Greg, you do much better with English than I EVER will with French - and the metric/English thing is a bona-fide nightmare...
First I'll try to explain how/why dimensional lumber, as purchased in the US, isn't what it claims to be - when sawmills first started standardizing on dimensions for sawn boards (as opposed to "go cut your own, flatten it with an adz or a draw knife, build your cabin, fight off the indians") anyway, at that time when you bought a 2x4, you got a rough-sawn board that was really 2 inches by 4 inches. At that time, near as I can tell, the "board foot" measurement came into being, for purposes of pricing. One board foot (at that time) = 12" x 12" x 1" thick. Using that value, 1 foot length of a 2x6 = 1 board foot (BF)
Then, somebody decided they would be easier to work with if they were smoother, so then you could buy either rough sawn (really 2 icnes by 4 inches) or S4S (Surfaced 4 Sides) which STARTED as a 2 x 4 but ended up about 1/8" smaller on each surface, or in reality you got a board that was 1-5/8" x 3-5/8" -
Finally, someone discovered that they could get more boards out of the same log by using more precise milling methods, so they started ripping 2x4's to about 1-5/8" x 3-5/8", and only planing them down to 1-1/2" x 3-1/2" -
Now, here comes the crass commercialism part - they still CALL it a 2x4, and guess what? They still CHARGE you by the board foot, based on what they CALL it, not what it REALLY is - so, a 2x4 gets charged for as if it really was 2" x 4", or 2/3 of a board foot per lineal foot.
The reality, for actual building purposes, is that US dimensional lumber is really 1/2" LESS in either dimension than its name would suggest.
This is why I settled on 1-1/2" for slat thickness (slot depth) - it was the closest depth to the requirements of this particular trap that wouldn't require thickness planing - a job that any but the most dedicated woodworker would not be equipped to do, and would have to hire it out.
Now, as for slat WIDTH - since a 2x4 is really only 3-1/2" wide, and since it has been planed and the edges radiused, it will not react the same to impinging sound waves at its edge as it would if it were perfectly square-cut. If you don't think this makes a difference, ask a few high end nearfield monitor manufacturers WHY they radius the edges of their speakers... Anyway, if you want to get rid of the rounded edges on lumber, you have to rip a small slice off each edge to get back to a perfectly square corner. Usually, 1/8" is enough, so that would reduce the width of a 2x4 from 3-1/2" down to 3-1/4" - same for the other sizes - they would end up at 7-1/4" and 11-1/4" respectively.
"So S1=top+bottom
S2=next
S3=middle
Means that looks like a mirror position,right?
Ok,i'm stuck there....If i put the slats horizontally means wall frequency division is ...vertically?And what about 24" division...?" - Yes, you appear to be thinking the way I was - see the next paragraphs -
As to construction, if you first build a frame with 2x4's, positioning the side of the frame that is toward the open area of the booth at 6" and 12" from the wall that will be inside the trap, that will establish the variable depth of the trap. I would fasten a 2x4 (laid flat) to the floor, and another to the ceiling, that runs from a point 6" from the wall at front, to a point 12" from the wall at the rear - You will need to cut these plates at an angle on their ends, so that they fit firmly against the wall on both ends. An adjustable carpenter's protractor will be invaluable here - adjust it for the angle you need and mark both ends of the floor/ceiling plates. If you flip the protractor over for opposite ends of the board, you will get the two end angles such that the board ends will be parallel but NOT square.
IMPORTANT: before you start construction, obtain the caulk you plan to use, along with some construction adhesive - here in the US, one brand is called "Liquid Nails" - it is VERY important that you test these on an actual (scrap) piece of the insulation board you're using, allowing the test piece to "cook" for at least 3-4 days - if the sample shows any signs of deterioration after that time, find a DIFFERENT brand/formula of adhesive and try again. The LAST thing you want to do is put everything together with an adhesive that is going to MELT your trap from the inside out...
Lay a bead of caulk (either flexible silicone or butyl) about 1" from each edge of the 2x4 BEFORE you place the board - press the board down firmly, then fasten to the floor (or ceiling) with screws that will penetrate far enough to hold well - preferably into framing members behind the floor/ceiling covering material. Cut 4 2x4's long enough to require tapping into place between these "plates" on floor and ceiling. These will be your framing "studs" - place one of the studs against the wall, at the 12" deep end of the trap - make sure the 2x4 is square with the base plate - since the angle of the baseplate to the wall isn't square, the inside edge of the vertical 2x4 will touch the wall while the outer edge will NOT. To make it easier to caulk this joint, I would run a heavy bead of caulk along the edge of the vertical stud that will touch the wall BEFORE you fasten this first stud.
Use a piece of the 24" wide insulation board for a guide, place it against the first stud vertically, and locate the second stud up against the insulation board. Toenail the second stud in place, using caulk on the ends of the stud. Continue this until you reach the other ends of the floor/ceiling plates - The last stud will be at the 6" depth, and only the FRONT edge of the stud will contact the wall (all the studs need to be square with the plates, or the slats will not mount firmly to the studs.)
