# Subwoofers + Statistics = Fun?



## Magialisk (Jan 17, 2008)

I think the closest fit for this is here in the acoustics forum, but if I'm wrong about that please correct me. Before I even start, I’ll say that almost all of the information in here is going to seem like common sense to us “enthusiasts”. However, using a little experimental rigor to test industry guidance and common sense is never a bad idea, so please bear with me.

For background, I am currently working towards a master’s degree in systems engineering and just completed a course on design of experiments (DOE). For my final project, I decided to apply the principles of DOE to our favorite hobby, specifically to see how the in-room response of a subwoofer changes with its placement in the room. The main goal was to support or refute industry guidance about avoiding corner placement. Ho-hum I know...

The room locations to test were chosen as follows:
1.) Front right corner – A common and convenient spot chosen to hide the subwoofer away that goes against industry and hobbyist guidance.
2.) Middle of front wall – Primary THX recommendation, and compatible with Dolby recommendations.
3.) Middle of side wall – A secondary THX recommendation when placing multiple subs.
4.) Against a low wall/bar to the open kitchen – Chosen due to the minimal amount of nearby walls without placing the sub in the middle of the room (something I assumed nobody would do, not even a bachelor).
I've attached a graphic to better depict my room and the selection of test locations.

Another thing I decided to test was the effect of opening the windows in the theater room. I’m sure we’ve all seen on one forum or another someone wondering whether an open window will act like a bass trap. The idea is that by allowing the sound wave to propagate outside rather than bounce off the wall and back into the room it’s effectively a very efficient absorber, much more so than a 4-6” trap. To my knowledge this concept has never been formally tested, so I figured why not throw it in to the experiment as well.

The four responses measured were maximum SPL (looking for peaks due to room modes), -3dB point (looking for in room frequency response), minimum SPL above the -3dB point (looking for nulls due to room modes) and finally maximum decay time (RT60). Room EQ Wizard (REW) was used to measure everything in case you’re interested. So without further ado, on to the summary of results.

First, about the windows as bass traps:
With the windows open, max SPL decreased by 2.32 dB and min SPL decreased by 2.53 dB. Overall the average SPL didn't change much, it was mostly just at the peaks and nulls (room mode responses) that the effect was seen. Max decay time was reduced by 96.95 ms and frequency response was unchanged (actually 0.08 Hz lower, but acoustically insignificant). It was pretty clear that at least in my room, opening the windows did have an effect similar to a bass trap. The decay time improved noticeably while there was a small loss in in-room SPL at modal frequencies. On the bright side, there was no detrimental effect on frequency response, so it basically did what it was postulated to do and no more. Of course I can't say this would hold true in all rooms, and the effect of the open window on the other speakers in the room was not tested. I bet they'd do a great job on first reflections from the mains.

Now about the room locations. I’ll compare each to the “default” corner location:
The primary THX location (mid front wall) reduced peak SPL by 2.28 dB but only reduced min SPL by 0.63. This is a positive result showing that the location helped tame annoying room modes without too drastically affecting the frequencies where the response was weakest. Further, the max decay time at this location was 141.09 ms less than in the corner.
The secondary THX location (mid right wall) increased peak SPL by 0.7 dB but increased min SPL by 2.57 dB. Again this is a positive result, albeit quite opposite from the last. It basically helped to fill in the weak portions of the response without reinforcing the peaks. We all know it's practically impossible to boost a null with EQ, so this natural boost could be quite useful in my room. Further, the max decay time at this location was a whopping 194.34 ms less than in the corner, even though the SPL was higher overall. For the record, neither of the two above locations produced a meaningful difference in frequency response when compared to the corner location (a few tenths of a Hz either way).
The fourth location, with minimal wall reinforcement, produced terrible results. Max SPL was lower by 3.325 dB, min SPL was lower by 15.42 (there were two strong nulls in play), and across the board the whole SPL graph was around 8-10 dB lower at all frequencies. The frequency response was also 2.04 Hz higher/worse (~18 Hz vs. ~16 Hz). Max decay decreased significantly, by 282.09 ms, but my belief is that this is largely due to the huge decrease in SPL across the board. In other words, when racing to 60 dB the guy starting at 80 db has a pretty huge advantage over the guy starting at 90 dB.

With the results out of the way, here are a couple interesting observations that may not fall under the common sense category:
1.) In my room at least, choosing the proper subwoofer location had a much more positive effect on decay time, and a slightly less negative effect on SPL, than did treating the room with virtual bass traps (open windows). The windows covered ~25% of the side wall and ~36% of the rear wall and must be considered more efficient an absorber than an ordinary trap, but they only reduced decay time by 97ms. Placing the sub in either of the two mid wall positions instead of a corner reduced decay by 141 and 194 ms. Moral of the story: Find the best location for your sub first (it's FREE!) and *then* spend money on room treatment. OK so fine, maybe that was still common sense...
2.) In the analysis of all four response variables, there was a significant interactive effect between the relative position of the subwoofer and the bass trap (open window). Looking at that result in reverse, this says that if you first found an optimal location for your subwoofer and then started treating your room with traps, you should expect the performance of the traps to vary with their placement in the room. For example the experts agree you should treat corners with traps before walls, but unfortunately I couldn't move my windows to a corner. I would like to look into this aspect further with additional testing, but unfortunately I don't own any traps at this time.

