Cardioid Bass

[gedlee]

The analysis assumes a source with free air response is flat to DC. So I'm looking at the transfer function between source and listening position which would then be superimposed on the woofer's actual free air response. When I say "as you might set up a bigger 3-way system" what I mean is that for the first 3 figures I positioned the source in the room as you migh position one speaker of a stereo pair, as opposed to how you would position a subwoofer. The last figure for corner placement was just for curiosity.

It's not FEM. It's a Green's function approach. Takes a fraction of a second per case. I'm putting a web page together on it. I'd appreciate your comments since I've not done anything like this before. It's only for rectangular rooms with perfectly rigid walls at present, but can be extended to walls with arbitrary admittance.

My PhD was on LF room modes using FEA, but I basically assembled the Green's function from the FEA modes.

My point is that handling sources in the Greens function approach can be tricky. For example a dipole is not too hard, two point sources out of phase, BUT what moment to use (the distance between the sources) makes a big difference? The cardiod is even tougher, but I would do it, as I said before as two point sources of different strengths that are out of phase - but what moment to use on the dipole portion?

Another difficulty is that the modes in a highly dampoed room are not orthogonal so one cannot exactly define a Greem's function. HOW you handle absorption is tricky and different approachs give different answers.

I don't think that the discussion is about woofers, but subs and I think that the location of the subs has to be allowed more freedom than that of the mains. I think it totally restrictive on the problem to assume the sub is at the location of the mains. If this is the asumption then my previous work would not apply since I would never place subs at those locations.

Taking statistics is IMO the only way to view the problem since specific situations will never be true in practice. But one could conclude from a large number of different runs what the most LIKELY situation would do.

 

[Salas]

I don't think that the discussion is about woofers, but subs and I think that the location of the subs has to be allowed more freedom than that of the mains. I think it totally restrictive on the problem to assume the sub is at the location of the mains. If this is the asumption then my previous work would not apply since I would never place subs at those locations.

I have a feeling that exactly the above is the root of your different view points about the usefulness of monopoles or cardioids in the nodal region. John makes stereo speakers with cardioid or dipole woofers, and you do installations with multiple subs and sats. It boils down to 2 fixed cardioid wide sources vs multiple distributed, tuned monopole sources IMHO.

 

[gedlee]

Just as a trial - I'll do more tomorrow, I ran the same room as yours, same basic speaker locations and mic position (maybe a little diferent). Attached are my results. They differ from your quite a bit, but mine shows the correct response at DC for the dipole. Yours seems to be missing that.

PS - how do you attach plots so that they show like yours? Do they have to be on the web? I can't load an image from my computer? Only as an attachment.

 

[gedlee]

I have a feeling that exactly the above is the root of your different view points about the usefulness of monopoles or cardioids in the nodal region. John makes stereo speakers with cardioid or dipole woofers, and you do installations with multiple subs and sats. It boils down to 2 fixed cardioid wide sources vs multiple distributed, tuned monopole sources IMHO.

This most certainly does make a difference, but then, to me, its no contest - multiple independent subs is the way to go. Everybody is coming to this conclusion, to wit the Toole interview (although I was doing this long before JBL.) It simply doesn't make sense to use the mains woofers as LF sources way down into the modal region. The mains have to be placed for best imaging of the HFs and the subs for best LF smoothness. There is simply no way these locations will be at the same places.

There would be distinct advantages to the cardiod from about 200 Hz to 500 Hz, but I never thought that the discussion was about this. Maybe a new post should be opened up to talk about subs in rooms as this is an important topic. But then the discussion should be about 150 Hz down and subs placed independently from the mains.

 

[gedlee]

Attached is another run with a better model of the cardiod and the sources adjusted for the same mid frequency (200 Hz) level. The room has more like the damping values that are found in real rooms.

 

[Pano]

Maybe a new post should be opened up to talk about subs in rooms as this is an important topic. But then the discussion should be about 150 Hz down...

