Think of three ranges. At highest frequencies the cone beams and will narrow down to less than 90 degrees, then less than 45, etc. For a 6" this may start around 4kHz, off the top of my head.
From this frequency down to a few hundred then the baffle is sufficiently large to constrain the directivity to hemispherical. i.e., 180 degrees. This is determined by the baffle size and nothing else.
Below that frequency the baffle is no longer big enough and the dispersion spreads towards Omni.
So to answer your question, the frequency is totally related to baffle size. If you use a program for determining "baffle step function" (cabinet diffraction response) such as Tolvin, "the edge", then where the response starts to shelve down is also where the polar pattern starts to spread from 180 to, ultimately, 360.
David
From this frequency down to a few hundred then the baffle is sufficiently large to constrain the directivity to hemispherical. i.e., 180 degrees. This is determined by the baffle size and nothing else.
Below that frequency the baffle is no longer big enough and the dispersion spreads towards Omni.
So to answer your question, the frequency is totally related to baffle size. If you use a program for determining "baffle step function" (cabinet diffraction response) such as Tolvin, "the edge", then where the response starts to shelve down is also where the polar pattern starts to spread from 180 to, ultimately, 360.
David
Take a look at the polar of this driver, it might give you a hint ( it begins to be directive as it approaches 1kHz, albeit only slightly, and reaches -5dB past 2kHz)
AL 170 - 8 Ohm
Huge horn or - to a certain extent as should obvious from the example above - large radiating area, either large Drivers (non-CD) or 2D Array. No free luch tho. Below 500 Hz Dipole might be the best bet.
My area of comparison is a 6" midwoofer as compared to say the common 12-15" woofers often associated with waveguide two ways. I'm trying to find the advantage of the large diameter drivers over the smaller. If we assume the same wide baffle needed to accommodate the woofer in a three way, the small 6" midwoofer should remain near constantly directive lower in frequency as the larger diameter drivers?
Your question was at what frequency the speaker goes omni. The answer is that it goes omni when the baffle is no longer large enough to support hemispherical radiation. It is down to baffle dimensions, nothing else.
Now if the question is at what frequency, going up, the driver starts to beam and narrow to less than hemispherical, then that is directly tied to driver diameter.
David
Now if the question is at what frequency, going up, the driver starts to beam and narrow to less than hemispherical, then that is directly tied to driver diameter.
David
Almost, hemispherical then (180¤) It is questionable if that should be called directivity.
http://www.acs.psu.edu/drussell/demos/baffledpiston/baffledpiston.html
Baffle step is actually the combination of 2 factors. At low frequencies frontal energy is allowed to bend around the cabinet edges into the back hemisphere. This is a loss in axial pressure as power escapes to the back side.
At the same time the low frequency loading is reduced and the actual system efficiency is less below baffle step than above.
Both factors contribute about 3 dB of step for a difference approaching 6dB.
David
At the typical crossover of a 2-way to a waveguide of say 700-100 Hz, only a large driver narrows enough to meet the waveguide's own directivity. A small one will radiate 180 degree resulting in an abrupt transition in directivity.
Dr. Geddes uses exactly this in his speakers. Of course, lower in frequency the larger driver also "blooms", but this is (arguably) an acceptable compromise.
Yes, but as already pointed out that constant directivity would be 180 degrees at best, which is pointless..
But all drivers do this right? At least in a close box. Dipoles don't - as much - but they have such low efficiency. If you really want a narrow directivity maintained to a lower frequency without a much lower efficiency then you need two drivers programmed to yield a hyper/cardioid. This works well, but dramatically increases cost and complexity - that is the trade off.
......but we're also talking horizontal here so when considering multiple drivers in a vertical array, we can gain some advantages over a single large format woofer.
If I build a waveguide two way, I'm inevitably going to have to deal with some floor and ceiling bounce cancellations. There's no way to get the midwoofer as close to the floor as it needs to be to avoid it. So if we/I substitute 4 or more 6" midwoofers and cross higher to the CD/waveguide I can match the horizontal directivity of the large format two way AND improve the vertical directivity.......yes?
If I build a waveguide two way, I'm inevitably going to have to deal with some floor and ceiling bounce cancellations. There's no way to get the midwoofer as close to the floor as it needs to be to avoid it. So if we/I substitute 4 or more 6" midwoofers and cross higher to the CD/waveguide I can match the horizontal directivity of the large format two way AND improve the vertical directivity.......yes?
Yep. There is no free lunch, cardioid is probably the best way to go at LF if efficiency is a concern.
No.
If you substitute the large woofer with several smaller in a vertical array, as I understand you suggest, you will not match the horizontal directivity if the larger one. You will have high directivity vertically, but the same directivity as 1 single small woofer horizontally. If you want to match the large woofer, you Need to make a 2D Array as wide as the large woofer (or a tapered one, like wide near the floor and narrower higher up above)
I once did a model with four small woofers at the corners surrounding the waveguide. I wasn't happen with the results. No crossover lobe, but poor directivity control in the woofer section and I just could not get the directivities to match at crossover without going very narrow with the waveguide or very low with the crossover. Some things seem like they should work until you actually get down to the nitty-gritty and then you find the problems.
For a given distance between two gradient sources a cardioid plays 6 dB's louder than a dipole at frequencies far below tuning. Quite worthwhile indeed. If you want to save cost, why not make a passive cardioid? Perhaps not easy to get right, but I've done some experiments with promising results.
Ive considered it in the vane of how Amphion approached a passive cardoid with an MTM waveguide loaded dome. The speaker sounds fantastic but ive only heard it in a large space so no real test of it's cardoid behavior. My sensibility in design thought now leads me back to a vertical MMTMM complimented by multiple subwoofers. The B&C 6MD38 which i'm very familiar with if used in a 2x2 parallel series scheme would still be quite efficient even with passive cardoid cancellation losses. Expensive though. There's a much cheaper option for a 6.5" midwoofer from both Eminence and Tymphany.
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!
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.
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