How much louder is a 2x12 than a 4x10? Physics help needed...

drdunwoody · #1 10-01-2010, 07:48 PM

Ok, if I remember geometry right the area of a circle is pie r squared so the area for a 12" speaker is 113.04 giving me 226.08 square inches of area in a 2x12 cab. The area for a 10" speaker is 78.5 giving me 314 sqr inches in a 4x10. 226 goes in to 314 1.38 times so the 4x10 has about 38% more area moving air than a 2x12.
First question, is that correct?
Second question, does 38% more area mean 38% louder?
I think I can simplify this question like this. If I have one 4ohm cab OR 2 8ohm cabs of the same type, is it now twice as loud? In other words, if I keep the wattage and ohms constant, does doubling surface area (by doubling the speakers) double the volume?
I'm trying to figure out just HOW MUCH louder a 4x10 is than a 2x12! My answer is 38% louder. Any help out there on this?

mulchor · #2 10-01-2010, 07:52 PM

I kinda think you'd do better to look at sensitivity (SPL at 1M with 1W, usually measured or fabricated at 1k Hz).

But going with the dimensions, perhaps I should remind you they're called speaker CONES.

Your approach seems not too misguided if you're lookin for a general guess that's not specific to any particular pair of cabs.

Jim Carr · #3 10-01-2010, 07:58 PM

Speaker area? Wrong formula and wrong approach. For area, you need truncated cones, but that won't help much, either.

I have had two 212 cabinets, a 65 Fender Bassman (loaner), and a Vox Essex 212. Both were utterly worthless. My long gone, modern, and not very loud (IMHO) WM15 would mop the floor with them.

Speakers are not just area, to say the least.

pin_head_47 · #4 10-01-2010, 07:58 PM

Barefaced Bass has alot of good technical info at their website here. Not all of it pertains to your question, but it's still a good read anyways. Alex is also a member here at TB, and I'm sure that both him and Bill Fitz Maurice will be chiming in shortly.

In short though, it has alot more to do with the specific speakers and cab than just the amount of surface area you have.

JimmyM · #5 10-01-2010, 08:01 PM

ya, generally speaking, you're correct. however, it's not simply a question of size that accounts for air movement. there are a handful of factors, one being the efficiency of the cab, another being the xmax (how far the cone travels), and a couple other factors that escape me atm.

billfitzmaurice · #6 10-01-2010, 08:14 PM

Quote:

Originally Posted by drdunwoody

I'm trying to figure out just HOW MUCH louder a 4x10 is than a 2x12! My answer is 38% louder.

No.
How loud a cab will go is the product of frequency response, sensitivity and displacement.

drdunwoody · #7 10-01-2010, 08:23 PM

Ok, Ok, I know about sensitivity and forgot about the cone thing but assuming sensitivity is equal, then what? Not sure how to factor in cone excursion...

billfitzmaurice · #8 10-01-2010, 08:38 PM

Quote:

Originally Posted by drdunwoody

Ok, Ok, I know about sensitivity and forgot about the cone thing but assuming sensitivity is equal, then what? Not sure how to factor in cone excursion...

Learn how to use WinISD Alpha Pro and it will do all the calculations for you.

drdunwoody · #9 10-01-2010, 09:05 PM

WinISD is Windows only and I'm on a Mac. Hmmm. I started another thread recently on deciding between keeping my Aguilar GS212 or getting a 4x10 because I'm playing with three guitarists, two of which are playing tube powered 4x10. I love the Aguilar sound but I'm running my Genz Benz GBE750 at 70% volume in our practice space and have been considering a 4x10 purchase to have the extra volume...hence the source of my consternation! I know that in the end I just need to A/B the cabs but that is easier said than done. I might just go out and purchase a used 4x10 so I can do just that though I know that manipulates too many variables at once. BUT, it is the only way to actually decide. I was trying to make the decision rationally (based on calculations) to help but I don't think that is helping. BUT, ALL other things being equal, the 4x10 will be thirty something percent louder?! Someone through me a bone! I know your all correct....ok, maybe I'll just get a 4x10....

JimmyM · #10 10-01-2010, 09:12 PM

i'm thinking you need more than a 212 or a 410 if that's the kind of volume you're playing at. maybe double up on the aggies, or get an 810 or something. that's a lot of juice for one 212.

Stick_Player · #11 10-01-2010, 09:20 PM

Quote:

WinISD is Windows only and I'm on a Mac. Hmmm.

I've heard that WinISD will run on a Mac using Apple Boot Camp.

But you know how rumors are...

