Originally Posted by AustinJerry
That is actually a good question, and the unfortunate answer is that the model probably doesn't apply, at least in the room height direction. Every discussion I have read pertaining to room acoustics mentions that most theories go out the window when it comes to odd-shaped rooms. So many modern floor plans are very open, creating some challenging issues with respect to acoustics.
To state the question a little differently, is there a way, using our measurement tools, to determine the standing waves in an irregularly-shaped listening area? I don't know the answer, but I hope we discover it along the way.
There is no way to do that using simple spreadsheets and such. As I explained before, there is a method called computational fluid dynamics where the room is fully modeled including the properties, and true shape of all the objects/walls in the room. Using that, we can then excite the room using arbitrary number and location of subs and see how it impacts the room at every location. Here are some pictures from my article that covers low frequency optimization
using various techniques including this one:
On the left we have a single subwoofer in the left corner. This is by the way what the simple mode calculators assume. That the sub is in the extreme one corner and hence "excites" all the modes equally. If you have your sub currently in a different location the predictions are not accurate and won't relate to your measurements. On the right we see what happens when three subwoofers are used, two on one wall and one in the ceiling. It is a little hard to interpret there so let's slice that into the one plane we are interested in: the ear height (this is for a different frequency):
Ideal response would have all the ears with the same color (which represents the sound SPL level). We see that the single sub on the left flunks that test completely. The three sub configuration does far better with all the seats having similar (yellow orange) color.
Note how the room has a soffit and hence is not rectangular.
As good as this technique is, it is expensive to run. The software costs is tens of thousands of dollars and it takes an experienced operator to get the model to converge. The one I am showing is from Keith Yates and he provides that service as a stand alone project but it still costs a few thousand dollars. If you are building a high-end theater this is the only way to go as it provides high accuracy results.
Another alternative which unfortunately is not available outside of Harman products is to use dynamic analysis and optimization using multiple subwoofers. This process starts with putting the subs somewhat optimally if you can (OK if you cannot) and let a computer analyze all the combinations of sub level, delay and filtering to find the optimal solution for multiple seats. There is a bit of that in the above article but much deeper dive with many actual measurements/examples is in this article: computer optimization of room acoustics
Back to mode calculator, be mindful of another important factor. The modes do not have zero bandwidth as the tools show. In reality, the modes have about 5 Hz of width (for most of their energy). This means that they can easily overlap and when they do, they can change the combined response that the microphone picks up and REW shows. In English
, this means that often you will have peaks and valleys that cannot be translated into actual modes easily. So even in perfectly rectangular room, don't be surprised if you can't match the measurements to the mode calculator.
Also, note that as frequencies go up, we care less about these modes as they start to pack closer and closer to each other. I think you had posted a graph asking about modes at a few hundred hertz. While I like the Harman spreadsheet you have been using, for this part of the analysis Ethan's mode calculator visualizes the situation better. Here is a snapshot for a random room:
Note that this shows the same thing as the Harman spreadsheet. The difference is the graphical representation. A few observations:
1. As I noted, when the frequencies get higher, we wind up with many modes. When that happens, we no longer see the massive peaks and valley contributions from each. They sort of cancel out each other's effects. The point where this happens depends on dimensions of the room. If you have a huge space, the point where that occurs is way down in lower frequencies. If I for example multiply the above dimensions by 10, the point where that occurs is less than 20 Hz! This is why the bass anomalies we have is due to our small rooms. Large rooms such as concert halls and such have far better bass response. The smaller the room, the worse the problem.
2. Note that in my sample room above there is a single mode at around 28 Hz and that is it. What this means is that we don't care about room modes below that frequency. There just isn't more of them to worry about! So if you see variations there, it is a function of your sub and such.
3. Look at the two modes right next to each other right past 50 Hz. Recall that I said modes actually have bandwidth of few hertz and are not those clean spikes. When you add that assumption you can see that the two modes will combine there and will result in a different waveform than what you expect there as one mode can be a peak and the other a null. Or two peaks.
4. Now look at the modes at 300 Hz. You see them packed tightly showing the effect I talked about earlier in that there is enough of them to mix as to create an average that is more or less independent of all the individual modes. A simple EQ to adjust their levels is probably all that you would want to do with them.
OK, this got long
. Hopefully it is useful addition to your excellent basic explanation of what is going on.