The following case study is an exaple of tangential modes playing a significant role in governing monitoring system respose. The study is based on ETF5 measurements that were performed by me at the listening position in my home studio. The room had no treatment and was completely empty except for two speakers, their stands, a computer desk, and a computer.
Room Description and Test Setup
The room is 159” x 118” x 96” (L x W x H). The walls and ceiling are plasterboard and the floor is hardwood. The two windows are blocked with ¾” HDF and sealed with rope caulk. There is a closet with a solid core door at the back of the room which was shut during the test. The solid core exit door was also shut. The center of the woofer cone center was 18” from the front wall, 35” from the left wall, and 39” from the floor. The microphone, a B&K 4007, was placed 60” from the front wall, 59” from the side walls, and 43” from the floor. The speaker faced the microphone. ETF was used in Long MLS mode with loopback.
Data
This first image is a plot which shows the modes for the room as calculated by the Rayleigh equation. This image is courtesy of Eric Desart.
This next image, also courtesy of Eric Desart, shows data from ETF5 with the calculated modal frequencies on the same scale. The data was exported as text from ETF and imported into Eric’s software for convenient display. The gate time was set to 200 milliseconds and the Hanning window function was used. Resolution is 1.46 Hz.
The final image is a waterfall plot of the same data.
Analysis
Starting from the bottom up in the second image, The first feature is the 47 Hz measured resonance which is clearly the (1,0,0) mode, which is predicted at 43 Hz. The (0,1,0) mode is identifiable with a measured frequency of 58 Hz and a calculated frequency of 57 Hz. The (0,0,1) mode is also present with a measured value of 72, Hz and a predicted value of 70 Hz. The next resonance at 85 Hz (85 Hz predicted) could be blamed entirely on the (2,0,0) mode, but it looks a little wide to me on the low side which I believe suggests the help of the 82 Hz (1,0,1) tangential.
There is a measured peak at 111 Hz which is close to two modes: a 110 Hz tangential and a 115 Hz axial. I believe it is the tangential and not the axial that is responsible for this. Frist, the speaker is located very near a null for the (0,2,0) mode which would prevent it from being activated. Also, the resolution of the ETF data is 1.46 Hz, which would be enough to single out a 115 Hz resonance if it were there. It is unclear to me what is going on in the 115-130 Hz interval. Could the 124 Hz resonance be the effect of the 124 Hz (2,1,1) oblique? No idea. If anyone else wants to guess, please do.
I believe that the peak at 139 Hz is another combination mode, consisting of the 141 Hz (0,0,2) axial, the 134 Hz (0,2,1) tangential, and the 140 Hz (3,1,0) tangential. Additional analysis with the more frequency accurate rectangular window indeed showed the resonance breaking into two distinct resonances at 135 Hz and 142 Hz. The (0,1,2) tangential also makes an appearance at 152 Hz.
Perhaps the most conclusive element of this study is the measured resonance at 164 Hz. Thanks to my unfavorable room dimensions, the predicted 165 Hz (2,0,2) tangential is the only mode within 5 Hz of the measured peak. There is no other plausible explanation; this is a dominant tangential mode.
The next measured resonance at 172 Hz coincides with the (4,0,0) 170 Hz and (0,3,0) 172 Hz modes, along with the (3,2,0) 171 Hz tangential. Now we begin to move into the area where modal density increases and the idea of assigning blame to any one mode becomes more and more dubious. It is for this reason that I have omitted data above 200 Hz. Even though the modal density is growing, there are no axial modes between 172 Hz and 211 Hz, which means that any resonances found in this area are likely due to non-axial modes. There are two measured resonances in this area, at 180 Hz and 191 Hz, and both appear to be combinations of non-axial mode resonances.
Conclusions
This case study shows that tangential modes can be a dominant factor in determining the frequency response of a monitoring system in a small room.
Special thanks to Jeff Szymanski and Eric Desart for their guidance.
Last edited by David French on Fri May 06, 2005 3:23 pm; edited 3 times in total
proudtower Recording Org Pro Audio Forums
Joined: Mar 14, 2005
Posts: 145
Location: achterhoek, netherlands
David, great stuff. Your attention to detail and organized presentation make for an efficient approach to actually learning something from the data.
Can you add more information about the exact wall construction:
How many layers of plasterboard per side?
How thick the plasterboard/s?
What is the stud spacing?
Wood or metal studs, and what size?
Single or double studs?
What's in the cavity?
The reason I ask is that I wonder to what extent floppier walls will shift the frequency response of the room, as Toole said in Getting the Bass Right. I'd think that if any of your wall panels were vibrating particularly strongly at certain frequencies, and if you knew what frequencies those were, that could alter the conclusions you arrive at.
I'm thinking out loud here about theory, but I'm trying to stay practical, prompted by Rod's and Brian's focus on the so-what of all these ruminations. They all boil down to two cases:
1) If we haven't built a room yet, how and how big should we build it?
2) If we have a room already, what more information do we need to gather to divine what to do now, so that we can successfully hear in it?
I wish I knew about the wall construction, but I do not. I don't think I can find out either unless one of you constructions guys can make an inference based on the home's age. Perhaps if you ask some diagnostic quesitons we can figure it out.
