Nice way to spend the day 
Possibly enough to begin returning some consistency? In any regard they may not be minimum phase. Not attenuating them should not be an option.
Well, the toilet didn't get cleaned, the carpet didn't get vacuumed, and the cat only got half as much petting as she'd have liked.Nice way to spend the day
On the plus side, I learned a little Python. It's a language I'm pretty new to. But if you want to generate plots from your program, and you're on Linux (as I am), then Python seems like a very good choice.
I'm pretty sure all normal physical resonances like this are indeed minimum phase.
But I think we shouldn't read too much detail into over-simplified mathematical models like this. I suspect it will turn out that only the modes below some quite low frequency - maybe 1 kHz, maybe 3 kHz - contribute to audible "boxy" sounds. Above that, who knows, maybe the modes contribute to the "screechy" treble we often hear from poor quality speaker systems.
Agreed. And yet it is surprising how often there is no attempt made at all to attenuate acoustic resonances in the speaker box - I've cut open several boom-box speakers in recent years, and never found any acoustic treatment inside a single one.
The same goes for almost every acoustic and electric guitar amp I've opened - no acoustic treatement inside. Also older "Hi-Fi" speakers from decades ago (which were really quite "Mid-Fi".)
Not surprisingly, most boomboxes, and guitar amps, and vintage Hi-Fi speakers, sound quite noticeably "boxy".
A friend who was a professional music composer for film and TV owned two pairs of quite expensive Adam Audio near-field monitor speakers, one smaller than the other. He used them to test his mixes, to make sure they sounded good on both. I'm quite sure they both had internal acoustic treatment, as does every reputable studio monitor.
At any rate, I got to hear both sets of Adams in his home studio some years ago. The small one sounded quite good on its own, until you heard the larger one. Then you really noticed how "boxy" the smaller one was by comparison!
For fun, I re-ran my program to generate modes for a 24" box (longest dimension), this time using the square root of 2 as the ratio of each pair of edges. The results are attached.
Maybe I'm missing something, but I'm not seeing any obvious signs that one ratio is better than the other.
-Gnobuddy
Attachments
Instead of maintaining thelong dimension the same, maintain the volume of the box otherwise one can not directly compare the results. ie the 2 graphes above ar enot directly comparable... one has a volume of 3264 in3, the other 4890 in3.
dave
Good idea, here's the mode plot for a 24" cube.
Doesn't look bad at all, no?
I think what you've pointed out is that just seeing the mode frequencies alone doesn't tell you how bad a box sounds. The problem with a cube is that the x, y, and z modes all fall at exactly the same frequencies, and reinforce each other's nastiness. And that doesn't show up in this plot, and I can't think of a way to actually demonstrate that problem on a plot, either.
So the cube plot actually looks more sparse than the previous two I posted - it looks as though there are fewer resonances, and this is actually true, because the x, y, and z resonances don't interleave, but instead all fall neatly on top of each other.
Anyone know of a way to demonstrate the badness of this?
The only thing I can think of is to assume a Q for every mode (say Q=20 or something), then check if multiple modes fall within the bandwidth of any given mode. If so, draw the corresponding line on the plot taller, to indicate a stronger resonance.
Does that sound as though it might be useful?
-Gnobuddy
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The fourth and fifth resonant frequencies are almost overlapping in the sqrt 2 ratio, while in the golden ratio box they are apart.
As planet10 pointed out, only frequencies below 1 kHz are relevant.
Instead of just counting them, add the together. so that reinforced resoances have a larger magnitude.
IIRC the availble spreadsheets that do the same thing you are attempying to do cover that off.
The 1st time i saw these kinds of calculations they were done in Fortran and the output was a set of numbers.
dave
Where I'd question this is where the dimensions exceed perception. For example, say at some higher frequency an individual event may be represented by one cycle. Although a continuous sine wave resonance would be about level, the single event would return an echo.
By contrast take a low frequency room mode that may be smaller in wavelength than the room, yet whose perception takes a few cycles and the resonance can be addressed more simply.. Notwithstanding spatial considerations.
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Yes. You will also need to consider mode coupling due to the driver position. If I were to do this I would consider raytracing. Since the driver is the focus of interest, it could then be reduced to a response plot. It would only hold true for continuous sine waves so if you wanted to guild the lily you could produce an excess group delay plot if this could be made to highlight the frequencies above which need to be attenuated.
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Thanks, I missed that post until now. I'd been hinting/asking about that very thing in several of my previous posts (i.e., how many modes actually matter before they're too high in frequency to matter?)
-Gnobuddy
What your sim seems to be neglecting to model is the drop off in amplitude as order increases as well as addition of contributions from multiple dimensions. i.e. the 3rd order mode should be 1/3 the amplitude compared to the fundamental. If two dimensions have the same length they add together.here's the mode plot for a 24" cube.
Doesn't look bad at all, no?
You also need to implement some width (finite Q) so that a peak of amplitude 0.5 at f=1.000 and a peak of amplitude 0.7 at f=1.001 equals a peak of amplitude ~1.2 at ~f=1.0005
After doing that you should see that the peaks are bigger in amplitude for a cube compared to a box with the golden ratios.
Allen, there are two opposite dangers when creating a mathematical model of a physical phenomenon.
The first danger is oversimplifying to the point where necessary physics is lost, and the model is therefore useless.
The second danger is over complicating, by including all sorts of imagined possibilities, which eventually turn out to be irrelevant, but stop you from proceeding at all.
I believe your suggestions are well down unnecessary over-complications path. Not only do you want to invoke non-minimum phase (which rarely occurs in nature), now you also want to invoke human perception, for which there is no mathematical model at all.
I think there are much more significant effects (than minimum phase) that we're not including, such as cone breakup modes, and the way the presence of acoustic stuffing alters the properties of air in the box.
What I'm doing here is just a first approximation - please let's not be under the illusion that it is going to lead to any sort of breakthrough in acoustics. This is stuff that was surely calculated on paper two hundred years ago, and then re-calculated in the early 1900s with the arrival of the first loudspeaker enclosures, and then recalculated a thousand times more in a thousand pieces of software during the last forty or fifty years.
I've made two changes at Planet10's suggestion: one, keeping the volume constant, regardless of shape (2.0 cubic ft), and two, only plotting modes up to 2 kHz.
With those changes, here are plots for a cube, and for a Golden Ratio enclosure.
As before, in these plots, the Golden Ratio enclosure actually looks worse, because the plots don't show the strengthened resonances that result from overlapping modes in the cubical enclosure.
-Gnobuddy
Attachments
Are you assuming equal energy per mode? Because the actual strength of excitation of each mode would be something quite complicated to calculate, as it would depend on the overlap integral between the sound waves coming off the back of the loudspeaker, and the geometrical shape of each mode.
Agreed, thank you for the suggestions. Something along these lines was briefly mentioned some of my posts earlier.
I'm not sure if I want to bother modifying the code that far, though. This was just intended to be a quick look at the original question that started this thread.
Unfortunately, coding takes time, time which you never get back - a lesson I learned the hard way in the 1990's and 2000's. When you finally pull your head out of the computer, you realize that you missed the chance to be with your loved ones, or making music, or having fun with a hot soldering-iron.
We'll see...maybe during some idle lunch-break at work!
-Gnobuddy
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