or not, I don't know, but since I turned the main valve off for the first time in a decade and turned it back on, I get the same sound you're referring to. Perhaps someone here can verify that and let us know if it's true or not, or if it's indicative of a problem. Thanks.

Adding sound insulation to stud walls will have little effect on sound transmission. The primary purpose of that kind of insulation is to slow down sound that enters a wall from a crack and travels to a crack on the other side. The more likely travel paths for sound are over the top of the walls, through ducts, back to back receptacle boxes, and light weight doors with excessive undercuts. Sound takes the path of least resistance. For instance, there is little reason to add sound insulation or drywall to a wall that contains a door. To improve the condition you should start with what is accessible like the doors. There is nothing that can be done about a hollow core door but a heavy solid core door can be greatly improved by adding a perimeter sound seal including a drop seal at the bottom. If you have access to the ceiling space from an attic you can fill the ceiling space above important walls with drywall and sealant or dense rock wool fire-safing.

Ear plugs. Yes they work!!! We nicknamed my sister E.P.D. ( ear plug dependent ) If you're sound asleep, I doubt you will notice the vibration. which may be structural and a gigantic expense, involving joists and lord knows. Call a structural engineer but brace your$$$$elf.. In the meantime?? below. Comfy, no worry. : ) https://www.amazon.com/Ear-Plugs-Sleeping-Individually-Reduction/dp/B00ZU2VIR2/ref=sr_1_2_a_it?ie=UTF8&qid=1541072536&sr=8-2-spons&keywords=ear+plugs+for+sound+blocking&psc=1 . Foam blocks under the feet of the bed?