Adding subwoofers and increase in loudness

On a couple of audio forums I frequent there seems to be some general confusion amongst members about how much additional output you receive by adding subwoofers (or any speaker for that matter). I am under the impression that adding an identical speaker, and providing it same amount of power as the other speaker (i.e. original speaker receives 100W, new speaker also receives 100W, totaling 200W), you will realize a 3dB gain, or ~20% increase in loudness.

To clear this up for myself and others, I'd like to present a few different scenarios and have the knowledgeable members of this forum (as there are many) reply with the decibel change in each situation. Thanks. Oh, and all numbers presented are for ease of computation, not realism.

Scenario #1:
Subwoofer A produces 100dB at 1m w/100W in an anechoic chamber. Add identical subwoofer and power it with 100W in the same anechoic chamber. How many dB increase?

Scenario #2:
Subwoofer A produces 100dB at 1m w/100W in middle of room (and assume no room gain). Add identical subwoofer and power it with 100W and corner load it. How many dB increase?

Scenario #3:
Subwoofer A produces 100dB at 1m w/100W and corner load it. Add identical subwoofer and power it with 100W and corner load it as well. How many dB increase?

Scenario #4:
Subwoofer A produces 100dB at 1m w/100W in an anechoic chamber. Add second subwoofer B that is identical in all characteristics as A except that assume it's cone area is DOUBLE the cone area of subwoofer A and power it with 100W in the same anechoic chamber. How many dB increase?

Scenario #5 (this one is about car audio):
Subwoofer A produces 100dB at 1m w/100W in the trunk. Add identical subwoofer and power it with 100W in the same trunk. How many dB increase? (I have a feeling this is the same as corner loading, but I'm not positive)

I think that's all the scenarios I wanted covered. Really appreciate any help.
 
Mutual coupling and such stuff

Hi

I can answer a few questions you pose.

#1
Adding a second sub as you describe results in a 6 db increase in SPL
3dB is from having 200Watts not 100 and 3dB because you have doubled the area and are now twice as efficient.

#2
In a room, the results are entirely dimension /frequency dependant.
While corner loading can increase the low end efficiency, it also maximizes the magnitude of the room modes. Best results (so far as the response being flatter in most places in the room) would be with sub (s) at the center points of the walls (Per Harmon).
If the subs were close together, you would get about 6 dB added to what ever the room response was with one.

#3
While a corner begins as a fractional space, it is also something like a horn.
Like a horn, the low frequency cutoff of that “horn” effect is governed by the rate the area expands.
That, combined with the other room dimension related stuff, makes a general answer impossible.
It can be said that as long as the second sub is very close to the first, one could expect the same approximate 6 dB increase as in half or full space.

#4
The larger radiator you describe has to have much more mass and motor strength to have the same parameters and efficiency. Adding a second driver of identical parameters but say half the area, results in the same 6 dB increase as before.
If big cones were an advantage, the 60-inch dia Mitsubishi and other monster size drivers would be the norm.

#5
In this case, one is in a volume who’s dimensions are small compared to the wavelengths being produced.
Once the room dimension is less than about ½ wl , the room becomes essentially a second enclosure, one you sit in. The room then has gain or “room gain” which can be a slope as great as +12 dB per octave in a sealed concrete bunker to as little as a few dB in an open house.
In a car, with the windows rolled up, the transition from “normal” radiation to this “enclosure” or pressure mode happens around 50 Hz.
In “normal” radiation, if one lowers the frequency one octave, one needs 4 times the displacement to get “flat” response. Once one is “in” the enclosure, then (if the enclosure is perfectly ridged and air tight), then the sound pressure is equal to displacement.
With a transition at 50 Hz. One can take a sealed box sub flat to 50Hz and in the car, have it measure flat to 15 Hz.
The –12dB octave roll off of the sealed box, off sets the +12 dB per octave gain one sees in the pressurization mode and viola, the response can be flat octaves below where the box really rolls off.
In this case, adding a second driver with the same displacement* would raise the air pressure by two, which produces a doubling of microphone voltage, which is 6 dB in SPL

* in this case the drive Voltage for two may be different than the Voltage for one at a given displacement.

In the olden days I thought it would be fun to see what it was like inside one of the big subs I was using.
When I had one apart, I got inside and had my supposed “friend” put enough of the bolts in to keep the cover from rattling.
I was pretty much pinned in although I could yell through one of the ports.
My friend says he really couldn’t hear me yelling to turn it down.
NEVER get inside a speaker cabinet unless you really trust your friend and he HAS NOT had a few beers.

Hope that helps

Tom Danley
 
Hi Tom

Thanks for providing such a comprehensive reply. Anyone else want to chime in to confirm what Tom has said or say anything more about room acoustics and adding extra drivers, etc.?

The only thing that confuses me (at first glance anyway) Tom is your answer to scenario #1 of 6dB. I was expecting 3dB, which is what this article: http://forum.ecoustics.com/bbs/messages/34579/109138.html seems to describe. Maybe my scenario is not the same as the one they describe, maybe you could take a look at it and clear it up. Here is an excerpt:

"When one speaker is producing a level of 90 dB, adding a second speaker playing at the same level only increases the overall loudness by 3 dB! (The loudness does not double!). So the two speakers in stereo produce a loudness level of 93 dB"

Thanks,
Evan Robinson
 

Salas

diyAudio Chief Moderator
Paid Member
2002-10-08 11:31 am
Athens-Greece
To get a 6dB increase the two drivers must be driven by a correlated source and be closely coupled.
This means that you get 6 dB from double woofers in clode proximity wired in parallel and driven by the same voltage source.
Another speaker driven from another channel somewhwere in the same room will give a 3dB total increase when fed by the same signal. In sound reinforcement world, the sound engineers assume a 3dB increase for each additional cabinet as a rule of thumb.
 
Hi

When two drivers are less than ¼ wl apart, then they feel the radiation pressure each produces. This “mutual coupling” that two drivers produce, raises the actual efficiency of the woofer system by 3 dB and having two motors allows twice the PHC which is another 3 dB.
On the other hand “in stereo” may mean they are far enough apart acoustically as to not have mutual coupling. In that case, the 3 dB increase is the result.

Tom Danley

Danley Sound Labs
 

Salas

diyAudio Chief Moderator
Paid Member
2002-10-08 11:31 am
Athens-Greece
If we bring system headroom into discussion, yes you end up with a +6dB max spl capability.
But if you just point your SPL meter after you have hooked up your second speaker to your other channel and play some pink noise, you are going to see +3dB.
If you stack a second sub on top of your existing one and drive it from the same channel in parallel, your reading is going to be +6dB. Hope this is simple for practical purposes.
 

SoundRight

Member
2010-07-28 10:47 am
I understand the increase in output when coupling two drivers...or more.

But it is well known that mutual coupling effectively creates a cone (and baffle) of "double the area" resulting in a change of radiation resistance which provides around a 1/3rd octave further bass extension....for free!! This is the same theory as coupling horn mouths.

So my guess is an additional 1/3rd octave extension for every doubling of area? Or is there a "proper formula" for this effect!! What would six coupled drivers produce in extension over one? Of course there are other effects caused by increasing the number of cones and consequently baffle area as the whole assembly now becomes more directional. You will not be able to use it much above bass frequencies but the chest compression may be worth it!!