Perceived volume vs. mathematical volume.

Ah, but many, many combos are designed to get the most out of the amp's power without regard to adding a second cabinet. It's a whole lot easier to market 200W combo than a 100W combo at the same price.

That being said, as long as the 8 ohm wattage is giving you an acceptable tone and you aren't turning way up, I bet the volume of the two setups is similar, and the two cabinet setup may be a bit louder. There are som considerations regarding efficiency and multiple cabinets/drivers that I don't feel qualified to expound upon.

At the very least, you probably hear the mids better with your 210 on top of the 2x12, right?

I'm guessing this may have been a marketing add-on feature by Eden rather than a feature designed in by engineering. Eden built a combo and maximized the performance by making the speaker load 4 ohms. After it was all designed (and probably in production) marketing said "It has to have a jack for an extension speaker." Engineering said "The amp won't survive with a 2 ohm load, so we'll have to make the jack series instead of parallel."

The only factor working in your favor here is that the increased speaker cone area will move more air, somewhat negating the effect of the increased impedance and decreased wattage.

Eden doesn't win any design awards for this gem!

I've always thought EQ has more of a "perceived" effect on volume than watts. Turn up the mids and see what that does to "perceived" volume.

When series wiring a second identical cab radiation efficiency is doubled, but the voltage sent to each cab is halved, so the net result is a wash. Only if the amp has significantly more power available than one cab alone can handle would two cabs be louder than one.

The total power is halved, and each cabinet is being powered by half of the halved wattage.

I think it's really more of a matter of whether you prefer the tone that comes out of both cabs vs. just the 2x10. You certainly aren't going to break anything by using the lower wattage.

Also, the efficiency of the extension cabinet could come into play. Bill points out that using a pair of identical cabinets radiation efficiency is doubled. If the 2x12 is a more efficient cabinet than the 2x10, I think you may in fact see an increase in volume by using both. You alluded to this idea when you talked about the 2x12 pushing more air. I'm not sure that purely increasing driver surface area necessarily increases efficiency, but the 2x12 may be more efficient, nonetheless.

Moving twice as much air would equate to a 6dB increase in SPL. But if you halve the power power doing this in each speaker you get a reduction of 3dB. You have another reduction from 200W to 150W which is a reduction of 1.25dB. I think your net increase is around 1.75dB (6 - 3 - 1.25). Which is not a whole lot. This would be equivalent to turning 200W into 300W into the same cabinet. But to answer the question 2 is louder than 1. Another question is does the efficiency of the speakers increase as the power is decreased? Not sure the answer on that one. At too low of volume the efficiency may not be good and the same is true for to high of volume.

DavePlaysBass said:

Moving twice as much air would equate to a 6dB increase in SPL. But if you halve the power power doing this in each speaker you get a reduction of 3dB. You have another reduction from 200W to 150W which is a reduction of 1.25dB. I think your net increase is around 1.75dB. Which is not a whole lot. But 2 would be louder than one.

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Say what now? Assuming the 2x12 is as efficient as the 2x10, he's getting a 3dB increase from adding the extension cab. The power decrease should account for around a 1.2dB loss and nothing more, if the specs are accurate. All other factors being the same, it should be around a 1.8dB increase, which probably isn't worth the effort of hauling another cab around. You're right on the money with your final calculation.

That 6dB figure you have is spread around quite a bit. That only happens if you connect the other enclosure in parallel - it's a 3dB increase from doubling speaker area at the same efficiency, and another 3dB increase from doubling power from the reduced impedance. That's optimistic, though. In practice, very few amplifiers double their output with half the impedance. Furthermore, you don't drop 3dB for less power, then proceed to drop the correctly calculated 1.8dB for less power as well. That would imply a power drop to around 65W.

EDIT: I may have worded some of that wrong. Rather, the 6dB figure that gets thrown around comes from doubling speaker area WHILE maintaining the same amount of power to each enclosure. IE: You have a 2x12 getting 300W. You add another 2x12 and it gets another 300W, while the first 2x12 continues to get 300W. THAT would result in 6dB increase.

Nick Kay said:

.

EDIT: I may have worded some of that wrong.

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All of you did. The correct answer is the one given in my first post. Two identical cabs series wired will have a net sensitivity increase of 0dB. BTW, power has nothing to do with it, voltage swing does, as it is voltage swing that determines cone excursion, and thus SPL. Power only enters the equation as a determination of the ability of an amplifier to deliver a given voltage into a given load.

