# Sound Wall Theory - Poke Holes In This?



## sandbag (Aug 2, 2009)

After constructive criticism of my sand bagged theater plans, I am considering other alternatives and hope to receive helpful comments/insights. Conventional theory proposes a two leaf double wall construction approach comprising a high mass soundroom wall having two layers of resilient damping adhesive between drywall sheets and secured to stud/joist surfaces. The 'receiving wall "mirrors this construction having internall open stud/joist edges "buried infiberglass thermal insulation. These two structures are separated by at least 1" of air space, again filled with fiberglass insulation. One could buy reprocessed cotton insulation to avoid the fiberglass inhalation issue but that should not be necessary provided the room has been properly sealed against air leaks and other flanking sound pathways.

So - this design comprises a high mass flat wall surface stiffened by longitudinal members (studs/joists). I propose that the functionality of this design utilizes the two sides and one edge of each stud coupled to the flat inner surface of the drywall as a series of radiator chambers having greater surface areas that the soundroom side of the wall. In theory, these vibrating edges convey sound energy from the resonating flat panel to the inner open insulated chambers. On a 3/5" - 1" - 3.5" wall, this creates a 7/5" deep series of linked resonating chambers 8' high by 16" to 24" wide. 

If I am correctly hypothesizing that these linked resonating chambers operate to transmit sound into the insulated chamber via their torsional vibration transmitted from their resonating secured edge ( the glued and screwed portion mechanically coupled to the 90 degree drywall surface, then it seems logical that the their thickness (1.5") and length (8'-0") might be limiting the total possible functional attenuation capacity of the combined two leaf double wall system. I agree that the between leaf air space should be as large as possible. We know for certain that sound energy is lost as it travels through atmosperic air, theoretically by causing gas and dust molecules to resonate, converting sonic energy to heat. This effect is theoretically increased when in addition to these molecules, polymeric silicon strands are incorporated into the space in the form of fiberglass insulation batts. (Think of the fiberglass as lots of dust permanently suspended within the air.) The linked air chambers surrounding the listening space should help sound attenuation over a broad spectrum especially where the space is filled with fiberglass to add molecular mass to that of the air for more sound energy to heat energy conversion. For a 12x15x8' room volume (1440 cu ft), one is creating a five surface dead air space of about (subtracting the wood volume): 1 ceiling(12x15x.5) + 2 walls(12x8x.5) + 2 walls (15x8x.5) 316 cu ft. for about a 1:5 ratio of insulating air chamber to room area ratio. The volume loss with steel studs should be much less. However, their "I" shape design comprising a pair of relatively rigid parallel edges linked by a web, itself having decreased surface area due to utility cable cutouts along the web may account for their wood stud like performance.

If, as is suggested here, the stud/joist "ribs" are significant resonators of sound energy, and logic dictates that they are, the reason one does not want to secure their inner edges is that they would lose a significant amount of vibrational freedom, or freedom to torque in response to energy transferred from the high mass flat panel. Sound energy will be instead propogated mechanically into the additional leaf, and resulting in the drumhead effect of the inner leaf.

What if, instead of traditional 2x4 stud "ribs," one used thinner (say .5" to nominal 1") stud ribs? Would these not radiate more vibrational energy into the dead air cavity, and to begin resonating at lower sound pressures? What if instead of 16" centers, they were installed at half the distance (for example 8") between centers? This would approximately double the side rib surface area, permitting the same 7.5 inch air space to attenuate nearly double the vibrational energy. Further, the closer the rib surfaces, the more likely it will be that interfering reflections will be produced.

Consider: l....l....l....l conventional 16" stud array vs l..l..l..l..l..l..l 8" stud array or even l.l.l.l.l.l.l.l.l.l.l 4" stud array. 

I suggest that the internal stud surfaces should be thought of as a type of Helmholtz transducer. The more stud depth, the more profound the attenuation at that wave length. Notice that a double wall system produces more attennuation that a staggered stud wall. Consider that many engineers are seen to line up the studs in the double wall system edge to edge, thereby creating full 7.5 inch cells, rather than staggered 4.5" cells. 

So - here is my thought problem. Would a double wall system comprising studs/joists of thinner material (say 3/4" stock) spaced 8" on center provide improved sound attenuation for an equivalent mass and depth system? 

Wall thickness. We know that neither the 8" concrete block wall, or an 8" thick two leaf, single stud wall (5/8 drywall on each side of 2x8 studs) accomplish nearly the sound attenuation that two 3.5" single leaf walls spaced apart by 1" does. If the theory is correct, then the addition of a limp mass membrane within the 1" airspace should provide significant sound attenuation by spreading the sound wavefront energy along the membrane. I have long thought that MLV, while expensive, is an app0roach that ought not be overlooked. As one would suspect, laminating MLV between two leaves, or merely using MLV as a semirigid face within a solid wall overlooks what the product can offer. Instead of securing it to either stud face, suspending it from the top plate, taping and overlapping its seams, and letting its lower edge brush the bottom of the stud spaces at the floor, would allow it to perform as intended - a limp mass sound deadener. Spaced 1/2" from the inner stud edges as I'm oproposing would limit vibrational coupling. 

Comments? 
A 

If I am correct that the detrimental effect of the linked leaf wall is related to its characteristic rigidity and mechanically coupled set of flat radiating surfaces planar to the direction of the sound waves, then eliminating the mechanical coupling should help. of concern, then


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## Ted White (May 4, 2009)

In the end, I rather liked the sandbag idea, actually…

Regarding your thoughts:

There is only 1 effective chamber, given that they are all united via common airspace.

The radiation from side A to side B is both from the framing/panel intersection (secured edge) as well as the panel itself. If you touched your finger to a vibrating wall you would feel (approximately) equal vibration on the stud as well as the panel. Keep in mind that we are describing very long wavelengths. Wavelengths longer than the individual studs and cavities. The entire leaf is oscillating.

The dimensions of the framing will not appreciably affect the Transmission Loss in a decoupled system. It certainly would affect things if it were a coupled, single stud system. This is precisely why a 25 ga steel (single) stud wall will outperform a wood stud wall. 

Limp mass inserted in the center of a double stud cavity will reduce your system to a triple leaf. Two smaller independently resonating cavities, both resonating at higher frequencies than the single large cavity. It’s a sure recipe to reduce TL in LF.


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