Step 1 — Damping

Question: what does the untreated box actually do, and what damping does it need? Result: three box resonances leak out of the port; a back-panel layout with one sheet of sheep's wool fleece per speaker plus a 50 g polyester pocket reduces them by 5–6 dB without touching the driver's direct sound.

Background: two terms

• Box modes. Above the bass, sound bounces between parallel inner walls and forms standing waves at f = c / 2L. In a vented box they escape through the port and colour the sound — "boxy" at the low ones, "honky" higher up. Damping material absorbs them.
• Fb, the port tuning. The air in the box acts as a spring, the air plug in the port as a mass; together they resonate at one frequency (a Helmholtz resonator, like blowing across a bottle). Fb is set by box volume and port dimensions, not by the driver. At Fb the port radiates most of the bass and the cone barely moves; below it the bass falls off steeply. A longer port lowers Fb.

Baseline findings

Untreated box: bare 44 mm port, no damping (L-z-00 impedance, L-00-baseline acoustic).

	Finding	Evidence
P1	The driver is the 8 Ω version. The supplied datasheet (Re 3.4 Ω, Fs 73 Hz, Qts 0.52) describes the 4 Ω version	impedance plateau 7.6–7.9 Ω; from the two peaks Fs ≈ 82 Hz, Vas ≈ 3.6 l (a new, stiff suspension)
P2	Port tuned too high: boomy, shallow bass	Fb = 74.4 Hz (predicted 61 Hz); bass sum +8.1 dB at ~75 Hz, steep fall below 55 Hz → Step 2
P3	Height mode at 350 Hz	+13 dB spike in the port near field; c / 2·0.486 m = 353 Hz
P4	"Honk" at ~950 Hz and ~1.5 kHz	~950 Hz = front-to-back mode (c / 2·0.188 m = 912 Hz); ~1.5 kHz = the short port's own pipe resonance
P5	Back panel leaks	taping the seams raised port output ~1 dB and moved its peak 1 Hz; refits moved it up to 10 Hz
P6	Treble peaks	+7 dB at ~6 kHz, +11 dB at ~10.5 kHz (cone break-up) → correction EQ

The box's dimensions predict the resonances that show up in the port output:

Resonance	Dimension	Predicted	Measured
Height mode	486 mm	353 Hz	350–360 Hz
Width mode	296 mm	579 Hz	not prominent
Depth mode	188 mm	912 Hz	~945 Hz
Port pipe resonance	44 mm + end corrections	≈ 1.5 kHz	~1.5 kHz

Rationale

Porous material absorbs where the air moves, not where pressure builds:

• Height mode (350 Hz): air velocity is highest halfway between top and bottom, across the whole cross-section → thick, loose fill at mid-height. The original plan points the same way ("50 mm foam … better against the 300 Hz mode").
• Depth mode and port resonance: the front-to-back wave reflects off the back panel, opposite the port's inner end → wool on the back panel, and fill that reaches into the box depth.

Design goal for the production layout: one sheet of wool fleece per speaker, everything mounted on the removable back panel.

The chosen layout

Part	Size	Position
Fleece layer	≈ 266 × 456 mm, one layer ≈ 10 mm (sheep's wool garden fleece, ≈ 140 g/m²)	inside of the back panel, within the cleats
Pocket	≈ 240 × 160 mm, made of the same fleece	across the back panel, 160–320 mm above the inner floor (middle third of the 486 mm height)
Fill	50 g polyester fibre fill, loose, puffed to 6–10 cm	inside the pocket
Clearance	≈ 5 cm	around the port tube's mouth and behind the driver

Test setup

The damping was studied as an experimental setup, not built as a finished interior: materials were added and taken out again between measurements, with everything else — microphone positions, gains, the box — held constant.

