Adventures in cardioid

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That last comparison post was very helpful and what I originally understood. Amazing how it seems relatively constant across the range.

You mentioned something about small rooms. How would this improve things in a very tiny environment, where reflections are a significant problem. In other words, a car environment.

As I was reading the thread, I got a light bulb for a possible application. Since my installation options are rather limited, something like this would be very beneficial for me when the drivers are mounted off axis.

Am I barking up the wrong tree here? Where would the benefits end in the higher octaves? I ask this because, what if I run a full range driver crossed over to a midbass driver for the front stage :eek:
 
The theory on early reflections and how to use controlled directivity to shape their effects has been developed in no small part by Earl Geddes ('gedlee' on this forum). On his website http:www.gedlee.com there is lots of material. The point in question is discussed in this presentation on the website.

In a nutshell, you don't want early reflections, because they destroy imaging and other things. But you want 10-50 ms delayed reflections, because they create spaciousness. So you use narrow directivity especially >1000 Hz and toe in the speakers heavily to aim them away fro the listener. As a result, on axis sound is directed to the opposite side wall and any reflections from then on are sufficiently delayed.

Additional benefit, if you sit in off center listening positions, the more off center you more the more off axis you get to the speaker on your side of the couch, and the more on-axis you get to the speaker opposite side. As a result the SPL of the nearer speaker becomes less dominant and this stabilizes the imaging - at least in theory, and his is mainly what I am after.

But to achieve this, you really need near constant and smoothly varying directivity.

In a car the distances are so small that it i very hard to achieve. 10 ms is a 3.5 m or 11 ft path length difference, hard to achieve in a car. But it's worth trying.
 
Very nice explanation. I think I may go ahead and experiment with your theory on my own. I don't have fancy measurement system, but I do have my ears :)

Please keep up the great work! Fantastic thread...
MBK said:
The theory on early reflections and how to use controlled directivity to shape their effects has been developed in no small part by Earl Geddes ('gedlee' on this forum). On his website http:www.gedlee.com there is lots of material. The point in question is discussed in this presentation on the website.

In a nutshell, you don't want early reflections, because they destroy imaging and other things. But you want 10-50 ms delayed reflections, because they create spaciousness. So you use narrow directivity especially >1000 Hz and toe in the speakers heavily to aim them away fro the listener. As a result, on axis sound is directed to the opposite side wall and any reflections from then on are sufficiently delayed.

Additional benefit, if you sit in off center listening positions, the more off center you more the more off axis you get to the speaker on your side of the couch, and the more on-axis you get to the speaker opposite side. As a result the SPL of the nearer speaker becomes less dominant and this stabilizes the imaging - at least in theory, and his is mainly what I am after.

But to achieve this, you really need near constant and smoothly varying directivity.

In a car the distances are so small that it i very hard to achieve. 10 ms is a 3.5 m or 11 ft path length difference, hard to achieve in a car. But it's worth trying.
 
MBK said:
The pic in post 15 shows the PVC pipe assembly BTW, a damped version which I also tried. But first things first, placing increasing baffle sizes (thin circular cutouts taped to front of muffler), what FR do we get?

Here is a combo of naked muffler - 12" baffle - 16" baffle FRs. The polars look less clean and at HF curves start to invert (off axis higher than on axis). The low end is lifted due to increased dipole separation distance, but at the price of a bump, described by Linkwitz here .

But still: the muffler improves a lot on the Linkwitz picture above (he uses a 16 in diameter baffle, so compare with the 16 in baffle FR graph attached, bottom). The resonant bump around 400 Hz is less pronounced, and e get no nulls higher up, just smooth on and off axis FR. The graphs of course are completely unequalized.

What jumps out at me is the line-crossing close to the zero-axis, and how quickly it shifts with small changes in emission angle.

The effects of the line-crossing are evident with the 12" baffle, and more evident with the 16" baffle, moving down in frequency from the 2~3 kHz trouble spot of the 12" baffle to the more severe 1.3~2 kHz trouble spot of the 16" baffle. What makes it malign is that it is happening close to the zero axis - even a small movement off-axis shifts the response in the affected region, and on-axis it is depressed by 5 dB with the 16" baffle.

It must be a function of the additional delay of the baffle compared to the front wave, since the diffracted and delayed rear wave is most coherent right on-axis, and thus is available to cancel the front wave. As you move off-axis, the summing of the rear wave is more spread out in time, and does not subtract the front wave as strongly. It is surprising how sharp the front null is, though - and the sharpness would make it undesirable to equalize.

