Directivity without Waveguides or DSP
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 Multi-Way Conventional loudspeakers with crossovers

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Patrick Bateman
diyAudio Member

Join Date: Oct 2006
Location: San Diego
Quote:
 Originally Posted by john k... I reall don't understand what you are trying to accomplish here. You have an array of 4 drivers, each separated by a distance, d, and each with successively increasing delay. d/c, 2d/c, and 3d/c. The claim is to control directivity. But the polar response vs frequency doesn't show much in the way of controlled directivity. Below F = c/8d the response is basically monopole. As the frequency approaches F=c/8d it becomes cardioid. As the frequency increases further and wavelength becomes shorter then the array length it degenerates into multi-lobed patterns with the number of lobes increasing with frequency. From one end the axial response is flat, as the delays compensate for the offsets, but from the other it shows as series of nulls and peaks in a pattern the repeats. Maybe I am missing the point here. Certainly you can construct an array that will have a cardioid response at F = c/8d, and monopole below, but the useful upper frequency would be F=c/8d as well because above that directivity is all over the place. The attached figure shows a simulation of such an array assuming omnidirectional sources. I'm not clear in what you are trying to accomplish. Certainly not wide band constant directivity.
Hi John, thanks for chiming in. I've had good luck with your u-frames in the past, but I no longer have a copy of mathcad to model them. (Does anyone know if hornresp can sim u-frames properly?)

I am interested in controlling directivity in the two octaves between 125hz and 500Hz. What do you think is the best option?

 27th May 2017, 02:03 PM #22 Patrick Bateman   diyAudio Member     Join Date: Oct 2006 Location: San Diego Answering my own question, it looks to me that John K's uframe would be a promising option, but I'd have to scale it down to make it work from 125Hz to 500hz. Here's a pic of John's uframe subwoofer. I don't know the exact dimensions but I'd estimate 14" x 14" x 18" Here's some measurements of a similar design from John's page (NaO U-frame). I'm seeing about two octaves of bandwidth (30hz-120hz.) So I'm thinking I could create something with a bandwidth of 125hz-500hz by using a box that's approximately 24% in size. So that would be a depth of 4.32" instead of a depth of 18" I checked in hornresp, and though it can simulate the effect of stuffing on a u-frame, I do not see any way to simulate directivity of a damped u-frame. AFAIK, John's mathcad worksheet is the only way to sim them.
 27th May 2017, 02:15 PM #23 Patrick Bateman   diyAudio Member     Join Date: Oct 2006 Location: San Diego FYI: the paper on cardioids linked on John's page appears to be dead. It's from the team that does Akabak? You can get it from the wayback machine here : https://web.archive.org/web/20050307...19_2003-lf.pdf
 27th May 2017, 02:24 PM #24 LineArray   diyAudio Member   Join Date: Mar 2008 This one is also interesting IMO, because of the comparisons made between monopole, dipole and cardioid in different settings: "MODAL COUPLING OF DIRECTIONAL SUBWOOFERS IN RECTANGULAR ROOMS" A Thesis in Acoustics by Philip Feurtado Pennsilvania State University, 2013 https://etda.libraries.psu.edu/files...bmissions/8634 It is purely "simulation based" (as i remember it), but there are a some unique settings/solutions described with respect to "woofer-/room interaction". E.g. Chapter 4.2. (Fig. 4.12) is interesting IMO due to possible (also practical) solutions or variants based on that "velocity source vs. pressure receiver" compensating effect, when using a dipole for the "lowest end" ... exiting a room (with respect to a preferred listening area) e.g. fairly below Schroeder Frequency ... __________________ Oliver, RFZ believer (?) www.dipol-audio.de Last edited by LineArray; 27th May 2017 at 02:53 PM.
 27th May 2017, 02:56 PM #25 LineArray   diyAudio Member   Join Date: Mar 2008 @Patrick I noticed your primary interest in the range around/above Schroeder up to about 500Hz and i feel you are essentially "well advised" (by yourself) with the way described in your post #22. Still there is more than one option how to make up a practical cardioid ... __________________ Oliver, RFZ believer (?) www.dipol-audio.de Last edited by LineArray; 27th May 2017 at 03:00 PM.
ICG
diyAudio Member

Join Date: Jul 2007
Location: Sound Cloud 9
Quote:
 Originally Posted by Patrick Bateman Answering my own question, it looks to me that John K's uframe would be a promising option, but I'd have to scale it down to make it work from 125Hz to 500hz.
Uhm, that does not work. At 500Hz you've got a wavelength of 0,69m, 1/4 Lambda is 0,1725m, that means you will get interferences at the upper end if you place the drivers directly in a row (one right next beside the next). Except you're going for quite small, much smaller drivers, but these will have a problem doing much at 125Hz.

