Wall resonation tuning formula:
fo = 2160*sqrt(r/((d*1.2*D)*(r+w)))
r = slot width
d = slat thickness
1.2 = mouth correction
D = cavity depth,
w = slat width
2160 = c/(2*PI) but rounded
c = speed of sound in inch/sec.
Perforated Sound panel absorption formula:
f = 200* (p/(d*(t+0.8*D)))^0.5
f - frequency
p - perforation %
d - airspace depth (in)
t - panel thickness (in)
D - hole diameter (in)
Note:
From what I've read, and I'm not a mathematical type, the panel formula assumes it's hanging on something infinitely thick.
Our studio is a "basement" type with 12" think tile and brick walls with a closed-cell foam and batt insulated 2x4 wall with the 2x4 wall 2" from the exterior wall. It's not infinite, but has high density.
Construction notes we gathered:
Must be airtight with only one surface opened.
(Historical example of Romans with clay pots on their sides in the theatre's to absorb sound.)
703 Absorption board is popular as alternative to rigid fiberglass.
Corner or wall/side traps diffuse highs. The wide wall absorbers do both.
Each wall has different signature on it's sound reflections. Analyze each wall.
Images from John Sayers below:
Low mid absorber and high diffuser:
( We have an odd-shapped room. We're building a version with a slight air space behind and the short end flush to the front surface of the slats. The size of the gaps and the slat widths are what you adjust to tune the room. )
Wall absorber:
Notice there are no slats to scatter/diffuse mids and highs. This absorbs "all" frequencies to a degree depending on the insulation type, thickness used, and the amount of airspace behind.
Absorption Table:
| Product | thickness | density | 125hz | 250hz | 500hz | 1000hz | 2000hz | 4000hz | NRC |  | |
| Linacoustic RC (roll) | 0.5" (13mm) | | 0.07 | 0.20 | 0.44 | 0.66 | 0.84 | 0.93 | 0.55 | | |
| Linacoustic RC | 1" (25mm) | | 0.08 | 0.31 | 0.64 | 0.84 | 0.97 | 1.03 | 0.70 | | |
| OEM Acoustical Board | 1" (25mm) | | 0.06 | 0.22 | 0.63 | 0.84 | 0.01 | 0.94 | 0.65 | | |
| AcoustaBlanket Black 150 | 1" (25mm) | 1.5pcf (24kg/m3) | 0.10 | 0.32 | 0.66 | 0.84 | 0.91 | 0.91 | 0.70 | | |
| AcoustaBoard Black 225 | 1" (25mm) | 2.25pcf (36kg/m3) | 0.06 | 0.30 | 0.58 | 0.85 | 0.91 | 0.94 | 0.65 | | |
| AcoustaBoard Black 225 | 1.5" (38mm) | 2.25pcf (36kg/m3) | 0.12 | 0.48 | 0.83 | 0.90 | 0.90 | 0.89 | 0.80 | | |
| Owens Corning Unfaced | 2.5" R8 | on wall | 0.21 | 0.62 | 0.93 | 0.92 | 0.91 | 1.03 | 0.85 | | |
| Owens Corning Unfaced | 2.5" R8 | 16" air | 0.59 | 0.84 | 0.79 | 0.94 | 0.96 | 1.12 | 0.90 | | |
| Owens Corning Unfaced | 3.5" R11 | on wall | 0.34 | 0.85 | 1.09 | 0.97 | 0.97 | 1.12 | 0.95 | | |
| Owens Corning Unfaced | 3.5" R11 | 16" air | 0.80 | 0.98 | 1.01 | 1.04 | 0.98 | 1.15 | 1.00 | | |