Nick Kay said:

Say what now? Assuming the 2x12 is as efficient as the 2x10, he's getting a 3dB increase from adding the extension cab. The power decrease should account for around a 1.2dB loss and nothing more, if the specs are accurate. All other factors being the same, it should be around a 1.8dB increase, which probably isn't worth the effort of hauling another cab around. You're right on the money with your final calculation.

That 6dB figure you have is spread around quite a bit. That only happens if you connect the other enclosure in parallel - it's a 3dB increase from doubling speaker area at the same efficiency, and another 3dB increase from doubling power from the reduced impedance. That's optimistic, though. In practice, very few amplifiers double their output with half the impedance. Furthermore, you don't drop 3dB for less power, then proceed to drop the correctly calculated 1.8dB for less power as well. That would imply a power drop to around 65W.

EDIT: I may have worded some of that wrong. Rather, the 6dB figure that gets thrown around comes from doubling speaker area WHILE maintaining the same amount of power to each enclosure. IE: You have a 2x12 getting 300W. You add another 2x12 and it gets another 300W, while the first 2x12 continues to get 300W. THAT would result in 6dB increase.

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Power is power. Conservation of energy applies regardless of parallel or series connection. The net result of adding twice as many speakers to the same power is 3dB which is exactly what I said (6dB - 3dB = 3dB gain). You state the answer. I state the way you get there. We are saying the same thing.

I'd get a power amp to power the 2x12. It'd be a cheap way for you to get from tall-but-quiet rig to a killer rig. Find something that can put 500 watts into 4 ohms (bridged mono)and you're set. On the used market you might be able to find one for $100 - $150.

billfitzmaurice said:

All of you did. The correct answer is the one given in my first post. Two identical cabs series wired will have a net sensitivity increase of 0dB. BTW, power has nothing to do with it, voltage swing does, as it is voltage swing that determines cone excursion, and thus SPL. Power only enters the equation as a determination of the ability of an amplifier to deliver a given voltage into a given load.

Click to expand...

Your orignal post you assume the VOLTAGE to each speaker is cut in half. If that was true, the SPL increase would be 0 as you indicated. However, the voltage does not get cut in half to each speaker as you assumed. If it did the power would cut in half for the 8-ohm load.

Here's my math.

Ptotal = Vtotal^2 / Rtotal

If Rtotal increase by a factor of two (4 to 8), then Vtotal increase by a factor of 1.414 to maintain the same Ptotal.

Or said another way, if Rtotal increases by a factor of two, and Vtotal stays the same per your original assumption, Ptotal would be cut in half.

If you look at most solid state power amp ratings, the 8-ohm rating is more than 1/2 the 4-ohm rating. This implies to me that the limit at 4-ohms is probably current or thermal related (current equates to heat and heat equates to failures). Where as at 8-ohm loads the limit is voltage related with the voltage capability being higher at 8-ohm than it is at 4-ohm. The 4-ohm condition cannot operated at the highest voltages of the 8-ohm situation because the current will be too high and make things too hot. The 8-ohm condition can not run the highest current level of the 4-ohm condition because it does not have enough voltage overhead. This is solid state of course. With tube amps there are output transformers that change the whole conversation. There are also control loop issues regarding damping that get worse at lower impedance conditions that can get in the way of things.


Here's some math around adding a second cabinet in series and manitaining a constant power to the combined cabinet load:

Constant power situation of 200W

@ 4-ohm load the voltage is 28.3V (V^2 / R = P)

SPL is proportional to 28.3V (agree?)



If we increase the load to 8-ohm because we have another cabinet in series, we must also change voltage to maintain constand power.

@ 8-ohm load the output voltage is 40V to maitain 200W load (V^2/R = P, 40^2 / 8 = 200).

Each 4-ohm cabinet sees half of this which is 20V

Each speaker has SPL proportional to 20V. If the speakers are in phase, the combined SPL is proportional to 40V (20V + 20V).

If we then go into the world of dB we use the equation 20*log(ratio) for SPL. Power uses 10*log (ratio) for reference.

20*log (40/28.3) = 3dB increase



Parallel or series it does not matter. Mother nature has that conservation of energy stuff figured out. What does matter are the constraints on the power amp. If going series the power amp must put out more voltage to maintain the same power because of the increase in total load impedance.





