I have a Jet Dust Collector that I use for my general woodworking in my external garage. It turns on and off with activation of most of my other woodworking tools. It's loud, but only for brief periods of time, so I've accepted it that way for the past 5 or 6 years.
With the addition of a Onefinity Journeyman CNC machine, I figured the DC will be running for extended periods of time and so decided that I needed to make it a bit quieter, so as not to be annoying while in my garage.
The garage door, that my DC is next to, is one of two and so is unplugged from the opener. I probably could have boxed it in completely, but I need visibility to the first stage drum and chute that feeds it. My J/P had the ability to over power the SuperDust Deputy XL and sometimes clogs, so I monitor the chute while planing.
Hence I figured I'd try some sound proofing with some Foamboard.
So I came across this suggestion on a Stumpy Nubbs video and decided to give it a try.
The cost of materials and items used was about $70, but I got a 9 decibel noise reduction which is noticeably quieter.
I have way access to the orange bucket, below the filter and access to the first stage drum. I did actually cover the metal drum with a complete Foamboard surround, but found it didn't alter the sound whatsoever, soI junked that idea.