Not a bad idea. Over in the Subwoofers forum?

.....and subs placed independently from the mains.

Or together. Might as well discuss the good and bad points of both.

 

[LineSource]

To John K and all WMTMW dipolers

Would a WMTMW dipole topology similar to your ICTA work, but with 15" woofers, provide some low frequency SPL smoothing advantages over a TMWW dipole topology in home listening rooms? Can your model cover this small design difference?

http://www.musicanddesign.com/icta.html

 

[Fosti]

An externally hosted image should be here but it was not working when we last tested it.

J.K.: The notch between 70 to 100 Hz, which you can see on the chart, is typical for a multitude of small audio control rooms as they can usually be found today. If there are now 10 db less sound level behind the loudspeaker, there is also a smaller superposition-effect for the formation of wavemodes. This leads to less ripple on the characteristics of the operational sound level, as one can see at the curve for the "cardioid". I emphasize again, however, that the shown curves are only valid for a specific room. Unlike this, the recordings of directivity are generally applicable. They were measured in a free-field situation with a measuring microphone in standard height of 1,40 meter so that the ground reflections were included. And they also influence the energy behind the speaker by sort of "crosstalking". If they weren't taken into account, the measurement would be unrealistic. By the way: not even in an anechoic room you obtain the required accuracy, because already the spacing between the wedges of the acoustic insulation leads to falsifications.

See full article: http://www.me-geithain.de/presse/ppeng/presseppeng.html

 

[john k...]

Here is the link to the web page I put up. I would expect some differences between this and any FEM result that include non zero admittance of the walls. Any way this is what I did. If there is anything in error let me know so that i can correct it. As I said, I've only spent a few hours on it.

http://www.musicanddesign.com/roomgain2A.html

 

[gedlee]

Here is the link to the web page I put up. I would expect some differences between this and any FEM result that include non zero admittance of the walls. Any way this is what I did. If there is anything in error let me know so that i can correct it. As I said, I've only spent a few hours on it.

John, as I said before, our results don't look quite the same but we are both using the exact same approach. You don't define how you add damping. This is a critical aspect of the problem and the books that you quoted don't show how to do this. I believe that my book does discuss this problem.

The biggest concern that I have is how your dipole does not go to zero at DC. It has to do this and any solution that does not do this cannot be correct. My solution does.

 

[john k...]

Hi Earl,

I did find a minor bug, but no big deal. The notch at 17 Hz for the monopolewas bugging me. Didn't make sense. The bug fix gets that out and corrects the dipole result as well. As I said I, I just threw this together. I can accept coding errors. They will get fixed.

A this point I don't have damping, and you are correct, it is a major concern. The first reference does show how to allow for nonzero admittance of the surfaces but I haven't worked through the details yet. I do have a FEM code that considers damping but I didn't write it and unfortunately it doesn't allow me to set up a cardioid source, not to mention that the procedure is very slow. I'm still working with the developer so hopefully at some time I can convince him to do cardioid. I'll keep pluging away. Something to do on a rainy day.

 

[gedlee]

Hi Earl,
A this point I don't have damping, and you are correct, it is a major concern. The first reference does show how to allow for nonzero admittance of the surfaces but I haven't worked through the details yet. I do have a FEM code that considers damping but I didn't write it and unfortunately it doesn't allow me to set up a cardioid source, not to mention that the procedure is very slow. I'm still working with the developer so hopefully at some time I can convince him to do cardioid. I'll keep pluging away. Something to do on a rainy day.

You won't find the discussion in Morse and Ingard very illucidating.

Basically what is usually done is to ASSUME that the eigenmodes don't change. This is a reasonable assumption for light damping, but fails for large damping. Basically whet happens in the physics is that the modes share energy. In other words the energy in one mode leaks into adjacent modes through the damping. Tis is why damping at LF is such a good thing.

