Power vs Speakers

[drpepper]

From agedhorse's earlier post: (He's an engineer experienced in amp & cab design and also experienced in PA setup and operation):

2. Doubling the number of speakers (with the same power as with the single speaker, so each speaker gets only 1/2 the original power) always equals a 3dB increase in SPL (but only below the critical coupling frequency, and minus any coupling inefficiencies, plus any reduction in power compressin losses)

I'm not an engineer experienced in amp & cab design, but I feel I have a fairly firm grip of logic. In that, there could be something I misunderstand here, or it's possible that agedhorse "misspoke" or was simply incorrect.

Is something here incorrect as to how loudness increases and decreases are described?

The sound of single strings on two identical acoustic guitars being plucked instead of one guitar alone = 3db increase?

The sound of single keys on two identical pianos being struck instead of one piano alone = 3db increase?

The sound of two identical drums being hit instead of one alone = 3db increase?

The sound of two identical kettles whistling instead of one alone = 3db increase?

If those are all correct, and doubling the number of speakers with equal power equals a 6db increase, then recording each of those scenarios and playing each back through individual, identical amplifiers and speakers, at the same level as the original sound, would mean that playing back the recorded sound of two drum hits would would be a 6db increase over one.

 

[Passinwind]

I'm not an engineer experienced in amp & cab design, but I feel I have a fairly firm grip of logic. In that, there could be something I misunderstand here, or it's possible that agedhorse "misspoke" or was simply incorrect.

Is something here incorrect as to how loudness increases and decreases are described?

The sound of single strings on two identical acoustic guitars being plucked instead of one guitar alone = 3db increase?

The sound of single keys on two identical pianos being struck instead of one piano alone = 3db increase?

The sound of two identical drums being hit instead of one alone = 3db increase?

The sound of two identical kettles whistling instead of one alone = 3db increase?

If those are all correct,

Nope, they are not. If you place two small-ish kick drums close enough together they can mutually couple on at least part of their frequency spectrum. None of your other examples will be able to do that very effectively.

 

[Rick James]

The sound of single strings on two identical acoustic guitars being plucked instead of one guitar alone = 3db increase?
The sound of single keys on two identical pianos being struck instead of one piano alone = 3db increase?
The sound of two identical drums being hit instead of one alone = 3db increase?
The sound of two identical kettles whistling instead of one alone = 3db increase?

6dB in every case. You're hung up on amplifier power, which doubled gives a 3dB increase. The correct analogy would be to doubling the amp output voltage. That gives 6dB.

 

[ggunn]

Are two speakers handling 50W each 3dB louder than a single speaker powered with 100W?

 

[agedhorse]

You have to consider the validity of the contributions of each term in the equation individually. Once these are confirmed, the net result is the sum of all valid terms.

I sometimes see folks fixated on the coupling term in doubling drivers to increase sensitivity, ignoring the critical distances... which results in perpetual motion after 5 or 6 doublings by yielding more acoustic power out than electrical power in. Usually, things that are presented in simplistic terms ignore some very important details once examined more thoroughly.

 

[Coolhandjjl]

Are two speakers handling 50W each 3dB louder than a single speaker powered with 100W?

Yes, but with caveats. How close together are the drivers, the lows typically couple together just fine, in our world of bassdom, generally 500Hz and lower. Above that, some frequencies may create acoustical interference, etc.

But these are general rules of thumb. It really is hard to isolate all the variables and test accurately.

But the old rule of thumb is tried and true. Add a second cab on top to gain 3dB, and if your head outputs more due to that parallel lower impedance, add dB accordingly. My amp puts out 500W into 8Ω, and 800W into 4Ω. So for me, adding a second cab on top yields +5db. That translates into +3dB for the added driver, and +2dB for the added watts. (If my head actually went up to 1000W at 4Ω, I'd be at +6dB.)

 

[agedhorse]

But the old rule of thumb is tried and true. Add a second cab on top to gain 3dB, and if your head outputs more due to that parallel lower impedance, add dB accordingly. My amp puts out 500W into 8Ω, and 800W into 4Ω. So for me, adding a second cab on top yields +5db. That translates into +3dB for the added driver, and +2dB for the added watts. (If my head actually went up to 1000W at 4Ω, I'd be at +6dB.)