Now the math behind the original post. 200W into one 4-ohm cab versue 150W into two 4-ohm series connected cabinets.

200W into 4-ohm speaker

Voltage is 28.3V

SPL is proportional to 28.3V




150W into 2 x 4-ohm series connected speaker

Voltage is 34.64V total which gets applied to the total 8-ohm impedance. Each speaker gets 17.3V. SPL per speaker is proportional to 17.3V. Total SPL for phase adding speakers is 34.6V (17.3V + 17.3V). The dB increase going from SPL proportional to 28.3V to 34.6V is 1.75dB (20*log(34.6/28.3) ) which equates to a power increase of 1.5.


The answer to the orignal post is a 1.75dB increase assuming the cabinets add in phase and are of equal efficiency. The larger area of the 2 x 12s may result in more than 1.75dB increase (or not). I personally think the 2 x12 setup would be a noticable improvement over the base setup. Also the perceived volume may go up because of a more complete coverage of spectrum with two differently voiced speaker cabinets


Dave, MSEE, PE

Why are you assuming constant power?

Bob Lee (QSC) said:

Why are you assuming constant power?

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I initially did this as a way to make a ball park calculation without getting out the calculator. I received some questions to this approach, so I have shown above the math used to get to the answer of 1.75dB.

This is a common question: "What happen if I run a 410 cabinet instead of a 210 cabinet with the same power". If you double the number of speakers and keep the power constant you get 3dB (series, parallel, does not matter as long as each speaker gets equal drive).

DavePlaysBass said:

Your orignal post you assume the VOLTAGE to each speaker is cut in half.

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It is. The voltage across two identical cabs series wired will be a 50-50 split. If a 28.3 v signal is available each cab will receive 14.15v. Your equation applies to power, not voltage, and to reiterate it is voltage swing that determines excursion and SPL, not power. BTW, the entire concept of SPL related to power is flawed. Loudspeakers are not measured with constant power, as power varies with impedance, and impedance varies with frequency. Speakers are measured with a constant voltage input, 2.83v/1m being the norm.

ashtray said:

But what everyone seems to be saying, is that the volume should increase with the 2 cabinets going.

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Remember that 1 dB is supposed to be right about the human just noticeable threshold for hearing a change in loudness. In practice is seems like 2-3 dB is a more widely accepted figure at the volume levels in question. That means that even if the volum should increase by 1.75 dB-ish, it's likely that under optimal listening conditions you would just barely notice the change.

billfitzmaurice said:

It is. The voltage across two identical cabs series wired will be a 50-50 split. If a 28.3 v signal is available each cab will receive 14.15v. Your equation applies to power, not voltage, and to reiterate it is voltage swing that determines excursion and SPL, not power. BTW, the entire concept of SPL related to power is flawed. Loudspeakers are not measured with constant power, as power varies with impedance, and impedance varies with frequency. Speakers are measured with a constant voltage input, 2.83v/1m being the norm.

Click to expand...

Based on what you are saying above, the situation is this:

4-ohm cabinet powered at 200W

When a second cabinet is added, the voltage is halved. The power draw from the amp is now 100W. While agree this is a 0dB increase, it does not address the original posters question or the behavior of most solid state amps I have experience with.

If indeed the power drops from 200W (4-ohm load) to 150W (8-ohm load) output, the voltage at 150W (8-ohm) setting will be higher. Thus you get more than 1/2 the initial voltage on each speaker. This implies the 200W rating IS NOT based on power amp voltage limitation but rather power amp CURRENT limitation.

Keep in mind, it is not only the speaker you need to consider, you also must consider the limitations of the power amp. And these limitations set the real world voltage available for different load impedances. In this case there is a higher voltage capability when driving 8-ohm loads.

Lelander said:

Remember that 1 dB is supposed to be right about the human just noticeable threshold for hearing a change in loudness. In practice is seems like 2-3 dB is a more widely accepted figure at the volume levels in question. That means that even if the volum should increase by 1.75 dB-ish, it's likely that under optimal listening conditions you would just barely notice the change.

Click to expand...

I agree. I doubt there is an earth shatterin change. But if the 2 x 12 cabinet is more efficient thant the 2 x 10, you might approach 3dB pretty quickly which would be like going from a 200W power amp to a 400W power amp.

Also the different frequencies provided by the 2 x 12 may give a fuller sound.

But at the end of the day, hook it up and see what you think. The best point of view would probably be 50' away in a loud band setting.