Finally, if anyone is actually interested in the statistics behind the analysis just ask, but here is the basic information: The DOE was a general full factorial regression model, 3 factors with 2, 2 and 4 levels. The factor I don't talk about above was Subwoofer A vs. Subwoofer B as I own two SVS CS-Ultras and used them individually for this testing. Two replications were performed with 32 total observations. Normality assumptions and model residuals were tested and other model indicators (R-sq, etc.) were good. Not everything I set out to test turned out perfect, but the basic results I give above were well supported.


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## bambino (Feb 21, 2010)

Very interesting test!


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## bpape (Sep 14, 2006)

> Moral of the story: Find the best location for your sub first (it's FREE!) and *then* spend money on room treatment.
> 
> Read more: Subwoofers + Statistics = Fun? - Home Theater Forum and Systems - HomeTheaterShack.com


Couldn't agree more. Getting the position if speakers, subs, and people correct is the first thing to be done and the least expensive. After that, we know what is left to be addressed with treatments.

Bryan


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## MatrixDweller (Jul 24, 2007)

Since you're working towards your Masters, do you plan on doing any computed fluid dynamic modeling of your room with the subwoofers in different positions? I believe Fluent has this capability.

Also do you plan on taking measurements in many different room locations?


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## Magialisk (Jan 17, 2008)

No CFD for me thanks! That's typically more of a mechanical/aerospace engineer I believe. At least that's who's doing the CFD around work...

This was just a simple class project I did over a couple weekends, not an overall thesis or anything, and I'm done with that particular class now. As part of my deliverables I did recommend additional testing for the placement of multiple subs, and also testing on placement of bass traps, but I didn't even mention additional seating positions. That would be another interesting side endeavor, but at this point I don't intend on continuing on unless I fall into a bunch of bass traps to test, or revisit this down the road in some kind of wrap-up project. Thanks for the interest anyways!


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## acoustat6 (Mar 7, 2008)

Hello, pictures are worth a thousand words. Would it be possible for you to posta few of those REW graphs?

Thanks,
Bob
PHP143
If the first 100db suck why continue?


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## Magialisk (Jan 17, 2008)

Bob,
I appreciate your suggestion as pictures would definitely help clarify this story. I took a look at some of the data again this morning, playing with overlays to see which kind of pictures would add the most value, and came up with a handful that I think will do the trick. I hope nobody feels I'm being disingenuous by cherry picking graphs that most clearly reflect my results. In reality, it's the statistics software that best tells you what's going on with the data and those results have already been summarized. These graphs are meant merely as a visual aid and for clarity, and I just grabbed the first few that looked halfway decent.

First, graph #01 shows the measured frequency response with the sub in the corner (teal) vs. the side wall (purple). They're almost the same up to 35Hz, there's the big room mode excitement in the mid 40's, but then after 65 Hz the side wall position is much flatter. In my original post this is what I called the "filling in" of the weak portions of the response.

The next graph #02 shows the waterfall response with the sub in the corner (teal) vs. the THX recommended front wall (red). It's easy to see that at ~17Hz and ~47Hz the corner position rings for over 100ms longer than the front wall.

Graph #03 shows the frequency response measured at the side wall with the windows open (teal) vs. closed (purple). The open windows rounded off the tallest peak by ~2.5 dB as stated previously, and surprisingly on this graph it even boosted the SPL below ~42 Hz. That was not an observation made across the experiment, but it's interesting to see it here in this one sample. In the more general case the open windows didn't have much effect (plus or minus) anywhere but at the frequencies corresponding with room modes.

Finally, graph #04 shows a waterfall plot of the same two measurements in graph #03. The purple response (windows closed) continues to ring at ~22 and ~29 Hz well after the open window response has settled.

Now with all of that posted I do want to leave one final caution. The graphs by their nature can only compare two individual measurements out of the total 32 collected. The statistics software compares average effects across the entire experiment and gives a much better picture of what's really going on in a general sense. While these graphs do lend some support to the prior claims in a visual, easy to interpret fashion, they can't be used on their own to make any conclusive determinations. Trying to do so would ignoring the potential effects of the other 30 measurements. This was evident in graph #03, which would lead us to believe open windows give a significant SPL boost below 42Hz, but that observation did not hold true across the board.

I hope this is along the lines of what you were looking for. Thank you for your interest.


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