I built my own muffler long ago well before I had a digital camera or any interest in sharing. I've built a couple since, one for me and one for a friend. When I get around to making another, I will take pictures and document each of the steps.
Regardless, here is what I say on my cyclone web page about building a muffler:
I like adding a muffler. PSI sells one for $49 that I have heard saves about 10 dB as well, but it only fits a 5" outlet that I think is too small. We really should use mufflers that are at least 7" and preferably 8" interior diameter on our cyclones. Quite a few have made their own mufflers out of screen wrapped with foam then fiberglass followed by being slipped into a larger tube. I tried making one using PVC pipe because PVC helps dampen the noise, but found sliding the outer pipe onto the insulated inner was too difficult. For my next I used snap lock pipe on a screen made of 1/4" hardware cloth (galvanized square heavy wire mesh) covered in landscape fabric then heavy fabric foam, fiberglass insulation and another layer of landscape fabric all covered by a piece of snap-lock pipe. With the snap-lock pipe it was bear to fasten that center seam but much easier than trying to slip that mess into a tight PVC tube. My Home Depot store had nice tapered HVAC reducers that ended up making a pretty good-looking muffler. After I went to all that work, Larry Adcock, creator of the WoodSucker, told me it would have been easier to just use a length of fiberglass insulated HVAC flex duct in place of the muffler as a long enough length does a better job and costs far less. I tried that and he was right!
I've since bought a good digital dB meter. I measured 96 db with the blower just going directly into the filter through metal duct. Adding my homemade muffler to that same setup dropped it to 88 dB. It went down to 92 dB using PVC duct and no muffler. Using insulated HVAC duct it went down to 87 dB with no muffler. Using insulated HVAC duct and my own homemade muffler it went down to 82 dB. These test results will vary considerably depending upon how you made your blower, your choice of impeller, motor choice, any coatings or insulation you use, and depending if you use anti-vibration mounts.
For those who still really do want a muffler, this is not rocket science. Today I would make a few minor changes to improve its performance. Use 12" snap-lock external pipe and make the internal mesh an 8" cylinder of 1/4" grid galvanized hardware cloth or expanded metal, cover that hardware cloth with landscape fabric or if can't get that use fiberglass window screen, add a layer of acoustic foam either from home construction or a sound shop, and then wrap all in fiberglass insulation before snapping on the exterior pipe and slipping on the ends.
Dave Belliveau built a muffler from my earlier plans and was kind enough to document his efforts with pictures. He also shared some noise control information links that are on my Links page. If you are interested in seeing his please click here and be patient while the pictures load.