What's the average directivity range of a typical 6" cone?

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I recently spent many hours with an enclosure, foam, and my measurement system trying to get a passive cardioid response. Nothing worked out very well for me. There was a very weak reduction in the rear SPL, but not much more. Maybe foam is just too porous, but it was about a foot thick. Should have done something!

Funny, been there and done that myself. Tried different materials, never worked well. It also rather reduced the bass output on axis (compared to dipole operation !) so I gave up, but maybe to soon.

Perhaps JohnK would tell us how that worked for him and with which material: DIY-dipole-1



With about 16.5" of mineral wool (one 5.5" batt cut into three sections) encased in microfibre fabric, I've measured high levels of attenuation that suggest I ought to be varying thickness (thinner at some parts). I think as you say, foam is just too porous.

As I understand, the material ideally should provide a significant flow resistance, but with low absorption/damping at LF (it could and probably should damp the quarter-wave resonance typically around 150-200 Hz).
Mineral wool is probably one of the better materials in that respect, but I don't know what would be ideal. I vaguely remember having heard people talking about something like "metal wool".
 
I wonder if anyone ever experimented with a square cross section cabinet, with four mid-bass drivers, one on each side of the cab at the same height... front and back wired in phase, two sides wired out of phase... Wouldn't that create a perfect 90 degrees of directivity for the front facing driver?

I know this is not practical, though it is tempting to try with inexpensive drivers at some point. If it was a pyramid shaped cabinet, you could load 4 tweeters the same way and have 90 degree front facing directivity through the crossover range as well, I think.

I guess the downside is that you would want such a speaker to be roughly 4 feet away from any back or side walls so the reflections from all the other drivers have as little impact on direct sound as possible.
 
Earl mentioned that a narrower pattern could be had with another active source but I haven't really looked into that yet. Maybe next year.

In terms of radiation theory the higher the radiation mode the narrower its response. A monopole can only achieve a single mode - 1 source, 1 mode. Two drivers can achieve any combination of a monopole and a dipole. Four drivers could achieve any combination of a quadrapole, dipole and monopole. This is true at LFs where the sources act as point sources. As the freq -> higher the sources inherent directivity enters into the problem - not intractable, but not trivial either.
 
I wonder if anyone ever experimented with a square cross section cabinet, with four mid-bass drivers, one on each side of the cab at the same height... front and back wired in phase, two sides wired out of phase... Wouldn't that create a perfect 90 degrees of directivity for the front facing driver?

This is a classic quadra-pole and should do as you say. Things would be different because of the boxes edge diffraction. If the box were a sphere than it would be very accurate to a quadra-pole - perfect 90°. Unfortunately quadra-pole efficiency is even lower than dipole. That would hurt!

What I would do is use a quadra-pole up higher, then rotate the phases to a dipole and finally to a monopole at VLFs. DSP could do this, but it is still four channels of DSP and four amps. But at least the efficiency wouldn't kill you.

You have to ask in all this where the cost/benefit tradeoff is. Talking about it is free, but actually building and testing is expensive, let alone considering making it a product.
 
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Do I understand correctly that a quadrapole would then have a 90° lobe on each side of the enclosure? That seems counterproductive unless I'm missing something. Is it somehow mitigated with dsp? I admit I have trouble wrapping my head around the phase interaction when we start taking about 3+ sources.
 
Thanks for commenting Earl, always appreciate your insight and have been following you on the forums for many many years now.

I always think in terms of DIY fun rather than products, it is such a tough business...

I think you have mentioned before that there is little if any benefit to maintaining directivity below around 800 Hz, is this correct? From most of your posts I have concluded that directivity consistency is the first priority, having it be narrow directivity is the second priority (but you feel this is important), and that keeping the crossover point as close to 800 Hz as possible is the next priority with you having some good success as high as 1.6 KHz??? but generally preferring the results as you work your way down. I think some of your earlier, smaller speakers did well in the 1.2-1.5 range but then you started pushing everything down to 1 kHz or less. Forgive the generalization here.. especially if I am off the mark.

Anyways, taking it back to the OP topic/intent, I believe the above is why you never got excited about 5-7.5 inch mid-bass drivers...because their directivity "match" with tweeter would only happen at a fairly high crossover point.
 
Do I understand correctly that a quadrapole would then have a 90° lobe on each side of the enclosure? That seems counterproductive unless I'm missing something. Is it somehow mitigated with dsp? I admit I have trouble wrapping my head around the phase interaction when we start taking about 3+ sources.