Until you subtract the effects of power compression, and imperfect coupling. Depending on the driver and the spacing, the theoretical maximum is +3dB for the FIRST doubling of drivers below the critical frequency. Same for power doublingn, the theoretical maximum is +3dB but you then have to subtract power compression effects (not just thermal but ALL of the electromechanical factors as well). On many drivers used in the bass guitar world, this will be between 1 and 2 dB once you hit around 50-75% of the thermal rating. It's not trivial, and in fact, the coupling gain may exceed the power compression loss which would mean that doubling up drivers at 1/2 the power each might yield more gain than just doubling the power into the original driver. It depends on the power levels relative to the thermal/mechanical rating of the drivers.

 

[drpepper]

6dB in every case. You're hung up on amplifier power, which doubled gives a 3dB increase. The correct analogy would be to doubling the amp output voltage. That gives 6dB.

Got it (I guess)

I appreciate the effort, but moving to voltage isn't helping. We can approach and understand things in different ways.

I read (some time ago) what I felt was a good explanation that presented the concept that two of some sound producing thing...a voice, a vacuum cleaner, a fan, or an amp of some specified wattage... (i.e., being twice as powerful as one; twice the energy) is defined as a 3 decibel increase in loudness. Thinking of loudness in these terms, it seems easy enough to come to an conceptual understanding of the scale and relationship between sound power increases loudness…that twice the sound production power is louder, but not twice as loud etc. up to ten times for perception of twice as loud.

I guess you're saying the concepts don't mix. Good enough.

 

[Rick James]

I read (some time ago) what I felt was a good explanation that presented the concept that two of some sound producing thing...a voice, a vacuum cleaner, a fan, or an amp of some specified wattage... (i.e., being twice as powerful as one; twice the energy) is defined as a 3 decibel increase in loudness.

Whoever wrote that was wrong. The acoustical engineering term that explains why two identical sources add up to 6dB more than one is mutual coupling. This is one source that explains how it works. The math is way beyond my comprehension, but I trust the guys who do understand it.
Invalid Link Removed

 

[drpepper]

Rather than being argumentative here on the forums...

Hey, I'm not beyond taking in new information or correcting information that I've taken in. I didn't intend to put anything forward that wasn't as "my understanding," which I know can be mistaken (except for the "magic" snipe…which was unfortunate…sorry to Downunderwonder).

Okay, so physics can be counter-intuitive. I think that knowing rules and formulas is not the same thing as understanding their bases and how they're applied to overcome apparent contradictions. I was trying to understand the basis on this specific example of two identical amps which seemed to bring some concepts I have into momentary conflict (i.e., I had a brain-fart).

What started me down the path I was on is that as many times as I've read (and even repeated and made correct comments based on it…accidentally it now appears) that "double the speakers and double the power into one speaker are the same thing; +3db," I had been considering it really without regard to power. On one level, I "knew" but had never considered two identical amps before and that unfixed notion (in conjunction with the notion that halving power to one speaker is -3db) caused said brain-fart. Now, I am corrected on that rule includes two speakers sharing the power.

In my conceptualizing these things, I was going back to my basic understanding of how we experience doubling of sound power, and I was considering the hypothetical identical amps as "sound producing" entities in the context of that basic understanding that two identical sounds added together are 3db louder than one alone (which Rick James tells me is wrong...can't wrap my ahead around that, and I'm not going to try).

Viewed as a single thing/summation; doubled in wattage (+3db) and doubled in speaker area (+3db), I can see the 6db.

 

[drpepper]

Whoever wrote that was wrong. The acoustical engineering term that explains why two identical sources add up to 6dB more than one is mutual coupling. This is one source that explains how it works. The math is way beyond my comprehension, but I trust the guys who do understand it.
Invalid Link Removed

Damn you, Rick James! I was out and you pulled me back in! Hahaha!

This started with you saying that two identical 200 watt heads and 410 cabinets would would represent an increase of 6db. That is correct.

I'll start by saying I could certainly be mistaken, but it appears that you're right about the 6db increase but wrong about the reason. Just glancing at a link, I can see that mutual coupling occurs only in specific circumstances and only "at frequencies below approximately 500hz."

 

[seamonkey]

6dB in every case. You're hung up on amplifier power, which doubled gives a 3dB increase. The correct analogy would be to doubling the amp output voltage. That gives 6dB.

But this shows 3db for adding a second violin
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The speaker to power stuff can go round and round. The actual produced and measured SPL at the desired frequencies on and off axis.
One thing for sure is most Amp makers are going to exaggerate their power, in fact they can't agree on what "Power" is. And most cab makers are going to exaggerate how much output they produce given such power. And Combo's rated in "Watts" is just plain silly.

Measurements and (peer) review are the only means to honest measurements. Bass gear won't get it. But it is there in so pro audio FOH gear.