Another thing is, I don't see this setup getting any smaller than a narrow beaming single horn.
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After all is said and done, usually more is said than done.

 27th May 2017, 08:07 PM #27 LineArray   diyAudio Member   Join Date: Mar 2008 I see no problem at all in realizing a "cardioid like" arrangement within Patrick's demands, having a bandwith of 2 octaves (125Hz to 500Hz). Suitable "pathlengths" may be between 20 ... 30 cm IMO, depending on the size of the driver(s) chosen and the front baffle's size ... In fact the inherent DI of those (drivers and baffle as to be chosen) will have to be regarded, when properly filtering the rear source. There are also "enough" drivers on the market available having sufficient volume displacement (possibly used in a multitude) to be used in such a project, without driving them into breakup modes at the "upper end" (because of too large cone area at given diaphragm structure). The question is to me : Where is the lower XO frequency (and steepness) ? Is it around 125Hz (12db/octave) ? Then the system will have to perform even below, which changes matters a bit and might call for slightly larger pathlengths ... __________________ Oliver, RFZ believer (?) www.dipol-audio.de Last edited by LineArray; 27th May 2017 at 08:28 PM.
 27th May 2017, 08:43 PM #28 LineArray   diyAudio Member   Join Date: Mar 2008 Pathlength/Lambda min = 0.33 may be seen as "hard upper limit" for pathlength (at the upper end), when making up a dipole from inherently nondirectional sources: http://www.musicanddesign.com/Dipole...n_baffles.html http://www.musicanddesign.com/images/DPOB3a.gif In a practical cardioid that limit can even be "exploited" just a bit IMO, depending on the DI of the front driver and baffle. Of course the rear source's low pass characteristics has to be adapted accordingly. __________________ Oliver, RFZ believer (?) www.dipol-audio.de Last edited by LineArray; 27th May 2017 at 09:07 PM.
 27th May 2017, 09:13 PM #29 LineArray   diyAudio Member   Join Date: Mar 2008 Just one driver example (availability in the US is unknown to me): W46-1316SM - 4x6" Paper Subwoofer - TB SPEAKER CO., LTD. This is a long stroke design with very sturdy/damped diaphragm and small size ... 500Hz and above should be no problem due to breakup modes IMO. If higher levels are needed: Use 2 or more. And "if needed" even this one can be equalized to operate up to the midrange ... https://www.parts-express.com/pedocs...ions-45667.pdf (yes it can ...) __________________ Oliver, RFZ believer (?) www.dipol-audio.de Last edited by LineArray; 27th May 2017 at 09:35 PM.
ICG
diyAudio Member

Join Date: Jul 2007
Location: Sound Cloud 9
Quote:
 Originally Posted by LineArray I see no problem at all in realizing a "cardioid like" arrangement within Patrick's demands, having a bandwith of 2 octaves (125Hz to 500Hz). Suitable "pathlengths" may be between 20 ... 30 cm IMO, depending on the size of the driver(s) chosen and the front baffle's size ... [...] There are also "enough" drivers on the market available having sufficient volume displacement (possibly used in a multitude) to be used in such a project, without driving them into breakup modes at the "upper end" (because of too large cone area at given diaphragm structure).
Er, no. The link you've posted is about a two driver dipole setup. But he wants a cardioid setup. For a cardioid setup you need at least 3 drivers. His intended drivers are so far 10", you're already over the critical distance. You need a LOT smaller drivers for that, probably 13cm or 10 (5"/4"). But that means even less horizontal dispersion control. It's pretty useless to have strict vertical radiation control but none horizontally.
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