| Owens Corning Paper Out | 3.5" R11 | on wall | 0.58 | 1.11 | 1.16 | 0.61 | 0.40 | 0.21 | 0.80 | | |
| Owens Corning Unfaced | 6.25" R19 | on wall | 0.64 | 1.14 | 1.09 | 0.99 | 1.00 | 1.21 | 1.05 | | |
| Owens Corning Unfaced | 6.25" R19 | 16" air | 0.96 | 1.03 | 1.13 | 1.02 | 1.04 | 1.13 | 1.05 | | |
| Owens Corning Paper Out | 6.25" R19 | on wall | 0.94 | 1.33 | 1.02 | 0.71 | 0.56 | 0.39 | 0.90 | | |
Owens Corning 703 FG
(>1 400Hz, 600Hz, and 800 Hz) | 2" | | 0.50 | 1.16 | 1.17 | 1.15 | | | | | |
Owens Corning 703
(>1 @200Hz, 400Hz, 600Hz, and 800 Hz) | 3" | | 0.42 | 0.21 | 1.27 | 1.14 | | | | | |
| Owen Corning 703, Rigid Cor (RC), plain, on wall | 1" (25mm) | 3.0 pcf (48 kg/m3) | 0.11 | 0.28 | 0.68 | 0.90 | 0.93 | 0.96 | 0.70 | | |
| Owen Corning 703, Rigid Cor (RC), plain, on wall | 2" (51mm) | 3.0 pcf (48 kg/m3) | 0.17 | 0.86 | 1.14 | 1.07 | 1.02 | 0.98 | 1.00 | | |
| Owen Corning 703, Rigid Cor (RC), plain, on wall | 3" (76mm) | 3.0 pcf (48 kg/m3) | 0.53 | 1.19 | 1.21 | 1.08 | 1.01 | 1.04 | 1.10 | | |
| Owen Corning 703, Rigid Cor (RC), plain, on wall | 4" (102mm) | 3.0 pcf (48 kg/m3) | 0.84 | 1.24 | 1.24 | 1.08 | 1.00 | 0.97 | 1.15 | | |
| Owen Corning 703, Rigid Cor (RC), plain, air | 1" (25mm) | 3.0 pcf (48 kg/m3) | 0.56 | 0.85 | 0.70 | 0.89 | 0.93 | 1.06 | 0.85 | | |
| Owen Corning 703, Rigid Cor (RC), plain, air | 2" (51mm) | 3.0 pcf (48 kg/m3) | 0.66 | 0.95 | 1.06 | 1.11 | 1.09 | 1.18 | 1.05 | | |
| Owen Corning 703, Rigid Cor (RC), plain, air | 3" (76mm) | 3.0 pcf (48 kg/m3) | 0.66 | 0.93 | 1.13 | 1.10 | 1.11 | 1.14 | 1.05 | | |
Auralex Acoustics:
www.auralex.com/testdata/ | | | | | | | | | | | |
| Rockwool RW5 | 1.25" (30mm) | 100kg/m3 | 0.10 | 0.40 | 0.80 | 0.90 | 0.90 | 0.90 | | | |
| Rockwool RW3 | 2" (50mm) | 60kg/m3 | 0.11 | 0.60 | 0.96 | 0.94 | 0.92 | 0.82 | | | |
| Rockwool RW6 | 2" (50mm) | 140kg/m3 | 0.20 | 0.75 | 0.90 | 0.85 | 0.90 | 0.85 | | | |
| Rockwool RW3 | 3" (75mm) | 60kg/m3 | 0.34 | 0.95 | 1.00 | 0.82 | 0.87 | 0.86 | | | |
| Rockwool RW5 | 3" (75mm) | 100kg/m3 | 0.40 | 0.75 | 0.90 | 0.80 | 0.90 | 0.85 | | | |
| Rockwool RWA45 | | 45kg/m3 | | | | | | | | | |
| Rockwool RW5 300mm gap | 1.25" (30mm) | 100kg/m3 | 0.40 | 0.75 | 0.90 | 0.80 | 0.90 | 0.85 | | | |
| Rockwool RW6 300mm gap | 2" (50mm) | 140kg/m3 | 0.65 | 0.55 | 0.75 | 0.85 | 0.75 | 0.85 | | | |
Sound absorption coefficient legend:
0.00 = no absorption.
0.50 = 50% absorption.
1.00 = 100% absorption.
ISO/ASTM C432 -based results from product web sites 2003-3006. Reverberation chamber method. Differences less than 0.15 are "not significant". 100% does not mean that 100% of sound is gone.
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