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Fender Rumble Club

And since radius is half the diameter, that becomes 1/4 when squared, and then it's also distributed across addition, then it also gets canceled. So basically, if you want to see what has more speaker area, just add up the square of the diameters for your comparison.

For instance, a 2x15" has less speaker area than a 4x12" because 15^2 + 15^2 = 450 and 12^2 + 12^2 + 12^2 + 12^2 = 576 and 450 < 576. HOWEVER, your average 2x15" cabinet is a lot deeper and bigger than a single 4x12", and your average 15" is more efficient than your average 12" speaker, so you have to consider all these different things when you think about how much air you're moving.

As for showing work, real mathematicians don't consider those steps to be worth showing. ;)
 
Dangit, now you are going to make me do the math...

A = π r2 (sorry not sure how to type the powers)...

Order of operations tells us to raise to the powers first.

So A = π 100 or 314.16 for a single 10" 628.32 sq/in for 2 10" diameter speakers.
So A = π 225 or 706.86 for a single 15"

This of course makes a bad assumption that the speaker circle area is a flat circle. It is not, It is a cone.

Care to do the math for that? I don't know what the cone depth of each is, but I suspect that there will be a similar difference...
 
Dangit, now you are going to make me do the math...

A = π r2 (sorry not sure how to type the powers)...

Order of operations tells us to raise to the powers first.

So A = π 100 or 314.16 for a single 10" 628.32 sq/in for 2 10" diameter speakers.
So A = π 225 or 706.86 for a single 15"

This of course makes a bad assumption that the speaker circle area is a flat circle. It is not, It is a cone.

Care to do the math for that? I don't know what the cone depth of each is, but I suspect that there will be a similar difference...

Invalid Link Removed

"How to calculate cone area Cone area = pi x (r x r) pi = 3.14 r = radius of sub One 8" = 50.27 One 10" = 78.54 One 12" = 113.1 One 15" = 176.71 One 18" = 254.47 Two 8" = 100.53 Two 10" = 157.08 Two 12" = 226.19 Two 15" = 353.43 Two 18" = 508.94 Three 8" = 150.8 Three 10" = 235.62 Three 12" = 339.29 Three 15" = 530.14 Three 18" = 763.41 Four 8" = 201.06 Four 10" = 314.16 Four 12" = 452.39 Four 15" = 706.86 Four 18" = 1017.87"
 
Invalid Link Removed

"How to calculate cone area Cone area = pi x (r x r) pi = 3.14 r = radius of sub One 8" = 50.27 One 10" = 78.54 One 12" = 113.1 One 15" = 176.71 One 18" = 254.47 Two 8" = 100.53 Two 10" = 157.08 Two 12" = 226.19 Two 15" = 353.43 Two 18" = 508.94 Three 8" = 150.8 Three 10" = 235.62 Three 12" = 339.29 Three 15" = 530.14 Three 18" = 763.41 Four 8" = 201.06 Four 10" = 314.16 Four 12" = 452.39 Four 15" = 706.86 Four 18" = 1017.87"

That is the formula for surface area of a circle, not cone. A = pi rxr or pi r squared. (Each order of power is the value times itself...)
 
From Eminence: Basslite S2010 - Peak Diaphragm Displacement Volume (Vd)140 cc
and, Surface Area of Cone (Sd)350.1 cm2
Speaker Detail | Eminence Speaker

and just for comparison's sake: Basslite S2012 - Peak Diaphragm Displacement Volume (Vd)270.1 cc, and, Surface Area of Cone (Sd)519.5 cm2

Basslite C2515 - Peak Diaphragm Displacement Volume (Vd)380.9 cc, and, Surface Area of Cone (Sd)856 cm2
 
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Well, in full disclosure, the details of the surface area and displacement are interesting, but I would much rather be PLAYING through my Rumble, whether it's the 200 with the 115 or the 500 with the 210.... Whatever mathematical manner that Fender applied to these, they just sound awesome!
 
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Here is the math I like best. My old 100 watt bass amp with a 15 inch speaker weighed 65 pounds. The Rumble 200 is 140 watts with a 15 inch speaker and it weighs only 34.5 pounds (65 - 34.5 = 30.5) Over 30 pounds less and it apparently doesn't have any cabinet rattles or people would be talking about that. I would think that is why you'd overbuild bass amps to begin with. Fender "subtracted" weight, in fact, almost "divided" it in half; "added" value, and has "multiplied" my desire to get me a Rumble.