Young's modulus is a measure of the elastic stiffness of the material, that is the stiffness of the material before it gets plastic (and permanent) deflections.
Elastic deformation = deformation where the material returns to it's original shape once the load is taken away. Most materials discussed here are both plastic and elastic; with increasing load they will first have elastic deformations, then plastic deformations. Plastic deformations are of no interest here, the loads are way too small for that.
Stiffness is a lot more complex than this. A lot. That expression describes the spring constant (k) for a rod under axial loading. If you start deforming a rod (or more correctly a beam) in a direction different than along the beam, you instantly get a much more complex equation which among other things is dependent on how the rod is tied in at the ends, if it can resist forces or moments etc, what kind of loading you have (load at one point, distributed loading or something different). Once you get into the realm of plates, which is the case for a speaker, it gets even more complicated.
It sure is more complicated for plates. The previous equation was a simplification that is OK if one dimension of a face plate is much smaller than the other dimension and was presented to show the simplistic relationship between stiffness and modulus of elasticity only. My point was that MDF and plywood are very similar in their bending behaviour as either beams or plates and the only variable to be concerned about when comparing the 2 materials is the modulus of elasticity if both cross sectional area and length are the same. Conversely if you want to achieve the same stiffness when using MDF you either need thicker material or the spacing between the braces will have to be smaller.
Yes, that is right. If I remember right, plate lateral stiffness (out of plane) is a function of the thickness cubed. It looks like BB ply is close to 4 times as stiff as mdf, which translates to a factor of about 1.6 in thickness.
In terms of the natural frequencies of the panels though, the mass also comes into play. I don't think the relative relationships for a rectangular panel is that difficult, I just need to dig it out of my head.
Plywood's modulus of elasticity is about 2 to 4 times higher than MDF so you'd need either 2 to 4 times the thickness or 1/2 to 1/4 the brace to brace spacing to get to the same stiffness (yes only for beams) or some combimnation between the 2 extremes.
The diamond modulus of elasticity is about 100 times greater than that of the best plywood so yes it could be stiffer for very thin layers if it could be manufactured in layers.
To continue with this theoretical example though, you would only need a 0.01" thich diamond wall to match the 1" plywood wall for stiffness but then the resonant frequency of that diamond wall would be around 400 Hz with 4" bracing.
Now I have to correct you. If we are concerned about vibration or movement in the plane of the panel in question, yes this is correct. But since we are discussing bracing I think we can assume that we are talking about movement perpendicular to the plane of the plate, and then the stiffness is a function of the thickness cubed.
In terms of braces it's also different. If you double the panel size in both directions, you get 16 times the deflection. So we are talking effects to the power of 4 here. So if we assume a factor of 4 for the modulus of elasticity between plywood and mdf, we end up with a factor of about 1.4 (or the square root of 2, more specifically) for the unbraced length.
Yes, I was still using the simplified beam equation, which would apply if the speaker wall was say 10 inches by 96 inches (a really tall and narrow enclosure).
For plates the "flexural rigidity" is
D is equivalent to (E * (h)^3) / (12 * (1 - (v)^2))
where
E is modulus of elasticity
h is thickness
v is Poisson ratio
Now where did I put the equation for deflection?
this is more like it, thickness cubed i have seen referenced before. and yes i accept that ply is better at a given thickness than ply, but these panel stiffnesses also assume that plywood is not anisotropic, and hence you have interply adhesion shear forces at play too surely?
i would think, without actually knowing i might add, that the adhesion between the compressed fibres and resin in MDF(perticularly exterior MDF) are perhaps better than that of adjacent plies in plywood;whatever grade it may be, and as such the damping better as a result.
Three things, both over my head at this point, but I'll comment anyways since usually lack of knowledge does not stop someone from having an opinion.
1) Wood defientely has different properties in different directions, along grain, across grain, etc and I'm not going to take the math that far since that usually involves differential equations and that makes my head hurt. For me these simplified equations are enough to show a trend.
2) The glue used to laminate plywood or stick together the fibers in MDF is typically stronger than the wood itself. For example when you break plywood, the plies do not usually separate, the wood ruptures or fractures.
3) Damping. I wish I could find some references that show the relative damping of plywood and MDF and a whole bunch of other materials. MDF may have better damping and may therefore be better than plywood but I can't say either way.
No, it's still wrong because that equation goes for axial deflection. The cube relationship holds for lateral deflection of a beam.
Alright, make me look it up!
Beam deflection is proportional to
(Load * (span^3)) / (E * I)
where I is moment of inertia and for a rectangular solid this is
I = (width * (thickness^3) / 12)
Dang, you're correct, cube relationship.
so
Beam deflection is proportional to
(span^3) / (thickness^3)
perhaps i would have beem more correct to say:
The compliance of the adhesive bond between layers/fibres, in ply/MDF; has an important role in material self damping, and in this respect i suspect this bond is more compliant in MDF, giving more self damping through frictional losses between fibres, but also giving the material less ultimate rigidity. I say this as i believe MDF will deform more readily than ply, which will bend really quite a long ways before breaking.
Great discussion by the way guys, im always learning, and i just have to question some of the more simplified models used...its in my nature..im still learning and its always a pleasure.
Try to absorbe my advices. The secret is to eliminate dynamic loss, you`ll never get it back later no matter how loud and big..
Asymetric cabinet w.diffractors/no absorbers is the way, but most builders are too focused on repeating sub-optimal solutions.
Since I'm new, I need a bit more explanation. What do you mean by dynamic losses?
Asymetric I understand and can do.
Diffractors I once again don't understand.
By no absorbers, do you mean no stuffing, no lining the walls?
Sound waves will travel through a medium whether it is resonating or not. A well braced box will resonate less but will still allow sound to escape.
It's important to remember that sound is energy and in order for it to dissipate, it needs to be damped. If I have one disagreement with Dave's method, it would be this: eliminating panel resonance does not help with energy dissipation, in fact it exacerbates the problem - a resonating panel can burn off a lot of energy.
The most effective sound proofing completely absorbs the sound, completely damps the energy within the sound proofing, not allowing it to pass through. It doesn't reflect it back into the room as an infinitely stiff barrier would.
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Well, why would you use stuffing in the first place? What do ypu think stuffing does wiyh sound
say what ?
Sound waves will travel through a medium whether it is resonating or not. A well braced box will resonate less but will still allow sound to escape.
It's important to remember that sound is energy and in order for it to dissipate, it needs to be damped. If I have one disagreement with Dave's method, it would be this: eliminating panel resonance does not help with energy dissipation, in fact it exacerbates the problem - a resonating panel can burn off a lot of energy.
The most effective sound proofing completely absorbs the sound, completely damps the energy within the sound proofing, not allowing it to pass through. It doesn't reflect it back into the room as an infinitely stiff barrier would.
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