Tuned Bass Trap for Room Modes - Folded Quarter-Wave Resonator Cells

This tuned bass trap is an experiment you can join. Nobody has printed these cells or measured them yet, and everything below is calculated, not measured. The models say that with medium walls (alpha 0.10, assumed) eight cells take the 42.9 Hz mode of an example room from a decay of 1.35 s to about 0.9 to 1.0 s, and I would like to know whether that is true in a real room. Print a block, measure your room before and after in REW, and tell me what you got.

A bass trap here is a narrow absorber for one room mode. Every cell is a slit 6 mm wide, folded to fit a face of 120 x 120 mm and 50 to 125 mm deep, and the length of that folded channel decides which frequency it takes energy from. It is a quarter-wave resonator, and the end cap you push into the side of each cell closes the channel at its far end. There are five blocks, one for each of five room modes of an example room of 4.0 x 3.2 x 2.6 m, and the generator below makes the one for your own room.

Make a trap for your own room: soundblooms.com/tools/diffuser-generator - enter the room, pick the mode that rings and download the files.

What to expect from a tuned bass trap, and why it is an experiment

The numbers below are the model's, for the example room with walls of medium absorption, alpha 0.10. That value is an assumption, not a measurement, and your walls are very likely different. I am not going to promise a result, and the honest summary is that the effect is modest, narrow and uncertain.

• One cell is practically inaudible. At 42.9 Hz it takes the decay from 1.35 to 1.30 s and lowers the peak by about 0.2 dB. That is below anything a listener can hear.

• Eight cells on the 42.9 Hz mode shorten its decay by x1.37 (cells tuned on the mode) to x1.50 (tuned 0.5 % above it, which these files use) in the 3D finite element simulation, and lower the peak by about 1.3 dB at alpha 0.10 (3D simulation; the model gives -1.4 dB). The generator's own model gives x1.55 for the same case, so treat it as the optimistic end: the 3D simulation gives up to x1.50. That is a decay of about 0.9 to 1.0 s instead of 1.35 s.

• There is a ceiling. However many cells you add, the 3D simulation (wall beta 0.01, about alpha 0.08, up to 64 cells) stops at about x1.5 to x1.75, because a bigger patch of cells pulls its own resonance away from the mode.

• The walls decide. In the example room the generator gives about x1.5 for eight cells with lively walls (alpha 0.05) or medium ones (0.10), and only about x1.05 with damped walls (alpha 0.20; this is the generator model, there is no 3D simulation at alpha 0.15 or more), because the trap only helps when the mode rings longer than the cell does. In a room that already damps the mode, it does nothing.

• Per cell, the tangential and oblique modes at a corner or an edge gain most. One cell at 95.2 Hz in the floor corner gives about x1.15 in the model, against about x1.0 for one cell at 42.9 Hz. The model marks those cases as approximate, and in the weakest case, the oblique mode with a low channel resistance, the 3D simulation gives practically nothing.

Here are the five modes, each at the best place the model found for 1, 4 and 8 cells. Factors are rounded down to 0.05, and a case marked approximate can be off by 25 % or more in the single-mode model, up to about 40 % against the 3D simulation. 'About x1.0' means no more than a few percent.

• 42.9 Hz, the axial mode (1, 0, 0), decay now 1.35 s. 1 cell in the floor corner: T60 1.35 to 1.30 s, about x1.0, peak -0.2 dB; 4 cells in the vertical corner edge at half height (2.6 m): T60 1.35 to 1.14 s, about x1.15, peak -0.7 dB; 8 cells in the middle of the 3.2 x 2.6 m wall: T60 1.35 to 0.87 s, about x1.55, peak -1.4 dB (the model; the 3D simulation gives x1.37 to x1.50 and a peak of about -1.3 dB).

• 53.6 Hz, the axial mode (0, 1, 0), decay now 1.28 s. 1 cell in the floor corner: T60 1.28 to 1.23 s, about x1.0, peak -0.2 dB; 4 cells in the middle of the 4.0 x 2.6 m wall: T60 1.28 to 1.08 s, about x1.15, peak -0.8 dB; 8 cells in the middle of the 4.0 x 2.6 m wall: T60 1.28 to 0.87 s, about x1.45, peak -1.5 dB.

• 68.7 Hz, the tangential mode (1, 1, 0), decay now 1.07 s. 1 cell in the floor corner: T60 1.07 to 0.98 s, about x1.05, peak -0.4 dB (approximate in the model); 4 cells in the vertical corner edge at half height (2.6 m): T60 1.07 to 0.73 s, about x1.45, peak -1.4 dB (approximate in the model); 8 cells in the vertical corner edge at half height (2.6 m): T60 1.07 to 0.72 s, about x1.45, peak -2.5 dB (approximate in the model).