Have you tried the muffler without the solid rear disk? That has to be creating a strong reflection. Maybe replace the rear disk with a blob of cotton in a mesh bag, or simply a large pillow?
 
Gainphile, Fast1one, thanks. And yes, in Singapore we have a few gardens left. The issue is the weather: the day can be a) scorching hot or b) pouring rain. You think you measure at night rather? You'll measure lots of A/C noise instead :D

Lynn, I second your thoughts. I am debating with myself now what to do with this result - the cleanest by far is really the "no baffle" muffler which due to the muffler space really means, a ca. 9" face plate for a 6.5" driver.

The issue I am most debating with myself is power now: the SPL on the graphs is reasonably calibrated, which means 2.83V gets me ca. 85 dB at 2m/4PI. At 300 Hz, intended crossover region, this drops to ca. 75 dB. Now say we use a LR crossover, so this is really 75+6=81 dB. Say we really listen at 2 m and room reverberation gives us an optimistic 3 dB boost, and we are always in phase with the 2nd speaker so we have now in-room SPL of 90 dB at 2.83V RMS. That is 4V peak, so my 36V rail amps will only give me ca. 18dB headroom for 90 dB listening volume. Feasible, but not generous...

Anyway back to the acoustics: the rear of the SS8543 is so large (magnet) that the rear plate likely won't change much, it only adds about 2" each side of the magnet. Also, the air has no special reason to try and go out by this way when it's less resistance to the side unless you force it to, which is the theme of the next paragraph!

Here it goes. I haven't presented the data on issue 4- yet: what if I indeed drill holes in the back plate where it surrounds the magnet, and close off the muffler's sides (cotton still identical)? The idea was that firstly I'd increase dipole separation, and secondly I force airflow through not just 1 1/2" cotton on the sides, but really through 3 to 4" path length across the muffler "ring" towards the back and out the exhaust (imagine now a truly oversized automobile exhaust model). This would be a transmission line model, though with little actual "pipe" length which is advantageous to prevent 1/4 wave resonances etc.

The result surprised me again. Attached, the FR's comparing the closed muffler, 9" diameter and 3" depth , back open (really drilled a dozen 1" holes), with an implied separation distance of 9+2x3 = ca. 15", to the familiar 16" disc in front of the conventional muffler with open sides sans back holes.

Clearly now, the system behaves more like a conventional box. No more cardioid or dipole radiation patterns, it is omni below ca. 600-800 Hz and directional above. But, we have now a really lumpy FR as well, so there still is some summing with the rear wave going on, except it doesn't help the FR or the directivity patterns at all.
 

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And my preliminary conclusions are...

Well. There are always trade offs.

Clearly the concept of flow resistance seems to work well with little fine tuning, using a simple material as cotton. On the other hand, in the mid range frequency range we get little in the way of low pass filtering. And this means we have a fairly conventional dipole loss.

On the bright side, dipole-beating clean cardioid directivity with low rear output apparently is not too hard to achieve in the midrange. And combined with a CD horn at 1200 to 1800 Hz crossover, this means we can now dream of a constant directivity, constant power response midrange-cum-HF unit. Below ca. 500 Hz this configuration turns into more and more of a dipole, which is a good thing if it is supposed to cross over to one at 300 Hz or so.

One thing I haven't mentioned yet is the directivity index. Arta calculates me a really nice 4 dB to 4.5 dB figure throughout both midrange in muffler versions AND the XT1086 CD WG. If this is true, then it matches the theoretical 4.8 dB of a dipole, per Linkwitz, almost ideally, which is what the bass is going to be.

Another thing is, the falloff of the 12"baffle muffler specifically, fits LR2/320 Hz not too bad w/o trying, see attached simulation overlaid on data. Ignore the 320 Hz dip and peak beow, this is floor bounce. This configuration could basically stand sans HP filter at all, the 12" baffle giving some LF boost without degrading axial performance too much in the 1000+ Hz region. So, currently I tend towards trying a well built version of the 12" baffle (or a bit less, say 10.5") muffler and cross it to the XT1086 at anything from 1250 to 1800 Hz. The higher frequencies would be feasible dispersion wise, but the separation distance between the drivers becomes too large, 1500 Hz might be the upper limit before exceeding one lambda.
 

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Once it starts behaving like a tube, you get all of the annoying tube-resonance problems - lumpy response, and unstable polar response (the two go together). The key concept is the tube is "leaky" across its whole length - thus, no chance of pipe modes getting started.