Materials	sheep's wool garden fleece — unbleached, sold as a plant-protection / mulch mat, ≈ 10 mm, 350 g per 5 × 0.5 m roll (≈ 140 g/m²); polyester fibre fill (the synthetic stuffing found in ordinary pillows), weighed per round; a thin fabric bag or a wool pocket to hold the fill
Fixing	staples into the back panel, so each variant can be changed in minutes
Per round	one change, then port near field (all rounds) and far field + near-field driver (full sessions)
Outcome	a layout to build neatly in the finished speaker — not the stapled test fixture itself

Note on the material: the original plan calls for dense 10 mm wool felt (≈ 1500 g/m²). The garden fleece used here is about ten times lighter and far cheaper — and with the pocket at mid-height it still takes 5–6 dB off every box resonance. Dense felt on the back panel would likely do more against the ~950 Hz depth mode.

Eight variants, measured

Round	Change	350 Hz	950 Hz	1.5 kHz
L-03	1 wool layer (~10 mm) on the back panel	−2.8	−0.4	−1.9
L-04	3 wool layers on the back panel	−7.0	−5.0	−5.6
L-05	3 layers + 50 g fill in a bag, free in the middle of the box	−9.7	−11.2	−8.1
L-06	fill as a flat cushion under one wool layer	−5.8	−2.8	−3.0
L-07	1 wool layer over the whole back panel	−3.3	−0.1	−2.7
L-08	1 layer + 25 g fill in a wool pocket at mid-height	−7.2	−3.3	−4.6
L-09	1 layer + 50 g pocket at mid-height — the production layout	−8.2	−5.1	−6.3
L-10	L-09, stapled, panel closed	−6.3	−4.7	−6.0

dB change of the band maximum in the port near field vs. the baseline L-00 (1/12 octave).

L-05 measures best; L-09 is the production layout: one fleece sheet per speaker, all on the back panel, better than three plain layers, within 1.5 dB of L-05 at 350 Hz. Only the depth mode stays ~6 dB behind — a free-standing bag reaches into the box depth, a panel pocket can't.

Photos of three variants

L-06: fill pressed flat — about half the effect of a puffy pocket	L-08: one layer + 25 g pocket	L-09: one layer + 50 g pocket

Test setup: material stapled in so it could be added, moved or removed between rounds. The finished speakers get the same layout, neatly made.

Result

Port output — what leaks out of the box through the port:

Port near field, 1/12 octave, 300 ms. The height mode, the depth mode and the port resonance are 5–6 dB lower.

Bass, driver + port — the hump at 75 Hz shrinks from +8.1 to +5.9 dB. The fill adds losses: the port gives up 1.5 dB at Fb and ~4 dB at 40 Hz, so the slope below 55 Hz gets steeper. The port tube in Step 2 moves this whole region.

Impedance — the tuning drops from 74.4 to ≈ 72 Hz (the fill makes the box act slightly larger). The dip between the bass peaks shrinks from ~3 Ω to ~1 Ω: more losses in the port circuit — the limit for further damping.

Direct sound at 50 cm (gated, room-free) — unchanged within ±1 dB, as intended: damping works on the box, not on the driver. In the room, at the mic, the 350 Hz region dropped ~2 dB.

Problem	Before (L-00)	After (L-10)	Status
P3 height mode, 350 Hz	+13 dB spike	−6.3 dB	largely solved
P4 depth mode ~950 Hz / port pipe ~1.5 kHz	clear peaks	−4.7 / −6.0 dB	reduced; 950 Hz could go further
P5 back panel leak	port peak 70–80 Hz depending on fit	71 Hz, panel closed	build the back with gasket + screws
P2 bass hump / Fb too high	+8.1 dB, Fb 74.4 Hz	+5.9 dB, Fb ≈ 72 Hz	→ Step 2
P6 treble peaks	+7 / +11 dB	unchanged	correction EQ

Limitations

• One speaker (L) measured; the second gets the same layout and one check measurement.
• The driver wasn't broken in: its suspension loosens over 10–20 h of use and moves the bass peaks a little.
• Port near-field data above ≈ 1.6 kHz are relative comparisons at a fixed position, not absolute levels.
• The friction-fit back panel's seating was the largest uncontrolled variable in the bass.
• The damping was measured as a test setup; the neat production version gets one confirming measurement.