• 95.2 Hz, the oblique mode (1, 1, 1), decay now 0.85 s. 1 cell in the floor corner: T60 0.85 to 0.72 s, about x1.15, peak -0.7 dB (approximate in the model); 4 cells in the floor corner: T60 0.85 to 0.65 s, about x1.30, peak -2.2 dB (approximate in the model); 8 cells in the floor corner: T60 0.85 to 0.65 s, about x1.30, peak -3.1 dB (approximate in the model).

• 107.2 Hz, the axial mode (0, 2, 0), decay now 1.28 s. 1 cell in the floor edge under the 4.0 x 2.6 m wall, middle of the 4.0 m edge: T60 1.28 to 1.22 s, about x1.0, peak -0.3 dB (approximate in the model); 4 cells in the middle of the 4.0 x 2.6 m wall: T60 1.28 to 1.06 s, about x1.20, peak -1.1 dB (approximate in the model); 8 cells in the middle of the 4.0 x 2.6 m wall: T60 1.28 to 0.93 s, about x1.35, peak -1.9 dB (approximate in the model).

Every number above rests on things nobody has measured yet, and this is why this is an experiment and not a product.

• The biggest unknown is the resistance of the printed channel, about 2 times either way. A printed wall is rougher and leakier than the smooth channel in the model. That can shrink the effect, and with a wider slit it can reverse it, which is why the slit is 6 mm in every file and nothing wider. Only a measurement settles it.

• The tuning is narrow. A cell that is 1 % off its mode loses 10 to 40 % of its effect, and a printed cell can be 1 to 6 % off, because roughness lowers its frequency by about 2.5 to 6 % and a leak at the flange raises it.

• The flange seal is untested. The end of the channel is where pressure is highest, so a leak there shortens the channel and raises the pitch.

• It is a narrow tool. For broadband bass, porous or membrane traps in the corners do more per kilogram. These cells are for one ringing mode, and at 42.9 Hz eight of them are 8 prints and about 3.3 kg of PLA for the blocks, 3.5 kg with the end caps.

Measure your room before and after

This is the part that makes the experiment worth anything. Put your measurement microphone at your listening position and sweep the room in REW from your speaker. Save the sweep and the decay plot, a waterfall or the T60 of the mode you are after, before you put anything on the wall. Then put the blocks up and measure again with the speaker and the microphone in exactly the same places, and compare the two decays of that mode. A few dB of peak and a shorter decay at one frequency is what the models predict; nothing at all is a result too, and I would like to hear it.

Post what you got as a comment here, or in the GitHub Discussions of the generator, with the room size, the mode, the number of cells and the place. Calculated, not measured, until someone measures it.

Where to put the cells: corner, edge or wall

A mode has its highest pressure at the walls and corners, so that is where a cell can reach it. In the example room the model puts the first cells of the 42.9 Hz trap in the floor corner, then up the vertical corner edge, and eight cells in a grid on the middle of a wall; the other modes have their own best places, listed above. Blocks are 50 to 125 mm deep, so a second block in a corner stands beside the first and not inside it. The face with the slit looks into the room, the back lies flat on the wall, and the block stands as it printed, with the slit running up and down. A room that is not 4.0 x 3.2 x 2.6 m has other modes and other best places, and the generator names them.

End cap and tuning inserts for the resonator

The end cap is the nominal insert and it is not optional: it closes the channel, and a cell without it is open and does nothing. There is one for every cell, on its own small plate for each block. Slide it into the window in the side wall until its flange lies flat, put foam tape around the window under the flange and aluminium tape over the edge of the flange. The tape is a suggestion I have not tested.

The other inserts are optional tuning parts. Each one is longer than the last and raises the frequency of the cell by 0.5 % of the mode, from -1 % to +4 %, and the plate holds all ten. Use them only with the measurement above: print them, swap the end cap for another insert, and measure again. Without a measurement there is no reason to choose any insert other than the nominal one.

Make a bass trap for your own room mode

The free Diffuser Generator has a Bass traps tab, and it works in three steps. In Room you enter the length, width and height of your room and choose how much your walls absorb: Lively (alpha 0.05), Medium (0.10) or Damped (0.20). You rarely know this, and it matters. In Pick a mode it lists the room modes up to 120 Hz with the decay of each and a verdict, and it flags the ones where the model is approximate or uncertain. You choose a mode and a number of cells from 1 to 16, and a What to expect card shows the decay before and after, the peak, the best place and the print. In Print you choose your printer bed, and it downloads a ZIP with the block STL files, the end caps plate and a README with the print plan; the tuning inserts are a separate download, offered only with a decay measurement. It runs in the browser and costs nothing. The files here are what it produces for the example room (the same room as the screenshot), so these five blocks are only a start.

Open the Bass traps tab of the Diffuser Generator

Files, print times and settings for the Bambu Lab P1S

• 42.9 Hz: a block of 1 cell, 123.6 x 120 x 120 mm, 10 h 28 min and 418 g. The end cap plate (1 cap) takes 0 h 27 min and 14 g, the tuning inserts plate 5 h 37 min and 242 g. Eight cells are 8 blocks: about 84 h of printing and about 3.3 kg of PLA for the blocks, 3.5 kg with the end caps.

