Quieting a noisy generator is a tough thing to do because of the way sound works--especially the low frequency/high energy range. The higher frequency/lower energy range is easier to attenuate. It is, however the low frequencies that make noisy generators so annoying. I copied the following explanation of dB from "How stuff works"
The decibel (abbreviated dB) is the unit used to measure the intensity of a sound. The decibel scale is a little odd because the human ear is incredibly sensitive. Your ears can hear everything from your fingertip brushing lightly over your skin to a loud jet engine. In terms of power, the sound of the jet engine is about 1,000,000,000,000 times more powerful than the smallest audible sound. That's a big difference!
On the decibel scale, the smallest audible sound (near total silence) is 0 dB. A sound 10 times more powerful is 10 dB. A sound 100 times more powerful than near total silence is 20 dB. A sound 1,000 times more powerful than near total silence is 30 dB. Here are some common sounds and their decibel ratings:
Near total silence - 0 dB
A whisper - 15 dB
Normal conversation - 60 dB
A lawnmower - 90 dB
As you can see, cutting the racket of a lawnmower to that of normal conversation means getting rid of a LOT of energy. The low end noises are best reduced by layers if lead, or tar, or dense rubber (horse stall mat) and in that order. Wood is not good nor is sheet metal. High end sound can be easily reduced with baffles or closed cell foam rubber. Just to complicate things further, sound is very good at getting through even the smallest cracks in sound proofing and then continuing on almost unabated.
Since it was necessary for my already quiet genny (Yamaha i3000seb 56-60dB) to be positioned half in and half under my bus in order to get it in at all, I devised an enclosure of 3 layers of lead, tar,and dense rubber with the result being a drop in dB to 46dB. Of course the heat load in the box required a pair of thermally controlled fans, a fire extinguisher, and several redundant temp and air flow sensors each capable of shutting down the genny (and its electric fuel pump) should specified condition be met. Since none of the small gennies have true oil pumps an external cooler would require some thought and careful fabrication but would go a long ways towards reducing heat build up in the sound suppression box. BTW, if you want a good laugh, type in "How to quiet a generator" in U-Tube. Try this one if you have ten minutes to lose of your life.... https://www.google.com/url?sa=t&rct=j&q ... 7201,d.cGE
Hope this helps. Jack
Edit: I'd be happy to discuss specifics on this topic if there is any interest--either here or in a PM as there always several ways to skin a cat.