Hardly, its not like it falls into a nice Z-transform relationship. Firings are not time synchronous (except at very low frequencies), the firings tend to be random. Intensity perception is encoded in the numbers of firings per time, and pitch mostly by the location of the nerve that is firing. An understand of DSP is of no help whatsoever in understanding hearing neural analysis.
But don't we listen in the near field in our small rooms? Fortunately most of us have a limited listening window.
Yes, I have your book in hardback paper copy no less and recently reread the section on arrays. It helps but I need a simulation program or at the minimum a spread sheet to make those equations come alive. I'm hoping that BWaslo's Xsim 3D will become a reasonably accurate predictor of line array performance.
It depends how you are using the term Sound Fields: Free versus Diffuse Field, Near versus Far Field
How about arrays with non-uniform element positions? How about frequency dependent shading?
Neither of those has a closed form mathematical solution, they have to be done numerically. That's not what I offered to do.
Numerically there is a theorem that makes most problems easier.
It is the source product rule:
Given a velocity distribution that is the product of several separate distributions, the directivity will be the product of the directivities. Its a linear system.
So in the first case above one would simply find the directivity of several unequal spaced point sources, which is just a summation problem and then multiply its directivity by the directivity of the individual sources. The horizontal directivity would be that of an individual source, only the vertical would need to be calculated.
The frequency dependent shading could be done the same way, by finding the directivity of point sources with that shading and multiplying it by the directivity of an individual source. Not difficult if the shading is something simple in frequency, but not so easy if it gets complex. again only the vertical would be complicated.
Years ago in my Program SPEAK, I had an array module which could build up highly complex arrays from compilations of simple points sources and specific source directivities. If I had an interest in line arrays I would certainly have further developed this, but as I have said before I am a point source kind of guy.
Numerically there is a theorem that makes most problems easier.
It is the source product rule:
Given a velocity distribution that is the product of several separate distributions, the directivity will be the product of the directivities. Its a linear system.
So in the first case above one would simply find the directivity of several unequal spaced point sources, which is just a summation problem and then multiply its directivity by the directivity of the individual sources. The horizontal directivity would be that of an individual source, only the vertical would need to be calculated.
The frequency dependent shading could be done the same way, by finding the directivity of point sources with that shading and multiplying it by the directivity of an individual source. Not difficult if the shading is something simple in frequency, but not so easy if it gets complex. again only the vertical would be complicated.
Years ago in my Program SPEAK, I had an array module which could build up highly complex arrays from compilations of simple points sources and specific source directivities. If I had an interest in line arrays I would certainly have further developed this, but as I have said before I am a point source kind of guy.
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Take a CBT array, place it in a room and observe it's reflections from the listeners point of view. It will react quite different to room boundaries than a more common 2 or 3 way.
While each individual driver has no change in directivity compared to the same driver as a single unit, the array of drivers will change (average out) reflections as each driver has a different distance to both the listening position as well as to the reflecting surfaces. The reflections of each driver in the array will be unique for that driver's position and don't line up to form a similar reflection as a point source device would create.
So while each of the individual drivers in an array may still have the same directivity, the array as a total will deviate from this, as observed from a listeners perspective. If we had 30 drivers in the CBT, the reflection of the first driver would be offset by 29 drivers, by having a slightly different position.
So when we look at directivity of a (CBT) array we should look at what it does inside our room too. Not just assume the directivity is unchanged compared to a single driver that makes up the array.
We do have walls, floors and ceilings, and often a lot more in our listening room. Not all of us have the luxury to keep our enclosures well away from near boundaries.
While each individual driver has no change in directivity compared to the same driver as a single unit, the array of drivers will change (average out) reflections as each driver has a different distance to both the listening position as well as to the reflecting surfaces. The reflections of each driver in the array will be unique for that driver's position and don't line up to form a similar reflection as a point source device would create.
So while each of the individual drivers in an array may still have the same directivity, the array as a total will deviate from this, as observed from a listeners perspective. If we had 30 drivers in the CBT, the reflection of the first driver would be offset by 29 drivers, by having a slightly different position.
So when we look at directivity of a (CBT) array we should look at what it does inside our room too. Not just assume the directivity is unchanged compared to a single driver that makes up the array.
We do have walls, floors and ceilings, and often a lot more in our listening room. Not all of us have the luxury to keep our enclosures well away from near boundaries.