• 53.6 Hz: a block of 1 cell, 102 x 120 x 120 mm, 8 h 42 min and 348 g. The end cap plate (1 cap) takes 0 h 25 min and 13 g, the tuning inserts plate 4 h 58 min and 209 g. Eight cells are 8 blocks: about 70 h of printing and about 2.8 kg of PLA for the blocks, 2.9 kg with the end caps.

• 68.7 Hz: a block of 2 cells, 80.4 x 120 x 240 mm, 13 h 44 min and 550 g. The end cap plate (2 caps) takes 0 h 35 min and 23 g, the tuning inserts plate 4 h 17 min and 179 g. Eight cells are 4 blocks: about 55 h of printing and about 2.2 kg of PLA for the blocks, 2.3 kg with the end caps.

• 95.2 Hz: a block of 2 cells, 58.8 x 120 x 240 mm, 10 h 17 min and 411 g. The end cap plate (2 caps) takes 0 h 31 min and 20 g, the tuning inserts plate 3 h 41 min and 150 g. Eight cells are 4 blocks: about 41 h of printing and about 1.6 kg of PLA for the blocks, 1.7 kg with the end caps.

• 107.2 Hz (the generator lists it as 107.3 Hz): a block of 3 cells, 51.6 x 240 x 240 mm, 13 h 42 min and 549 g. The end cap plate (3 caps) takes 0 h 46 min and 30 g, the tuning inserts plate 3 h 30 min and 141 g. Eight cells are two of these blocks (about 27 h) and a two-cell block from the generator; three of these blocks (nine cells) are a little better than the eight in the table.

Every mode has the same three kinds of file, as STL and as a 3MF sliced for the P1S: the block, the end caps plate and the tuning inserts plate. With the Generic PLA profile the blocks take 8 h 42 min to 13 h 44 min. The two-cell block of 68.7 Hz and the three-cell block of 107.2 Hz take 13 h 44 min and 13 h 42 min, over the 12 hours the generator aims at, because its own estimate is calibrated on the faster Bambu PLA Basic profile (about 11 hours for these two) and Generic PLA prints about a quarter slower. The blocks of 42.9 and 53.6 Hz stay at one cell, because a second cell would take 17 and 14 hours on the generator's estimate, and the block of 95.2 Hz stays at two cells, because a third one, in an L shape, would take 12.4 hours on that estimate and more with Generic PLA.

All files were sliced for a Bambu Lab P1S with a 0.4 mm nozzle, a Textured PEI plate and PLA (the Bambu Studio Generic PLA profile, any PLA will do), with the part fan capped at 80 %, no supports, no brim, and the chamber fan off. The channel runs along the print axis, so every layer has the same cross-section and nothing overhangs but the roofs over the folds, which print as short bridges of about 7 mm.

• Blocks: 0.20 mm layers, 3 walls (the walls are 1.2 mm, so three perimeters), 15 % lightning infill.

• End caps and tuning inserts: the same settings, flange on the bed.

Do not make the slit wider or the walls thinner to save time. The channel is the whole part, and 6 mm is the one width these numbers are calculated for. All times and grams on this page are from Bambu Studio slices on the Generic PLA profile. The generator's own estimate assumes the faster Bambu PLA Basic profile, so eight cells at 42.9 Hz are about 67 h on the generator page and about 84 h in these slices. The same settings work on other printers, and every block fits a bed of 256 x 256 x 256 mm with 5 mm to spare, which is the P1S and X1. For a smaller bed the generator packs fewer cells per block.

Where things stand and how the numbers are made

Nothing has been printed and nothing has been measured. The pictures are renders of the STL files, in filament colours I chose for the picture, and the times and grams are from slices. The geometry is the cell of the research, built by the generator code, and checked on the mesh for closed shells and for the volume the generator expects. A mesh is not a printed part, so the first real print may show something I did not expect, and I will update this page when it does. The acoustic numbers are the model's and the 3D simulation's, and neither has a measurement of a printed cell or a real room behind it.

A room mode is a standing wave with a decay rate that the walls set. The trap changes the characteristic equation of the mode: the mode and the cell become two coupled resonances, and the slower of the two roots is the decay that remains. The radiation mass of the patch of cells pulls the resonance down, so the cells are designed for the mode frequency times 1.005. Every 90 degree bend shortens the channel acoustically by 0.245 times the slit width, which the files already include. The full chain, the assumptions and the limits are on the maths page in the generator repository.

Licence and credits

This is my own design, not a remix, and it is shared under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 (CC BY-NC-SA 4.0). The geometry, the model and the code that generates them were written with AI assistance, and the AI label on this page is set to Yes. The acoustic diffuser tiles that go with these traps are another model of mine.

More from Soundblooms: soundblooms.com - audio prints, apps and DAC measurements. Questions or ideas? Discord.