121 dB for a sub to hit ref level with All Small? Why not only 116.8? (1 Viewer)

[Doug BW]

Well, this is driving me crazy.
In the year or so that I've been lurking on this forum, I've often seen it said that in order to get reference level bass with all speakers set to small, a subwoofer needs to deliver an SPL of 121 dB at the seats. SVS says the same thing on their web site.
So where does this "121 dB" number come from? My understanding is that in a 5.1 system, the LFE channel by itself can generate a maximum of 115 dB. But, with bass management sending the bass from the other five channels to the sub, the sub needs to be able to deliver MORE that 115 dB. But how much more? Is it really 6 dB more?
I think the number is more like 1.8 dB. That is, 116.8 at the seats is all that's required for reference level. I'm sure I must be wrong, but I can't figure out why.
Would someone please check my assumptions and my math and tell me where I've gone wrong?
Here are my assumptions:

• The left, right, center, left surround and right surround channels (the "5.0 channels") can EACH generate a maximum of 105 dB of bass.
• The LFE channel (the ".1 channel") can generate 115 dB of bass.
• A 3dB increase in SPL is a doubling of SPL.
• A 4.8 dB increase in SPL is a tripling of SPL.
• A 6 dB increase in SPL is a quadrupling of SPL.
• A 7 db increase in SPL is a quintupling of SPL.

How am I doing so far?
Okay, so if we have the 5.0 channels that can each generate 105 dB of bass, altogether they'll generate 112 dB. (112 dB is a quintupling of 105 dB.)
Since the LFE channel can generate 115 dB of bass, it can generate double the bass of the five other channels combined. (115 dB is 3 dB more than 112 dB, so it's double.)
Thus the maximum SPLs generated by all 5.1 channels is triple the SPLs generated by just the 5.0 channels.
Since the 5.0 channels can generate 112 dB, then triple 112 dB is 116.8 dB. Not 121 dB.
This is really driving me nuts. Please help me figure out the right way to get to the 121 number! Thanks!

 

[Glen_L]

I wondered the same thing a long time back, and Stan Marcewitz (misspelled, I'm sure...TV knows who I'm talking about) explained it in great detail. I had found a website that explained that two different sound sources (windmills in the case of the page) on either side of a listener producing the same SPL (90dBSPL for example) would result in a 3dB increase (93dB) over just one windmill. I did the math and arrived at the same figure you did.
The difference, as Stan explained it, has to do with the bass being in phase, or phase correlated. When this is the case, the two sources will produce a 6dB increase rather than 3dB. It is for this same reason that you want to put both of your subs as near each other as possible to net maximum SPL.
So, say you have one main speaker which is asked to reproduce bass down to 20Hz at 105dB. Two then would produce 105 + 6 = 111dB. Adding another pair (remember, each doubling results in a 6dB increase) of mains (the surrounds, let's say) puts us at 111 + 6 = 117dB. A 5th channel, say the center, is tougher to add--I had to find a chart to figure out how to add 117 + 105dB. It turned out adding two SPL figures that differ by 12 result in a 1dB increase. So, 117dB for the fronts and rears + 105dB for the center = 118dB for the potential loudness of all the mains summed.
Then you add the 115dB from the LFE into the picture. Again, I had to look at some charts, but it turned out that 118 + 115 = ~121dB, just like SVS (and THX, I might add) said it would. Sorry if this is a rudimentary explanation, I'm going from memory of a year ago. Hope this helps.
EDIT: Here's an old website that I dug up that may help a bit. Especially read the part about halfway through the page under the gray box where there is a summary.

 

[Doug BW]

Glen, thanks for the information! The link you gave points to the second of a two-part article that contains some great explanations about decibels and their signifcance when used in relation to SPLs. I recommend that others who are interested follow your link. I think I'll need to read the articles a few more times before it all sinks in.

It's definitely not intuitive as to when two sources of equal sound add together to give a 3 dB increase and when they give a 6 dB increase.

I had heard that two subs next to each other give a 6 dB increase (and had wondered why), but didn't think that this would apply to my original question since the five "5.0" speakers are NOT next to each other in a home theater....and are REALLY far apart in a "real" movie theater.

Thanks again.

 

[Glen_L]

It's definitely not intuitive as to when two sources of equal sound add together to give a 3 dB increase and when they give a 6 dB increase.

No, it's not--hopefully somebody with more experience in the area will happen by to help out. Looking back over the article makes me wonder if I ever really had a firm grasp on it. Tom? Ron? Vince?
When it states that the "same sound" will cause an increase of 6dB rather than 3, I think that's the key to the 121dB figure. The 5 main channels are certainly capable of producing the same sound simultaneously, and the more "alike" the signal is in each channel with respect to material below the sub crossover, the closer you'll get to the 118dB figure I calculated for the mains.

 

[Steve Stogel]

Interesting thread.
But 117 versus 121 at the listening position at 20Hz, either way I think you're going to be bathed in bass. Of course, since most people run their subs a little hot, I think 124 to 130@20@the seats is the main goal, right? I never even questioned the number, but I don't know all those EE type things. Thanks for the info, Doug and Glen.
Steve