Then assume that only the Eigenvalue chnges, it becomes complex. The denominator has the eigenvalues squared. So expand the complex eigen values into real and imaginary parts. Discard the terms in the imaginary parts squared as these are small. The remaining complex term will have a real part times the damping value (the imaginary part). If you leave this like this you will find a strange thing happens because the damping will rise with frequency and the room will flatten way out at higher frequencies. I end up with

(i * kn * pi *c - eta)^2 for the denominator eigenvalue squared, where eta is the damping, assumed small, usually about 20 in english units. This works pretty well. Any other approach that I have tried yields very strange results.

 

[Graham Maynard]

Comments made here by Lynn Olson would also relate to EQed dipole+monopole 'systems' generated cardioid bass.

http://www.diyaudio.com/forums/showthread.php?threadid=100392&goto=newpost


Cheers .......... Graham.

 

[john k...]

You won't find the discussion in Morse and Ingard very illucidating.

Maybe I am missing something but they seem to present a very straight forward discussion for the corrections to the eigenfunctions and eigenvalues for small admittance. So if I assume that the wall admittance is small but real, then energy is lost to the wall and that should provid the damping, no? As you note, the eigenfunctions don't change much for small admittance so initially I will not alter them. It becomes a matter of how the eigenvalues in the denominator change.

 

[gedlee]

Maybe I am missing something but they seem to present a very straight forward discussion for the corrections to the eigenfunctions and eigenvalues for small admittance. So if I assume that the wall admittance is small but real, then energy is lost to the wall and that should provid the damping, no? As you note, the eigenfunctions don't change much for small admittance so initially I will not alter them. It becomes a matter of how the eigenvalues in the denominator change.

Quite correct and my last post on this was wrong. (Sorry about that.) That was an earlier attempt. If you look at the equation you can see that I just use a complex eigenvalue with mode independent damping. M&I use mode dependent damping, which is more accurate if the damping is only on one wall, but if the damping is well distributed, as I always try and do, then a mode independant form is completely accurate. ALL OF THIS ASSUMES small damping which is the real problem.

 

[john k...]

Well, I have modified my room mode analysis to include frequency dependent “real” admittance (conductance) and "tune" the admittance model using FEM simulations from SoundEasy. The agreement between SE for monopoles and dipoles is very good. I then redid the calculations for the monopole, dipole and cardioid I had previously posted.

http://www.musicanddesign.com/roomgain2A.html


While there are differences, I think I have to pretty much agree with Earl that at low frequency there is little differences between sources (except below the room fundamental) unless they are placed in very critical (not necessarily good) positions. The dips you see in the 30 to 40Hz region, which are common to all source types, have more to do with the listener position than source position, type, or orientation. The null is basically a result of the listener being center left to right in the room. Being centered there is little SPL generated at the listening from the first mode in the side to side direction which is at 34.4 Hz since this position is a pressure node for that mode, and all odd numbered nodes in the side to side direction. Looking at the plot at the lower right, where the listener is off center, you can see that region begins to fill in for all sources. But remember, this is for a dipole and cardioid source orientated at an angle to the walls. If the dipoe and cardioid are orientated with the axis parallel to a side wall the dipole wil sill have the deep null when the listened moves to the left or right of center. The cardioid will behave much like a monopole and the null will fill in.

 

[gedlee]

While there are differences, I think I have to pretty much agree with Earl that at low frequency there is little differences between sources (except below the room fundamental) unless they are placed in very critical (not necessarily good) positions.

John

Timely. I just finished my analysis which took a lot into consideration. I used four source positions and seven almost random) listener positions (all near the room center, basically any of these locations is a likely listener). I normalized all sources to have a flat average response at the listener positions (basically they all have flat power response into the room). This is the most logical thing to do since all sources are then on an equal footing - all are EQ'd to flat power.

After all this data I conclude that no source is statistically any different than any other. Basically, the room dominates the problem and the source type makes no real difference. We appear to completely agree on this point .