Bert,
No! You pointed out my mistake! I edited the post to reflect the fact that the room was empty. Thank you!
proudtower Recording Org Pro Audio Forums
Joined: Mar 14, 2005
Posts: 145
Location: achterhoek, netherlands
OK!
Going to give a link to the google pro group where a similar thread is going on, if you don't mind, although i'm clearly an idiot.
Maybe they can learn something from your great initiative.
The microphone, a B&K 4007, was placed 60” from the front wall, 48” from the side walls, and 43” from the floor.
We talked about this and I thought the mic was placed at 1/2 the width? Or not? We had debated a little about whether it was 48" from the side walls or 59". Clarify?
Other than that, thanks for including me in the study!
_________________ ---lovecow---
"You've got to be very careful if you don't know where you're going, because you might not get there." - Yogi Berra
David French Respected Past Moderator
Joined: Jun 19, 2002
Posts: 2852
Location: Indiana
Woah! That is a long link! Could you (or a mod) please edit your post using the url tags so that the page isn't so elongated. My graphics make it bad enough for people with low screen resolutions. Here's an example for the unlikely event that you don't know how to do this:
Code:
[url=http://biglonglink.com]discrete link title[/url]
Ethan Winer Respected Past Moderator
Joined: Mar 19, 2001
Posts: 3209
Location: New Milford, CT USA
I agree with the others that you did a great job. We need more people here to do this too, because a rectangular room with good speakers and removeable treatment turns out to be rare.
I do have a few comments:
The lowest mode is off by almost 10 percent, so I'd be careful not to assume too much at the other frequencies. However, if non-rigid walls can be shown to account for the disparities, it is possible that the disparity becomes less the higher in frequency you look. Though so far nobody has explained the mechanism for this shift other than to blame "construction" generally.
> There is a measured peak at 111 Hz which is close to two modes: a 110 Hz tangential and a 115 Hz axial. I believe it is the tangential and not the axial that is responsible for this. <
I'm not so sure. If you look carefully at the ~110 Hz peak you'll see a hint of a peak on the left side. So I might conclude that the major peak is the 115 Hz axial and the smaller is the non-axial at 111 Hz.
> Perhaps the most conclusive element of this study is the measured resonance at 164 Hz ... There is no other plausible explanation; this is a dominant tangential mode. <
Maybe, or maybe this is just another case where the measured and predicted responses disagree by 20 percent. There are a lot of axial modes within 20 percent of 164 Hz! The main reason I doubt this resonance is non-axial is because it's the second largest peak in the graph. Then again, it could be more prominent simply due to boundary effects.
All in all, this is an excellent contribution to the topic at hand, and yet another piece of valuable - and apparently valid - data. Thanks very much for doing that.
> Special thanks to Jeff Szymanski and Eric Desart for their guidance. <
Both of you witnessed a large discrepancy between the predicted and measured lowest mode. The common thread between both your (David's and Ethan's) analyses was ETF. Perhaps this observed discrepancy is some unknown limitation of the software? (I do not not not mean to question, or otherwise imply anything about, the validity of ETF here. Just speculating on an apparently common theme...)
FWIW, I didn't use ETF in this analysis and got almost exact correlation between predicted and measured lowest mode (38.1 Hz and 38.4 Hz, respectively).
Food for thought. Remember, too, that we will undoubtedly generate 10^n questions for every n answers we think we have.
_________________ ---lovecow---
"You've got to be very careful if you don't know where you're going, because you might not get there." - Yogi Berra
David French Respected Past Moderator
Joined: Jun 19, 2002
Posts: 2852
Location: Indiana
Glad you decided to chime in Ethan. I was hoping this would be more of a discussion than a congratulate David kind of thing.
Ethan Winer wrote:
The lowest mode is off by almost 10 percent
Like Jeff said, using percent is not a good idea. We alreay have good metrics; they're called Hertz. If you have something agains Herts, al least let's use something meaningful like cents. I'd rather just stick to Hertz. It seems that refering to percent is just a way to dramatize the difference
Ethan Winer wrote:
However, if non-rigid walls can be shown to account for the disparities, it is possible that the disparity becomes less the higher in frequency you look.
Definitely looks that way to me from both of our data. The measured modes correlate rather well in the rest of my data; the (1,0,0) is the farthest off and needs not set a precedent.
Ethan Winer wrote:
If you look carefully at the ~110 Hz peak you'll see a hint of a peak on the left side. So I might conclude that the major peak is the 115 Hz axial and the smaller is the non-axial at 111 Hz.
Seems unlikely to me since the correlation betweenthe measued resonance and the predicted tangential is so strong. Also, the next nearest more on the low side of 111 Hz is quite far away at 102 Hz.
Ethan Winer wrote:
or maybe this is just another case where the measured and predicted responses disagree by 20 percent.
Just because you may have found this one time does not a precedent make.
David French Respected Past Moderator
Joined: Jun 19, 2002
Posts: 2852
Location: Indiana
If you look carefully at the ~110 Hz peak you'll see a hint of a peak on the left side. So I might conclude that the major peak is the 115 Hz axial and the smaller is the non-axial at 111 Hz.
As I stated in the analysis, the speaker is located very near a null for the (0,2,0) 115 Hz mode, so it would not be active. How do your argument deal with this?
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