I think driver phase stays perfectly 180 degrees out of phase throughout the operating range of the driver, minus any diffraction effects, between each "neighbor" of the mid-bass drivers (and tweeters if you did a full two-way quadapole, if I understand this correctly).

So the lobes between like drivers should be very narrow and at exactly 45 degrees off each of the four axis of each driver in the horizontal plane. You would still have a lobe between mid-bass and tweeter in the vertical plane, but that would follow the same parameters/conventions as any two way speaker design.

This is all just wild speculation on my part...
 
Do I understand correctly that a quadrapole would then have a 90° lobe on each side of the enclosure? That seems counterproductive unless I'm missing something. Is it somehow mitigated with dsp? I admit I have trouble wrapping my head around the phase interaction when we start taking about 3+ sources.

That would be the case if you could only wire them in-phase or out-of-phase. But if you had arbitrary control over each source then you could combine the monopole, dipole and quadra-pole responses to give you close to a forward 90° pattern with highly suppressed off angle responses. All of the cardioid, hyper-cardiod, etc. are just various weighted sums of a monopole and a dipole.
 
I think you have mentioned before that there is little if any benefit to maintaining directivity below around 800 Hz, is this correct?
Below 700 Hz I believe the benefits are diminishing fast because by the time we reach the modal region any talk of directivity is unsupported by the facts. So I am not against it, if it can be done reasonably, but if I have to make tradeoff then this is where I would start.
From most of your posts I have concluded that directivity consistency is the first priority, having it be narrow directivity is the second priority (but you feel this is important), and that keeping the crossover point as close to 800 Hz as possible is the next priority with you having some good success as high as 1.6 KHz??? but generally preferring the results as you work your way down. I think some of your earlier, smaller speakers did well in the 1.2-1.5 range but then you started pushing everything down to 1 kHz or less. Forgive the generalization here.. especially if I am off the mark.
This is correct, but narrow is a co-highest priority - narrow AND constant. Results get better the lower one can push the crossover down, but never will I allow the crossover to dramatically change the polar response. It must be maintained smoothly through the crossover. This is key and quite difficult as there just are not a lot of options. I have worked this problem forwards and backwards and I always come back to the same solution. I would love to see others, but I haven't.
Anyways, taking it back to the OP topic/intent, I believe the above is why you never got excited about 5-7.5 inch mid-bass drivers...because their directivity "match" with tweeter would only happen at a fairly high crossover point.

Exactly - does not meet the criteria of seamless crossover.
 
OK, now I am hi-jacking a bit but I have to ask....

Earl, is your focus on the "narrow" all about minimizing room reflections? I have a small agenda here as I am knee deep in a significant DIY project and even though I started out looking for a waveguide based solution, I ended up back to more conventional approaches and instead tried to keep everything close to 180 degrees directivity as much as possible with woofer, mid-bass, mid-dome and then dome tweeter... From your perspective, what is my downfall here in terms of in room performance? I am assuming I can still get fairly smooth power response by having 4 different drivers handing off to each other well within their passband and before any beaming takes place. So aside from the multiple crossover points, is it just room reflections that will be a problem compared your preferred design approach?
 
Its all about minimizing very early reflections (VER). VER degrade imaging, but do enhance spaciousness.

With a wide directivity you have two options 1) kill the early reflections with absorption, this will enhance the imaging, but degrade the spaciousness. 2) Don't do anything and live with a degraded image.

With a higher directivity you can have both great imaging and spaciousness. Point the speakers away from the walls, and leave the room very reflective. The low VER are minimize by the directivity while the spaciousness is enhance by the later lateral reflections in the live room.
 
Its all about minimizing very early reflections (VER). VER degrade imaging, but do enhance spaciousness.

With a wide directivity you have two options 1) kill the early reflections with absorption, this will enhance the imaging, but degrade the spaciousness. 2) Don't do anything and live with a degraded image.

With a higher directivity you can have both great imaging and spaciousness. Point the speakers away from the walls, and leave the room very reflective. The low VER are minimize by the directivity while the spaciousness is enhance by the later lateral reflections in the live room.

These don't seem like different cases to me. If you have wide dispersion but deal with the early reflection or alternatively use narrow dispersion but aim it away, wouldn't you end up with the same thing?

Assuming spaciousness is related to the general level of the reverberent field, we only care about directivity index. The wide dispersion speaker has a low d.i. and therefor a relatively high reverberant field.

Now at first glance we would think that the directional speaker gives a lower reverberant field via its higher directivity, but if we aim it away from the listener we are reducing effective directivity index as the off-the-beam listening axis is nearer the average spherical level.

