Loudness SPL vs. Number of Speakers

[fast_frank_d]

I feel like this should be simple, but I have to ask. Let's say I have a 400W bass amp driving one speaker capable of 450w rms with a huge xmax that never farts out. Then I add 3 more identical speakers in series-parallel, quadrupling the speaker area, but impedance remains the same.

What is the theoretical effect, if any, on SPL ignoring thermal power compression?
What is the approximate effect on SPL with only 100 watts to each speaker reducing thermal power compression? Just talking rough numbers here.

Discuss!
Frank

 

[Mr. Foxen]

3db every time double speaker area, so 6db. But wind up perceiving less and you just made it loads more directional and you mostly wind up off axis, so it seems like more bass.

 

[MarkA]

I'll take a stab at it, though my own understanding is incomplete.

I believe that you'll get an additional 3 dB for each speaker. If you're at 90 dB with one, you should be at 99 dB with four.

I also believe that you get more than that in the low end (6 dB instead of 3?) due to coupling, if you're stacking speakers, but I'm unsure of the exact amount and of what factors influence where and how this transitions back to 3 dB. I also don't know if this holds equally for all types of speakers (sealed, ported, other configurations).

Finally, I'm not sure that you get every last bit of that 3 dB and I seem to recall that there there is a point of diminishing returns, past which adding more speakers doesn't get you much... double-fridge players will tell you that it's somewhere north of 16.

Not my area of expertise, so I'm happy to be corrected on any of the above.

 

[MarkA]

3db every time double speaker area, so 6db...

Well, looks like I might have made a mistake already -- if this is the case then my theoretical 4xwhatever would be at 96 dB instead of 99.

Edit: More I think about it, more that seems likely.

 

[Rick James]

I feel like this should be simple, but I have to ask. Let's say I have a 400W bass amp driving one speaker capable of 450w rms with a huge xmax that never farts out. Then I add 3 more identical speakers in series-parallel, quadrupling the speaker area, but impedance remains the same.
What is the theoretical effect, if any, on SPL ignoring thermal power compression?

With no change in the amp settings you'd get 6dB. You'd get 6dB from just adding a second cab in parallel, 3dB from increased sensitivity, 3dB from the halved impedance. You don't get additional output from the second pair wired in series because of the return of the overall impedance back to that of the one driver. You will get a total of 12dB maximum SPL from four speakers compared to one if you have enough power, because maximum SPL is determined by total driver displacement. Every doubling of driver displacement gives 6dB additional maximum SPL.

 

[agedhorse]

Note that the (theoretical) doubling of SPL due to coupling only occurs in the lowest couple of octaves where the distance between driver centers is small compared with wavelength of the signal. As the distance increases, this effect begins to disappear. Otherwise, you could keep doubling drivers until you exceed 100% efficiency. Also, it's important to note that a part of why this works is that the motor strength also doubles with each doubling of drivers, otherwise this wouldn't hold true. Doubling of the area of the diaphragm (cone) without increasing motor strength is not the same.

As far as thermal power compression, it depends where you are on the curve for a single driver to be able to extrapolate to its effect on multiple drivers. There is also electro-magnetic power compression to consider.

 

[BogeyBass]

Just like women the more the merry

Keep adding more and it gets louder

 

[Rick James]

Note that the (theoretical) doubling of SPL due to coupling only occurs in the lowest couple of octaves where the distance between driver centers is small compared with wavelength of the signal. As the distance increases, this effect begins to disappear. Otherwise, you could keep doubling drivers until you exceed 100% efficiency.

The distance isn't the reason why you can't keep increasing efficiency by adding more drivers. If you're comfortable with a lot of math this explains what happens:
http://www.xlrtechs.com/dbkeele.com/PDF/Keele (1991-10 AES Preprint) - Max Efficiency of Speakers.pdf

If you know how to model with HornResp you can see what happens with multiple speakers.