Do some research.

interstatejoe · #12 10-01-2010, 10:06 PM

Too many unknown variables. Its like asking how much faster is a Corvette than a Camaro? If it has a 38% larger engine does that equal 38% more power? Does that also mean its 38% faster?

Son of Bovril · #13 10-02-2010, 01:19 AM

your best answer will be to go to a music shop and hook up different cabs to the same head at the same volume...

Sometimes a cab just sounds louder because of the tone of the cab... some have a mid boost while some have mid cut or a higher low end roll off, so really the only way to know for sure is to test them... and testing them in a band practice is even better...

BassmanPaul · #14 10-02-2010, 06:53 AM

Quote:

Originally Posted by drdunwoody

WinISD is Windows only and I'm on a Mac. Hmmm. .

WinISD will run quite happily from the Linear website using Safari. If you have an intel Mac it'll run Windows natively or you could use Parallels or VirtualPC

lomo · #15 10-02-2010, 06:54 AM

If your head is 2 Ohm stable I'd consider adding another 12 or 212

billfitzmaurice · #16 10-02-2010, 07:53 AM

Quote:

Originally Posted by drdunwoody

I know that in the end I just need to A/B the cabs

That's your only option. Even if you knew how to use WinISD that does you no good if you don't have all the driver parameters, and that's something you can't get.

Quote:

I'm running my Genz Benz GBE750 at 70% volume in our practice space

That's also something you have no way of knowing, as you don't know what its displacement limited power is, and I doubt very much that you have a voltmeter telling you how much voltage your amp is producing.

georgestrings · #17 10-02-2010, 08:16 AM

Quote:

Originally Posted by JimmyM

i'm thinking you need more than a 212 or a 410 if that's the kind of volume you're playing at. maybe double up on the aggies, or get an 810 or something. that's a lot of juice for one 212.

Agreed - it also sounds like you'll be damaging your current 212 if you keep pushing it that hard in an attempt to keep up...

- georgestrings

Bmorefoozler · #18 10-02-2010, 11:16 AM

Quote:

Originally Posted by interstatejoe

Too many unknown variables. Its like asking how much faster is a Corvette than a Camaro? If it has a 38% larger engine does that equal 38% more power? Does that also mean its 38% faster?

NO, but you actually brought up an example that can be used to help the OP in one way.

One question you asked, is 38% more air 38% more volume is FALSE. Much as in a car, as you add power, it doesn't get louder(faster) linearly. A 400 HP Corvette could have 38 % more power then a roughly 290 hp Camaro, bu tit would NOT likely go 38% faster. It would be more like 10%, all other things being equal.

So all other things being equal, but using displacement instead of area(3 dimensions, in and out too), 38% displacement will not get 38% louder.

Twice as loud is mopre like double the power and 4 times then speaker displacement then it is doubling your current setup. If you add a combo amp, to another combo amp, they are not twice as loud together. But if both have parrallel outs that double their watttage, then one alone is half as loud as both with ext cabs, roughly and generally speaking.

alexclaber · #19 10-02-2010, 11:32 AM

To go twice as loud in the mids requires either 10dB more sensitivity or 10x the thermal power handling or a combination of the two (say 4dB more sensitivity and 4x the thermal power handling), thus getting you 10dB more output which equates to ~10 phons.

To go twice as loud in the lows you probably don't need 10dB more SPL, more like 6dB more SPL to hit 10 phons (google equal loudness curves to see why). This requires 4x volume displacement, which is equivalent to having 4x excursion limited power handling and no change in sensitivity, or 2x excursion limited power handling and 3dB better LF sensitivity (which is what you get when you add a second matching cab).

However, 99.999% of bass cabs are worse at producing LF SPL than midrange SPL so that's usually your limiting factor - you might be well within your midrange SPL limits but already hitting the LF SPL limits, in which case the easy way to get louder is to compromise on the amount of bottom in your tone.

Regarding the 2x12" vs 4x10" - how well designed is the cab, how good are the drivers and what were they designed to do, what do you want from it, etc etc. It's like saying "what's quicker from 0-60mph, the car with two 12" wide rear tyres putting down the power or the car with four 10" wide tyres (i.e. 4WD) putting down the power?" Too much missing information - how much do the cars weigh, how powerful are they, what are their aerodynamics like, is the road wet or dry, etc etc. That's a good analogy, I think I'll reuse that in a magazine article!

Jim C · #20 10-02-2010, 02:43 PM

I think what the senator was asking is, based on standard cabinets available from the same manufacturer with similar effeciency ratings, which box makes more racket; 2x12 or 4x10?

Is there a generic answer that is somewhat accurate?

edit: corrected to say 4x10