A CBT is not really a line array, but a curved array, but anyways ... Yes a line array will react differently but that doesn't mean better. To me what you have is a small advantage on top of a big disadvantage. There will be a small time smear of the reflection but this will vanish as the reflections progress (consider the image source model, the line array is still a line array in the reflection, but its getting smaller and the time smear is going away. But the disadvantage is the large intensity of the first reflection which can be avoided altogether with a high DI point source. A high DI line array might alleviate that issue, but I have never seen anyone do that (except in large pro installations.)
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I will try in a week or so....
http://www.diyaudio.com/forums/full-range/325085-fr10hm-corner-ceiling-floor-array.html#post5493601
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http://www.diyaudio.com/forums/full-range/325085-fr10hm-corner-ceiling-floor-array.html#post5493601
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POST #21
some practical considerations
How do we "realize" an infinite vertical line source? I'm sure many are aware of the "image theory" of reflections : to first-order, a reflecting surface can be replaced by a "virtual source" behind (or above, or below) the surface, and the same sound field will result. So, one very practical way to create an essentially "infinite" line is to build a floor-to-ceiling line, and allow a reflecting floor and reflecting ceiling to "extend" the line.
How do we build a floor-to-ceiling line source? Most commonly, of course, from a vertical array of small-ish drivers. The CTC (center-to-center) spacing rules have been well-developed elsewhere ... anyone may please feel free to add some info to this thread!
What about wall reflections? Another big topic, to be sure ... but, following the same "image theory" of reflections, it's pretty tempting to consider putting floor-to-ceiling line arrays right in the forward corners of the room, to virtually eliminate the 'earliest' wall reflections. Certainly, some wall treatment would be in order for the first reflection of the left speaker from the right wall, and vice versa. But please remember that this whole plan is certainly not screaming for floor or ceiling treatments ...
And this pretty much describes something that i would personally consider to be a very interesting "experiment" :
- floor-to-ceiling line sources, made of an array of smallish drivers
- uniformly driven (or excited), but we'll need some good EQ (probably FIR) for that ~3dB per octave issue
- place a stereo pair right in the forward corners of a rectangular-ish room
- the only room treatments to consider, at first, may be wall treatment on the left wall for first reflection from right speaker (and vice versa)
- I might just be bold enough to suggest that we can get away with no center channel, for movies ... the "virtual center" approach may be good enough, because of the wider "sweet spot" from only -3dB per doubling-distance
I haven't built what i've described ... but i bet others have (or something close). So ... time for everyone to share thoughts, opinions, and experiences!
My work here is done
Great thread, thanks Werewolf et al for the time you put into this. It takes a lot of effort to talk through they grey world between the "yes/no oversimplifications"
I've always 'assumed' the worst about an 'infinite' line in a listening room (and embraced the 'point source with constant directivity' approach instead)
So?!?! ..... "Should I get a big box of 3" drivers delivered ... and build an 'infinite' line in the corners of my room???" .... I'm starting to think maybe it IS something I should try.
I've always 'assumed' the worst about an 'infinite' line in a listening room (and embraced the 'point source with constant directivity' approach instead)
So?!?! ..... "Should I get a big box of 3" drivers delivered ... and build an 'infinite' line in the corners of my room???" .... I'm starting to think maybe it IS something I should try.
3", or 3.5" or smaller ones, like in this commercial example: Audio Machina XTAC
There are lots of different line array projects on it's way, lots of finished examples and reading material. I never regretted the time I put into mine. The question is Dave: Do you really want more?
There are lots of different line array projects on it's way, lots of finished examples and reading material. I never regretted the time I put into mine. The question is Dave: Do you really want more?
Do you really want more?
(Dave Moore)
This is where I am now: "Synergy Corner Horns and Bass Bins"
I find the corner line interesting from many perspectives ... a) Academic b) I'd like to experience it c) It would claw back some floor space in a room that's going to be increasingly shared with little people in the coming years
I think I will give this a go.
guess where I am? doodling a line array for use in my new house that lacks a useable pair of corners. if I had designed more vertical pattern control into my corner horns I might not be doing that; I might be be trying to talk my wife into a false corner instead.
I am looking forward to more ambience from a larger room and its reflections but I wonder if I'll bemoan the lack of horizontal pattern control with line arrays out in the room
I am looking forward to more ambience from a larger room and its reflections but I wonder if I'll bemoan the lack of horizontal pattern control with line arrays out in the room
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