 

[agedhorse]

The distance isn't the reason why you can't keep increasing efficiency by adding more drivers. If you're comfortable with a lot of math this explains what happens:
http://www.xlrtechs.com/dbkeele.com/PDF/Keele (1991-10 AES Preprint) - Max Efficiency of Speakers.pdf

If you know how to model with HornResp you can see what happens with multiple speakers.

The issue with distance is that once you get to a large enough distance with respect to wavelength, the far field phase cancellation gets pretty close (and eventually equal to) the 3dB increase due to coupling, resulting in zero net gain. Not only this, but the peaks and valleys in the response will become more pronounced due to a change in the radiation pattern.

The simplified math is:

Say with 1 driver the efficiency is 4%, by doubling the drivers with a 3dB efficiency gain:

1 = 4%
2 = 8%
4 = 16%
8 = 36%
16 = 72%
32 = 144% *** physically impossible as it violates the first law of thermodynamics.

 

[monsterthompson]

Otherwise, you could keep doubling drivers until you exceed 100% efficiency.

Kinda reminds me of Zeno's Paradox

 

[Boundary Effect]

Don't forget the electrical aspect. Given a 400 watt amp cranked into a single 8Ω speaker, let's assume 1/8 power or 50 watts RMS. That would be 20 volts RMS across the single 8Ω driver. Now connect the 4 drivers in parallel-series for a total load at the amp of 8Ω and same output. That results in 10 volts across each individual 8Ω driver (12.5 watts). Excluding coupling, etc, each driver theoretically will receive 6dB less signal in the 4 driver setup as compared to the single. This before coupling.

 

[agedhorse]

Kinda reminds me of Zeno's Paradox

Yup!

Don't forget the electrical aspect. Given a 400 watt amp cranked into a single 8Ω speaker, let's assume 1/8 power or 50 watts RMS. That would be 20 volts RMS across the single 8Ω driver. Now connect the 4 drivers in parallel-series for a total load at the amp of 8Ω and same output. That results in 10 volts across each individual 8Ω driver (12.5 watts). Excluding coupling, etc, each driver theoretically will receive 6dB less signal in the 4 driver setup as compared to the single. This before coupling.

Correct, then you add the SPL contribution of each driver (4 x 12.5) and you are right back to 0dB difference compared with 50 watts into a single 12(plus any coupling gains)

 

[2tonic]

Thank you Boundary Effect and agedhorse for finally addressing the OP's question. I was pulling my hair out reading all the replies, hoping someone would acknowledge that the power output would remain constant and each spkr would receive a smaller share of the amps output, before I got to the end!

In theory you put 10 watts into a transducer and generate a measured spl. You want a 3dB increase......put 20 watts into it, or add a second transducer with its own 10 watts.
Coupling gains are frequency-dependent, and are affected by temperature, humidity levels, altitude, and what space situation the transducer is in (half space, quarter space, corner loaded, etc) and are neither predictable or consistent in all conditions.

Edited to add: Adding multiple drivers only increases the power handling capability. unless there is a commensurate increase in wattage applied, ie. the amp puts out a max of 100 watts into an 8 ohm speaker, add another 8 ohm spkr, in parallel, netting a 4 ohm load on the amp, which can then push 200 watts into the pair.

It's advantageous to view these questions in the form of ADDING POWER.
You can keep doubling the wattage into the cab for each 3dB increase until you reach the mechanical limits of that driver (power compression aside), then you have to add another driver AND an equivalent amount of wattage to it to see more gain

 

[Rick James]

Excluding coupling, etc, each driver theoretically will receive 6dB less signal in the 4 driver setup as compared to the single. This before coupling.

Except the OP is concerned with the end result, which includes coupling. Two drivers parallel wired with voltage input unchanged gets 6dB more output. Series/parallel wire two more with the voltage still unchanged is also 6dB more output than one driver. What I said, eight posts ago.