If we put a more directional speaker in an intentionally more reverberent room, then clearly we may end up with a relatively high reverberent field, but how is that different than a normal dispersion speaker in a normal room?

The inference that a directional speaker might be aimed to increase the gap between direct sound and early reflections is true, but if you are allowing for absorbtion of some early reflections from the wide dispersion speaker, then how are the two cases at all different?

As an aside, This week I have been experimenting with some wide dispersion speakers and measuring their reverberent field. In my case the earliest discrete reflections are the wall bounce directly behind the system and a double bounce from the near corner of the room (surprisingly the side wall bounces were not evident). It was very simple to kill both of these reflections with some modest MDF reflectors, carefully placed. The energy was preserved just by bouncing the sound away to return after a few more bounces. This would seem to meet your requirement of sufficient initial gap plus generous later reverberance for spaciousness.

Perhaps expensive and highly directional speakers aren't required?

David
 
These don't seem like different cases to me. If you have wide dispersion but deal with the early reflection or alternatively use narrow dispersion but aim it away, wouldn't you end up with the same thing?
No, you say so yourself below.
Assuming spaciousness is related to the general level of the reverberent field, we only care about directivity index. The wide dispersion speaker has a low d.i. and therefor a relatively high reverberant field.
Except that this isn't true. A low DI does not imply greater reverb field.
Now at first glance we would think that the directional speaker gives a lower reverberant field via its higher directivity, but if we aim it away from the listener we are reducing effective directivity index as the off-the-beam listening axis is nearer the average spherical level.
I don't know what "effective DI" is, I only know the real DI which does not change off axis for a CD speaker.

If we put a more directional speaker in an intentionally more reverberent room, then clearly we may end up with a relatively high reverberent field, but how is that different than a normal dispersion speaker in a normal room?

The inference that a directional speaker might be aimed to increase the gap between direct sound and early reflections is true, but if you are allowing for absorbtion of some early reflections from the wide dispersion speaker, then how are the two cases at all different?

They are different in that the narrow directivity speaker has greater later lateral reflections than the wide speaker with side wall absorption.

The gap between the direct sound and the onset of reverb that a directional speaker achieves may seem like a small thing, but it is precisely this very early sound that the ear is most sensitive to.
 
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If we just took an apples to apples approach in terms of room reflectivity, but varied the size of the rooms...

1) Narrow directivity design in a small room, say 12 x 15 feet with speakers along the short wall, 8 feet apart and 2 feet in from the side walls, and 2 feet out from the back wall...

2) Wide directivity design in a medium/large room, say 17 x 25 feet with speakers along the short wall, 9 feet apart and 4 feet in from the side walls and 3 feet out from the back wall...

Would it be correct to assume that the narrow directivity design offers clearer advantages in the small room where reflective surfaces are closer to the speaker and thus arrive "early" but would have less clear benefits in the larger room where the travel time of reflected sound is now much later?

I have failed to provide any good definition of "early" vs "late" reflections and know very little about how the listener is affected by the transition between the two, but I was always under the impression that room treatments were much less necessary when the speakers have enough breathing room to prevent very early reflections. From other forum sources I thought a distance of 3 feet or greater would usually cause the reflections to arrive late enough to avoid the worst effects.
 
Would it be correct to assume that the narrow directivity design offers clearer advantages in the small room where reflective surfaces are closer to the speaker and thus arrive "early" but would have less clear benefits in the larger room where the travel time of reflected sound is now much later?

In general I would agree with that, because in a very large room it clearly cannot make any difference which is wider or narrower to a single listener (regarding early reflections, later reverberant field may be different).

The larger room is harder to get higher levels of SPL and needs the more powerful speakers however and here directivity is preferred, but for a completely different reason.
 
A bit slow to respond as we were at a Boston Symphony matinee followed by a reception for Leo Beranek's 100th birthday. Happy birthday Leo!

Except that this isn't true. A low DI does not imply greater reverb field.

Certainly it does. For a given direct field level (axial response) a low d.i. means a higher reverberant field level. Conversly, high d.i. means more distance between axial level and reverberent level. This is all defined in the Hopkins-Stryker equation.

I don't know what "effective DI" is, I only know the real DI which does not change off axis for a CD speaker.

Directivity index compares the axial response to the mean spherical response. The measurement presumes some definition of on-axis. This can be defined variously as perpendicular to the center of the box, on the horn's centerline, or at whatever spot gives highest output level. The assumption is that the listeners will sit on this axis and the Hopkins-Stryker relationship will then define the reverberant field level.