The last opening between studs will probably NOT come out exactly 24" wide, so the pieces of insulation board will most likely need to be trimmed to fit. A razor knife can work for this, if you use a board for a straight edge guide - if you try to saw the insulation board, have a dust mask and a vacuum cleaner handy - not a good idea.
Once the framing is complete, I would mount the insulation boards in between the studs, placing them back from the outer edge by at least 1/4", preferably 1/2" - one way would be to cut some 1" cleats and place them flush with the INSIDE edge of the studs, floor to ceiling - run a bead of construction adhesive all the way around the cleat, then press the insulation boards up against the cleat. Wait a day or so (check the label on the adhesive for recommended cure times) then caulk around the edges of the insulation board with silicone or butyl caulk. At this time, the only way for air to get inside the trap should be THROUGH the insulation board. Make sure EVERY seam is caulked, without the caulk getting in the way of the flush front of the frame.
Now, since the bottom 1-1/2 inches is already blocked by the floor plate (ceiling too) I would start at both bottom and top with a horizontal 2x2 (not really 2", see the first part of this post) - you can use the factory-radiused edge toward the floor, since it will be caulked, but one side of the first real "slot" will be formed by the upper edge of this bottom board, so the upper side should be square cut. If you rip one 2x4 in half, you could use half at the bottom and the other half at the top. These, allowing for a 1/8" kerf width (typical table saw blade width) would end up being 1-11/16" wide, or 1.6875", which is just under 43mm.
To simplify, here are some definitions, after which I'll refer to the simple name to save space and typing ;
For SLATS, NOT STUDS - (studs are left at nominal purchased dimensions, or 1.5" x 3.5")
2x2 = 1.5" x 1.625", or 38mm x 67mm (the dimension you get when ripping a 2x4, minus the 1/8" kerf)
2x4 = 1.5" x 3.25", or 38mm x 82.5mm (1/8" ripped from each side)
2x8 = 1.5" x 7.25, or 38mm x 184mm (1/8" ripped from each side)
2x12 = 1.5" x 11.25, or 38mm x 286mm (1/8" ripped from each side)
From bottom to top, here are the #'s I came up with -
2x2, 1.5mm slot, 2x12,1.5mm slot, 2x12, 1.5mm slot, 2x8, 4.5mm slot, 2x8, 4.5mm slot, 2x4, 6mm slot, 3 more 2x4, each with 6mm slot between, then a 6mm slot and an "adjuster" slat, which will be about 5.2" wide, this is the last slat to be placed - Now, starting from the TOP, a 2x2, 1.5mm slot, 2x12,1.5mm slot, 2x8, 4.5mm slot, 2x8, 4.5mm slot, and the previously mentioned "adjuster" slat.
If your 7.19 foot height dimension is accurate, these #'s should work. If not, you will need to adjust the width of the "adjuster" slat, but keep the same slot widths. Any variation of slat width on this one board will only help broaden the response, which is fine.
Again, the variable depth of the trap will smooth out the gaps that would be caused by only 3 slat/slot widths - I would cut the "adjuster" slat LAST, after all the other slats are in place and fastened down with countersunk 3" brass wood screws - measure between the lower board of the top part, and the upper board of the bottom part, subtract 10.5 mm and that is the width of the "adjuster" slat. Place that last slat with a 6mm gap from the 2x4 below it, and the gap above should come out to 4.5mm.
Also, in answer to one of your questions, since sound PRESSURE is at maximum at boundaries and high frequencies have several wavelengths between walls, It isn't real important that the different slots are placed vertical or horizontal. The design of this trap makes it a pretty broadband device, with more absorption at the 3 lowest modal groups of this particular size booth.
When attaching the slats, I would run a bead of caulk under each slat where it contacts the studs, and then screw it down with 2 screws per stud for narrow boards, and 3 or 4 screws per stud for the wider ones. The caulk will keep the slats from rattling later. The ends of the slats should be caulked, and carefully cut to extend the full distance between walls. You could glue and nail a small cove moulding vertically at the junctions between slats and walls for a more finished look.
What I SHOULD have asked you before I even STARTED, is what actual sizes of dimensional lumber are available to you at YOUR location, and then used those dim's for calculation - if you can get that information, post it back here and we'll start over. (When I can get some more time)
I'm not sure how much more to tell you, other than do everything as if you were building a boat and didn't want it to sink - A lot of the reason it is expensive to hire a proper studio built is this serious attention to detail. An average framing carpenter would waste your time, money and materials if you asked him/her to build such a structure - minute gaps in construction are no big deal for most houses, but can totally negate the initial plan for anything involving acoustics.
Gotta go, graveyard shifts start tonight... Steve