 

[agedhorse]

Correct, there are two inter-related effects involved, each responsible for a theoretical 3dB increase.

 

[JW56789]

How would this change in the real world IF each cabinet had its' own built in power amp?

 

[agedhorse]

How would this change in the real world IF each cabinet had its' own built in power amp?

Good question... not at all if the total power and power per driver were the same.

 

[JW56789]

OK, so with the long wavelengths involved, distance from the cabs, phase cancellation, all the points discussed above. . . . . if the obvious answer (professional reinforcement with competent FOH guy)is not an option, what DO you do to be louder?

One more example of the utterly aggravating parts of playing bass, trying to constrain the whale of low frequency in confined, non-acoustically designed rooms. IF ONLY I'd taken up a treble clef instrument . . . . . hearing myself properly drove me out of gigging quicker than anything else.

 

[agedhorse]

So now you are onto the difficult questions...

The easier of the two is that when presented with a difficult environment, you want to avoid exciting that space with frequencies that decay slowly. Digging into my pro audio background, we sometimes dealt with venues like this, usually larger venues like arenas and multi-purpose venues.

There is a measurement called RT-60 which describes the decay of the sound to 60 dB down (it could be another value but 60 is common) as a function of frequency. The longer the energy takes to decay, the more remains present and it will appear louder. What you will usually see is longer times at the lower frequencies, so you want to reduce the lower frequencies to reduce the total amount of energy that remains. Theses are the effects of boundaries and complex reverberation between those boundaries that reflect rather than absorb sound.

The first thing to do is turn down... just a little bit can make all the difference in the world. Same goes for other "loud" players in the band.

The D-800+ would be helpful in these cases because the adjustable HPF allows you to roll off the extreme low end which usually has the longest RT-60 time. You may also find resonant peaks in the rooms response due to the cavity effect of the room, for this, generally tuning the low mid to the area of resonance and then taking a little cut will help. Note that just a 3dB cut will reduce the energy put into the system at that frequency by 50%, so it may not take as much as you think.

Also, you are not going to get perfection, so don't get worked up over something unattainable no matter what you can do. I learned a long time ago that you do the best you can and then make up for it by playing well. That's what people remember (unless the audio is a total poopie & splatter-fest).

Hope this helps.

 

[Wasnex]

OK, so with the long wavelengths involved, distance from the cabs, phase cancellation, all the points discussed above. . . . . if the obvious answer (professional reinforcement with competent FOH guy)is not an option, what DO you do to be louder?

One more example of the utterly aggravating parts of playing bass, trying to constrain the whale of low frequency in confined, non-acoustically designed rooms. IF ONLY I'd taken up a treble clef instrument . . . . . hearing myself properly drove me out of gigging quicker than anything else.

IMHO. In really bad acoustic environments, get the speaker up high and aim it at your head. This reduces coupling with the floor (the first boundary). Also gives the shortest distance to your ears which increases the ratio of direct to indirect sound. It also gets your ears in the dispersion pattern for all frequencies the speaker produces. This also increases the ratio of direct to indirect sound you hear. With this approach you can turn down so you excite the room less, and yet still hear clearly.

I used to do a lot of gigs in high school gyms. In this nasty acoustic environment, I would use an Eden 210XLT stacked vertically on a 10 space rolling rack with a Countryman Type 85 wedged under the front edge to tilt it back so it aimed straight at my head.

For monitors I used a pair of Galaxy HotSpots spread out at 45 degree left and right in front of me and approximately equidistant from my ears with the 210. The HotSpots were on mic stands a little higher than waste level. They were high passed pretty high as they don't put out much of anything below about 200 hz anyway. I ran a bit of bass in the mix (sometimes a lot) to get extra mid range clarity as needed.

In better acoustic environments, my wedge was typically something super HiFI like an Apogee AE6. Usually I didn't run bass in the mix with decent monitors as I didn't like the feel of the low end fighting between the monitor speakers and my bass rig.