Now, if you purposely sit off the main axis at a position of lower overall level, then you have effectively reduced the difference between your lstening axis and the mean spherical level. You have effectively reduced the directivity index.

They are different in that the narrow directivity speaker has greater later lateral reflections than the wide speaker with side wall absorption.

The gap between the direct sound and the onset of reverb that a directional speaker achieves may seem like a small thing, but it is precisely this very early sound that the ear is most sensitive to.

I know that you would like to believe that there is only one solution to your desired outcome but it simply isn't the case. In the end there are only two factors under consideration: direct to reverberent ratio and initial delay gap.

For direct to reverberant ratio the only factors involved are directivity index, possible reduction of effective d.i. (sitting off axis), room livelyness and listening distance. If you want more reverberation for a given direct field level, you can use wider dispersion speakers, sit farther away, increase the RT of the room or aim the speakers away from you. If you want a dryer sound then adjust any of those factors in the other direction.

This gives everyone a wide latitude in possible direct to reverberent level. Most people could easily move their speakers to half distance, for example, and increase the direct to reflected ratio by 6dB. Or move them farther for the opposite effect. Sitting on or off axis is probably good for a 3dB change in ratio. Room acoustics of various room types must encompass a 3 to 6dB range. The range of speakers? Wide dispersion probably means a d.i. rising from 3dB at mid frequencies to about 6 at high. A narrow dispersion CD system probably has a d.i. Of 9 to 12 (if you sit on axis!).

With all these variables available I would guarantee that I could use wide dispersion speakers and match the direct to reflected ratio that you shoot for.

As to the initial delay gap, I was just this week measuring the room impulse response of a popular direct/reflecting speaker (no points for guessing the brand) and was easily able to kill the first three strong wall bounces with simple reflectors. (Absorbers would have worked as well.). Late lateral reflections, if desired, could also be enhanced with simple reflectors.

There are many ways to skin this particular cat.

David
 
Very enlightening post Dave.......and probobly the greatest example of why direct radiators have flourished in popularity for home stereo and cinema. The end user has in many instances the ability to achieve the desired results of directivity through placement options. Of course as the speakers get closer together and farther from reverberance creating boundaries, the imaging changes and that's a tradeoff one doesn't have to endure with waveguide systems.....among other challenges such as less than ideal placement ergonomic ally speaking.

My recent group of threads have been aimed at designing systems for my particular, although typical room which I've found is something overlooked within DIY circles and yet the single greatest advantage we DIYers have towards getting great sound.

If we take bass in general as example and the typical rough in room response below 300hz or so, it's clear to me that some of these modes and nulls can and should be addressed with design and room constraints in mind yet more often get overlooked. The multiple sub approach only addresses the problems in their passband, leaving 100-300hz a wash with irregularity. Most mid high DIY designs also ignore it and induce it somewhat by placing the midwoofer high above the floor which creates it's own special set of problems.

Of course as many including yourself and Earl have pointed out, there's no overall perfect design. But if we as DIYers focus on our rooms and placement limitations first the choices we make narrow significantly and the chances for success increase inversely.

Looking at the need for a new design in my space has forced me to look at where DIY is at now. The modern commercial mantra of small or narrow baffled systems with 6" midwoofers are taking a back seat to the larger formats of the past. This trend typically overlooks available vertical real estate so to speak. Through listening evaluation and experiment, the advantages of waveguides are clear and positive. I'm just not convinced that 15" or wider baffles are the only way to reap the benefits or that large format midwoofers are the ideal solution for midrange reproduction.......in my space of course. Taken as a whole, I'm finding that systems that take advantage of the vertical such as WMTMW or MMTMM arrangements offer just as many advantages as the large two ways with more flexibility in typical home environments. Symmetry IMO has to account for something in a closed 3D acoustic space.

Now this approach isn't a challenge to Earl's philosophy on design but simply put, these designs don't work in my space where the front stage uses a pull down non acoustically transparent screen. This leaves an extremely limited area for mains placement which forces me to think tall and narrow instead of low and wide. My point is there's a case to made each and every time a design is created and examined for its rewards or benefits if the in room response is considered primarily and not just nearfield and polar maps. Take those outdoor created normalized polars and consider the changes when the speaker is within 18" of a perpendicular wall or boundary.......not so pretty anymore in real world examples. In many typical spaces, every inch counts and can be the difference between ok or great results.
 
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