in my opinion to make your solder fume extractor quiet.
add wool felt sheet to around the inside of the air bell just inside the end of the flexible hose pipe
and add more wool felt sheet to around an up-right cone in the middle of the twin filter rings
you may also like to mount the fan motor on a anti vibration bed or foam rubber block.
also add more wool felt sheet to around the inside of the air out take of the fan
as this is the acoustic choke points of the sound . see my diagram of solder fume extractor.
Note- grammatically incorrect air ball?
is bell as-in a trumpet bell.
at this diagram representation description was made quickly before the thought ended
update-
even if you do not have an anechoic test chamber or soundproof room.
in my opinion one can still test sound levels with nothing more then an
oscilloscope & microphone . so getting that anechoic muffler or anechoic baffle set just right inside your unit
the ideal situation is to have all additional anechoic modifications reversible or otherwise removable.
wool felt has excellent sound deadening properties. and can be glued to a backing material
in the case of a flexible hose pipe. a pvc pipe 5 or 10 cm wide collar with a gap cut out of it so it works as a spring.
a little larger than the inside diameter of the flexible hose pipe.
the wool felt would be glued to the inside of the pvc pipe collar with a gap cut out of it. so its a "C" type spring.
inserted into the end of the flexible hose pipe inside the air bell, the then moved back or forward for the best
air flow vs sound suppression.
2: as for the fun / motor anti vibration bed.
the idea is to have a block of foam rubber screws to the motor unit top-down.
and second set of screws go in a added collar under the foam rubber go up but not touching the other screws to the motor unit.
so the fan motor unit it is on a floating bed of foam rubber. stopping vibrations entering the case of the extractor.
if constructed right, the collar under the foam rubber will mirror the holes in the top of the motor, longer screws
will hold it in place. so you have two sets of screws in-between each other.
this is all assuming that their is space for the added foam rubber inside the case.
-as a foam rubber or wool felt baffle set in front of the fun out-let on the inside of the case, can also good for sound suppression