I have mine in a tub, filled with sound foam, which is in a LARGER tub, also filled with sound foam with feed and intake tubes in/out. This large tub is also resting on an anti-fatigue mat from the dollar store. I also zip-tied all by air stones to my net pot in each growing site, keeping them about 1-2inches off the bottom of the tank.
Even with the zip-ties, the vibration through the stones still could be felt/heard UNTIL the root mass surrounded it adding a netted layer of vibration suppression.
Doing all this means: NO SOUND; but there are STILL vibrations traveling through everything as I’m doing all this on the 2nd flood of a 1960’s home.
I’ve recently added a 650L/Min agitation pump with aerator into my reservoir to boost oxygenation in the solution before traveling down the pipes and into the growing sites; and this thing is SILENT and VIBRATION FREE. You only hear the water movement when I open the res!
So, I may end up ditching air pumps and getting 4x more of these little units; one for each site. Though, I want to do more research to see if anyone else is solely using power-heads/mini water pumps with aerators rather than loud bubbles.