Now as for issues with baffle delay (and that is clearly what we are seeing with the 12 and 16-inch baffles) there's another way to go about it: instead of a small cylindrical muffler and a large flat baffle (with lots of diffraction and re-radiation for the waves passing in each direction), make the muffler bigger, so it matches the size of the baffle!

It's the baffle edge that's creating all the trouble. It supports and extends the bass, true, but makes a hash of the midrange. This is why "extended" baffles that overlap the fronts of conventional boxes only make the sound worse, not better. Sharp edges of hard, reflective materials are not good. OK for musical instruments, not OK for loudspeakers.

When the muffler is the same size as the baffle, two things happen: there's no distance between the resistive mesh and the baffle edge, thus reducing diffraction effects for the rear wave spilling over towards the front, and the proximity of the resistive mesh to the baffle edge also improves the transition of the baffle edge for front waves spilling over to the rear. Both front and rear waves see a softer transition. This is already what's happening for your muffler that is the same size as the driver.

You could also make TWO concentric mufflers: one the size of the driver, and another the size of the baffle. Twice the absorption, half the energy flowing to the baffle edge. This way you get more bass (more absorption of the backwave at low frequencies) and a larger baffle too. It would probably also make the traditional, rectangular off-center-driver baffle behave better.
 
Re: And my preliminary conclusions are...

MBK said:
On the other hand, in the mid range frequency range we get little in the way of low pass filtering. And this means we have a fairly conventional dipole loss.

I should rephrase this. What I mean is this: The cotton is actually a very good HF filter, so it is a LP. But the cutoff is high, and when I tried to increase if with the closed sides muffler, all I got was directivity getting back to closed box patterns while FR getting worse. So it is not the LP filter effect of the cotton that is really interesting here, but the airflow resistance effect. And increasing the cotton load does not improve airflow resistance, but it does increase LP filtering to a point where it is counterproductive.

So conclusion, use cotton not to dampen absolute SPL, but to manipulate air flow.
 
Came too late for your reply Lynn.

As of above I suspect too much of more cotton would not help: too much actual LP filtering. But I'll ruminate on it, I thought of a more moderate addition, say 2 1/2 " cotton instead of 1 1/2", for a baffle of 11" dia instead of 9".
 
Think about a distributed path for the backwave instead of a single path (as it makes its way to the front). This is what the muffler is doing, as well as acting like a LP filter. The LP is pre-filtering the HF energy reaching the baffle edge, which is good, but the energy is also taking many paths from the muffler as well. Using a second, larger muffler increases the diffusion, as well as adding a second pole to the LP filter.

By the way, since you're using a powerful tool like ARTA, the impulse response over a 3~5 mSec interval would be most revealing. Based on the FR data, I'd guess the muffler with no baffle (or concentric baffles) would have the least stored energy. That's my figure-of-merit for the system. I'd leave bass-lift EQ issues for another driver to handle - I wouldn't sacrifice time-domain performance, which lies outside the scope of equalization.
 
Well the reason why I think too much damping (LP) may not be a good thing is the closed side muffler experiment. I interpret is as such that the rear wave has now been attenuated to such an extent that it is unable to help the dispersion in a meaningful way. The extended hump in the 300 Hz region is qualitatively not much different from the hump of the 16" baffle, or the rectangular baffle. But the polar response is very different.

But I agree that a moderately larger baffle should have a muffler to match in size. It just happened to be easier to stick a baffle to the existing muffler than to produce several muffler sizes, for this first batch of experiments.
 
You're on the right track. Supplement the data with impulse response for each type of muffler and it should be most interesting.

Since impulse responses are hard enough to read, I'd break them out for each bearing angle, instead of trying to stack all of them in a single graph. Line-crossing is quite meaningful in the frequency domain, but it would just look like an unreadable hash in the time domain. Separately plotted impulse responses for 0, 7.5, and 15 degrees should be plenty.

The warning for a bad condition is when they look completely different for emission angles that are this close together - and this is something I've seen before, so it can really happen. When the impulse response for the left and right ears are different, this can really screw up stereo perception, no matter what the FR graphs say.
 
Not the worst I've seen by any means. I agree the furniture is giving short-term reflections in the first 500 uSec. There is a very small artifact, looking a bit like a reflection, in the 12" baffle data - it looks like a small down-peak around 800 uSec, and followed by two ripples in the positive direction. I suspect that's the baffle doing that, and if the muffler wasn't there, it would be bigger.
 
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