Does this make sense for a more manageable 4x12?

[cdemike]

I was digging around to read about the different ways people have tried to make more portable rigs that still sound like big 4x12's. As I understand it, there seem to be a number of sonic qualities that come specifically with how 4 speakers interact both with each other and with the cabinet itself that are not really possible to capture in a 2x12. That made me wonder about lightweight 4x12's, and it seems like the very small ones can bring weight into a range that's sometimes comparable with heavier 2x12's. So I wanted to see about a lightweight 4x12 build that involves minimal sonic compromise versus a full-sized 4x12. I'm not as knowledgeable about acoustic design, so I wanted to run my thinking by everyone first.

My benchmark is a Marshall 1960B/1982B, and my understanding is that the cabinet's depth is a critical part of sound because of the reflection of waves 180 degrees out of phase with the sound leaving the cab. But to cut down on weight and to help with portability, reducing the volume overall makes sense overall as the greatest possible weight savings, so I'm thinking 26"x26"x14" maximizes weight savings while retaining some of what makes a Marshall 4x12 sound the way it does. Because down-scaling the other dimensions involves considerable changes to the sound of a cabinet, so I wanted to see if it'd be possible to use changes to the materials to compensate for the sound difference. Specifically, reducing the baffle's area will increase its resonant frequency, which could be offset by using slightly thinner material, which would reduce the (1,1) plate bending mode.

Here's the math
(1,1) Plate Bending Mode (i.e., f₁₁):

f(1,1).PNG (2.75 KiB) Viewed 18340 times

where λ^3 is the plate constant, D = flexural rigidity, p = density, h = thickness, Lx = width, and Ly = height

For these calculations I used a plate constant for a clamped square (35.99)

Flexural rigidity (D):

Flexural rigidity.PNG (2.13 KiB) Viewed 18340 times

where E is Young's modulus and v = Poisson's ratio.

Using the dimensions described in this plan for a 1960B/1982B, the baffle's dimensions come out to roughly 730mm x 730mm:

These are the values I found for Baltic birch plywood:
E = 10.5 GPa
p = 680 kg/cubic meter
v = 0.3

If constructed from the typical 18mm birch plywood, D comes out to 5,609 N, producing f₁₁ = 231 Hz.

Adjusting for the smaller (26"x26") and thinner (15mm) baffle, the values come out to D= 3246 N and f₁₁ = 235 Hz.

So there would be minimal difference in the bending frequency of the baffle with the compensated thickness. With the smaller cab having 86.78% the surface area and with 15mm ply being 83.33% as thick as 18mm ply, the total weight of the cab alone would be 72.32% as heavy as a Marshall 4x12 if you're not counting the back cover. So while a typical Marshall 4x12 weighs 40-50 lbs unloaded, this reduced size version would weigh 30-36 lbs. The reduced size would also mean it'd be a little easier to carry, maneuver through doors, and fit on tighter stages.

Does this seem like a reasonable line of thought to get a more manageable 4x12 that doesn't sound terribly different than a full-sized version made from typical 18mm birch plywood?

[Roe]

I was digging around to read about the different ways people have tried to make more portable rigs that still sound like big 4x12's. As I understand it, there seem to be a number of sonic qualities that come specifically with how 4 speakers interact both with each other and with the cabinet itself that are not really possible to capture in a 2x12. That made me wonder about lightweight 4x12's, and it seems like the very small ones can bring weight into a range that's sometimes comparable with heavier 2x12's. So I wanted to see about a lightweight 4x12 build that involves minimal sonic compromise versus a full-sized 4x12. I'm not as knowledgeable about acoustic design, so I wanted to run my thinking by everyone first.

My benchmark is a Marshall 1960B/1982B, and my understanding is that the cabinet's depth is a critical part of sound because of the reflection of waves 180 degrees out of phase with the sound leaving the cab. But to cut down on weight and to help with portability, reducing the volume overall makes sense overall as the greatest possible weight savings, so I'm thinking 26"x26"x14" maximizes weight savings while retaining some of what makes a Marshall 4x12 sound the way it does. Because down-scaling the other dimensions involves considerable changes to the sound of a cabinet, so I wanted to see if it'd be possible to use changes to the materials to compensate for the sound difference. Specifically, reducing the baffle's area will increase its resonant frequency, which could be offset by using slightly thinner material, which would reduce the (1,1) plate bending mode.