 

[ThisBass]

I'm not an engineer experienced in amp & cab design, but I feel I have a fairly firm grip of logic. In that, there could be something I misunderstand here, or it's possible that agedhorse "misspoke" or was simply incorrect.

Is something here incorrect as to how loudness increases and decreases are described?

The sound of single strings on two identical acoustic guitars being plucked instead of one guitar alone = 3db increase?

The sound of single keys on two identical pianos being struck instead of one piano alone = 3db increase?

The sound of two identical drums being hit instead of one alone = 3db increase?

The sound of two identical kettles whistling instead of one alone = 3db increase?

If those are all correct, and doubling the number of speakers with equal power equals a 6db increase, then recording each of those scenarios and playing each back through individual, identical amplifiers and speakers, at the same level as the original sound, would mean that playing back the recorded sound of two drum hits would would be a 6db increase over one.

Addition of coherent signals: +6dB
Addition of incoherent signals: +3dB

Two identical instrumets playing just the same note I'd expect to be incoherent due to phase differences:
+3dB

Two loudspeakers positioned side by side playing just the same program I'd consider as coherent signals:
+6dB

 

[Coolhandjjl]

....Okay, so physics can be counter-intuitive....

Yup. For example, to increase dispersion in the horizontal plane, you stack cabs vertically. Took me a while to wrap my brain around that one until I read some posts on Bill FitzMaurice's forum.

 

[ticol07]

After reading this very instructive thread, I have an interesting question since I am asking it to upgrade my rig.
I have a combo with a 15" speaker rated at 4 ohms fed by à 250 w amp. So I use the full power of the amp.
Let say I plug this amp in 2 8 ohms cabs, designed exactly as the 4 ohms cab.
So the amp would send the exact same power.

Will the sound be louder due to the 2 speakers ?
Will the sound be different ?
If I stack the 2 cabs vertically, will the horizontal dispersion be different than with only one 4 ohms cab ?

 

[Coolhandjjl]

But this shows 3db for adding a second violin
Invalid Link Removed......

You're not going to get much if any coupling effect from them. That's why it is theoretically 3 instead of 6

 

[seamonkey]

Addition of coherent signals: +6dB
Addition of incoherent signals: +3dB

Two identical instruments playing just the same note I'd expect to be incoherent due to phase differences:
+3dB

Two loudspeakers positioned side by side playing just the same program I'd consider as coherent signals:
+6dB

So somewhere between 3db and 6db, but you can most count on 3db, especially for bass because bass get's no breaks.

Bass is harder to hear, and harder to reproduce, it is probably going to be 3db

 

[ThisBass]

So somewhere between 3db and 6db, but you can most count on 3db, especially for bass because bass get's no breaks.

Bass is harder to hear, and harder to reproduce, it is probably going to be 3db

Coherent signals generated by two different players on identical instruments imo that's not possible. I myself add two identical intruments by +3dB.

Low E swing is around 41 cycles per second, that means a very tiny slice for two players to hit coherent signal constellation.

 

[agedhorse]

Addition of coherent signals: +6dB
Addition of incoherent signals: +3dB

Two identical instrumets playing just the same note I'd expect to be incoherent due to phase differences:
+3dB

Two loudspeakers positioned side by side playing just the same program I'd consider as coherent signals:
+6dB

As the signals can't possibly be coherent, the sum and difference peaks and valleys will combine to a doubling from coupliing and a doubling due to twice the acoustic power BUT you must also consider the cancellations that in theory could result in zero as well.

Now the reason why the two violin sources sound louder is because they are not coherent and the energy density is doubled. There is more going on than just amplitude, there is the integration of power into energy and this energy occurs over time so you have an energy density factor as well, that is responsible for perceived loudness. This gets int dynamics management, or spreading a finite amount of signal around over time. This is a big and important aspect of what is perceived as fullness, or thickness, or fatness. It's not any single variable that is responsible, it's all of the variables in context. Otherwise, it's oversimplification which then becomes inaccurate.

 

[seamonkey]

Coherent signals generated by two different players on identical instruments imo that's not possible. I myself add two identical intruments by +3dB.

Low E swing is around 41 cycles per second, that means a very tiny slice for two players to hit coherent signal constellation.

Anything above 3db is a bonus. A slight different in cab tuning, driver suspension, spiders, distance of a few CM between drivers and ears, and who knows - Manufacturers shouldn't sell it as more unless they can produce some measurements, multi axis, that can be duplicated in the real world.