Of course the cardiod and dipole require a lot more power at the low end to achieve a flat room sound power, which is not an insignificant factor.

I will post my paper shortly, which I am going to write up and send to JAES.

I expect that this will shake up some people .

Its good to have collaborations from two people who initially disagreed. Good work.

(Although, I would like to point out that our analysis differ substantially in detail. And close inspection of yours will find that your figures 3 and 5 should be very similar and they are completely different. I don't find this much change with such a small movement of the source and receiver.)

 

[john k...]

Its good to have collaborations from two people who initially disagreed. Good work.

(Although, I would like to point out that our analysis differ substantially in detail. And close inspection of yours will find that your figures 3 and 5 should be very similar and they are completely different. I don't find this much change with such a small movement of the source and receiver.)

Well, I would say we agree on most of the issues. I'll still say that directivity matters, but at the same time, it only matters if you happen to be so unlucky as to place a monopole woofer exactly at a pressure node or a dipole exactly at a velocity node. There the cardioid has an advantage, but as you note it is countered by the added complexity of eq for the gradient roll of and the need for more power.

I am also putting a page up on the effects of orientation which show that a dipole doesn't excite modes orthogonal to its axis. Certainly the differences between cardioids and monopoles are less significant that those of a dipole. But I think the idea that a dipole is better because it excites fewer modes is just incorrect. If the dipole is positioned so as to excite fewer modes then the end result can only be dips in the response at those modes that can not be corrected by equalization. The only thing left is what happens below the room fundamental.

I am glad I got involved in this thread. I have previously based my opinions on what I have read by other researchers. I never bothered to take a deeper look into this myself until getting into this thread. I had made some assessment using the SoundEasy FEM analysis but I really had to look at the math to see what is going on.

All in all I still think, for those who love dipole midrange the NaO Mini is spot on. It has the advantage of dipole mids which morph to cardioid in the 100 Hz region and then to monopole at low frequency when set up as designed. Still, since the woofers a in separate, self powered enclosures, they can be positioned in any manner the listener prefers to optimize the low frequency response if the design configuration doesn't work out for them. The flexibility of detached woofers is really what it is all about.

As for the differences you site with figure 3 and 5, all I can say is that is what comes out of the analysis and in view of the conformation I made with the SoundEasy FEM code I don’t know how to respond. I’ll try to make a direct comparison with Se for those cases and see.

 

[augerpro]

I hate to oversimplify this-just trying to wrap my brain around it- but are you two in agreement that for bass there is no advantage to any of these forms assuming you didn't just happen to place in the worst possible place? How about if you were running a woofer up around 200-300hz, any advantage to cardioid over monopole considering front wall reflections? From power response and polar response perspective are these forms still about equal-considering they are running up to 200-300hz? I should mention I ask these questions in the context of a 3 way design where the mid (and possibly tweeter) are dipole.

 

[gedlee]

I hate to oversimplify this-just trying to wrap my brain around it- but are you two in agreement that for bass there is no advantage to any of these forms assuming you didn't just happen to place in the worst possible place? How about if you were running a woofer up around 200-300hz, any advantage to cardioid over monopole considering front wall reflections? From power response and polar response perspective are these forms still about equal-considering they are running up to 200-300hz? I should mention I ask these questions in the context of a 3 way design where the mid (and possibly tweeter) are dipole.

Our discussion has been about LF - below about 150 Hz. You are correct, in general, for typical locations of sources and listeners it makes no difference the source type - except for the need to EQ dipoles and cardiods. Your not likely to get much agreement on the frequency range that you mention.

I would tend to say that there would be some advantage to directivity in this frequency range, however, I have found that unworkable in practice. Of more importance to me is narrow controlled directivity above 1 kHz and a match of directivity at the crossover. The need for directivity control below 1 kHz IMO becomes ever less and less important. Its certainly not a bad thing so long as nothing important is given up to achieve it. I just haven't found it to be practical (read cost effective) to do that.