Here's the math
(1,1) Plate Bending Mode (i.e., f₁₁):

f(1,1).PNG
where λ^3 is the plate constant, D = flexural rigidity, p = density, h = thickness, Lx = width, and Ly = height

For these calculations I used a plate constant for a clamped square (35.99)

Flexural rigidity (D):
Flexural rigidity.PNG
where E is Young's modulus and v = Poisson's ratio.

Using the dimensions described in this plan for a 1960B/1982B, the baffle's dimensions come out to roughly 730mm x 730mm:
marshall 4x12.gif

These are the values I found for Baltic birch plywood:
E = 10.5 GPa
p = 680 kg/cubic meter
v = 0.3

If constructed from the typical 18mm birch plywood, D comes out to 5,609 N, producing f₁₁ = 231 Hz.

Adjusting for the smaller (26"x26") and thinner (15mm) baffle, the values come out to D= 3246 N and f₁₁ = 235 Hz.

So there would be minimal difference in the bending frequency of the baffle with the compensated thickness. With the smaller cab having 86.78% the surface area and with 15mm ply being 83.33% as thick as 18mm ply, the total weight of the cab alone would be 72.32% as heavy as a Marshall 4x12 if you're not counting the back cover. So while a typical Marshall 4x12 weighs 40-50 lbs unloaded, this reduced size version would weigh 30-36 lbs. The reduced size would also mean it'd be a little easier to carry, maneuver through doors, and fit on tighter stages.

Does this seem like a reasonable line of thought to get a more manageable 4x12 that doesn't sound terribly different than a full-sized version made from typical 18mm birch plywood?

18mm birch plywood makes it less managable. 5/8" is correct. If you go thinner, you may add bracing like you do on a boat

[cdemike]

18mm birch plywood makes it less managable. 5/8" is correct. If you go thinner, you may add bracing like you do on a boat

Thanks for the correction! Re-running the numbers, 5/8" birch plywood in a 730x730mm baffle comes out f₁₁ = 203 Hz. That might make 1/2" birch plywood a good option with f₁₁ coming out to 199 Hz. Weight savings between 5/8" and 1/2" look marginally less appealing (30.3 lbs - 38 lbs), so this may be more about the advantages associated with a slightly smaller cab while keeping the sound as close as possible.

At that point, I'd be wondering if people have tried making 4x12's out of 1/2" birch plywood and encountered any issues with durability. But it would mean essentially identical frequency response from the baffle with considerable improvement in portability and a slight improvement in weight (though still well over 50lbs loaded if using the typical Celestion drivers).

[xtian]

Are you ever going to be able to play loud enough for cabinet thump to be a thing?

[cdemike]

Most of the drummers I play with are pretty hard-hitting, but point taken that for most cases a 4x12 is a pretty overkill piece of gear. Once in a while I do get to play outdoor shows where I can open up an amp unattenuated. So I guess I’m lucky that I get to play pretty loud enough to actually feel and hear that.

All that said, main reason I’d be using the 4x12 is for the interaction between the speakers and with the cabinet when recording.

[Geeze]

A bit late to the party on this.

Have you thought of other shell materials? Speaking strictly from a weight perspective do you know what the weight of a cubic foot of BB style plywood is? Marine grade 3/4" is listed as 75lb for a 4x8' sheet The same area of Radiata piine is 68lb. The reason for the ask is there are many sources of weight between wood species in addition to the physical characteristics - thinking modulus of elasticity [stiffness] - as a weight saving method vs. plywood.

While not a 4x12 I have built several TL-806 cabs with plywood, african mahogany with the specified 3/4" plywood baffle and back plus few experiments with Radiata pine [Lowes, HD & Menard's] and 1/2" ply backs and baffles. They are lighter and more lively - if that is a sonic word - and deliver more low end than the others. I built a working musician a one off in 2013 and he came back last year for another stating it was the best cab sound wise he owns for performance and recording.

On a smaller 4x12 a livelier cab might be a benefit - just spit balling here.

Russ

[chaccmgr]

You could also look at poplar plywood if this is available in your region. It is significantly lighter than BB

[M Fowler]

I like the Marshall 4x12 myself but colossal was saying he likes a detuned 4x12 using only two speakers not four.

Mark

[Colossal]

I like the Marshall 4x12 myself but colossal was saying he likes a detuned 4x12 using only two speakers not four.

Mark

For my own tone chase, I am always after string to string clarity and separation with a lot of detail. I am playing through a pair of Forte style 2x12s these days, the bottom speaker is closed and the top has side vents. But I did like the sound of the so-called detuned 4x12.

[M Fowler]

Chasing tone right Dave!