Infinite Line Source: analysis

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being part of the tech crew i tend to get sent up a ladder with a ratchet strap and closable links and an angle finder to tweak the arraying and splay, so while i'm up the ladder the i don't get the inside track on the the DSP magic happening at the FOH.
i do get to hear the difference from where it was (initial hang) to the new "tweaked" result.
when the FOH guys are happy i take that as correct
 
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mark100 and turk182,

In my experience the moving of the image/sound stage moving up with you is a characteristic of listening in the near field. PA arrays operate primarily with far field radiation thus you would not have the experience the image/sound stage moving as you go from seated to standing position.

Jim
 
Jim must be right. Listening a tall array at home is nearfield, and then virtual image height floats with the listener.

Wesayso, I think that you didn't catch what I said. When I stand up in front of Acoustats, the virtual image stays the same but elevates with me.

This is a fundamental feature of arrays and difference to nearfield stereo with point source sound.
 
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One shoud not think that I dislike arrays or consider the concept wrong. No, it is just one way to fool our hearing system, and dipoles do pretty much the same but are more critical to positioning and reflectiveness of surfaces.

Two-channel stereo is based on fooling sound perception, and is very simple and clumsy in that. But it is the standard and most recordings and live broadcasting are done that way, mixed and mastered in nearfield with point source speakers in a well damped room. I want to leave it to the end user, if she wants to enhance the listening experience with some random reflections! And it is nice that we have options with different charasteristics to do that.
 
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I fell for arrays because, during my first experiment with 8 FR drivers per side, the detail seemed to come out exponentially as the volume is increased. Not 'linear' like in a typical 2 or 3 way setup. Certain recordings beg to be listened to at 90dB, others not so much. Subwoofers needed for the Full Rangers.

now planting my *ss, down in front
 
what about units?

Since I recently started my own line array project, without much theoretical background knowledge, I really applaud this effort.

Presenting the theory in the form of a network analysis is also very appealing to me due to my EE background.

However, the provided equations come with legends but no units. For example, what are the units for A0 and rho?

In order to use these equations in a computer program, I would like to know how to treat the attenuation factor for distances (r) close to 0?

Thanks, Simon
 
rho is 1.19 kg/m^3 and I assume that A0 is in m^3/s^2 - the volume acceleration. I don't know if he plans on doing the near field problem, it can get quite complicated. In my book I solve the near-field problem on-axis as that's the only place that has a nice solution for a finite length array. An infinite length one would be easier as there is a close form solution for that.
 
Jim must be right. Listening a tall array at home is nearfield, and then virtual image height floats with the listener.

Wesayso, I think that you didn't catch what I said. When I stand up in front of Acoustats, the virtual image stays the same but elevates with me.

This is a fundamental feature of arrays and difference to nearfield stereo with point source sound.

Fair enough, I did misread/misinterpreted that part :). Unnecessarily defensive on my part due to years of defending arrays against all kinds of preconceptions, no doubt. Sorry about that :p
 
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frugal-phile™
Joined 2001
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XenForo is a BBS software platform. The current platform is no longer in development and is getting creaky. I understand that XenForo has some of the developers from the older platform diyAudio has been running on.

The goal is to port to the new platform and while keeping it as close to the current experience as possible, fix know problems (blog/gallery/wiki) offer/add new useful features. For instance i guess that the add-ons Eriksquires is asking after give greater support for mathematics formatting.

dave
 
Well, i planned to leave our little point source here ... all by itself :) There is certainly more that can be developed, even for this (seemingly) simple source ... namely, Velocity Potential and Particle Velocity, from which the "near field" and "far field" regions are readily defined (they are not at all obvious from the pressure alone!). Going further, we could then discuss Acoustic Impedance and Sound Intensity ... but i fear that we may get too bogged-down in mathematics, even before we get to the real point of this thread :(

One simple way out, of course, is to just state the results ;)

For a simple point source radiating into 4pi space, assuming constant volume acceleration = Ao :

Velocity Potential = [-Ao/(jw*4pi*r)] * exp[j(wt - kr)]

Particle Velocity = [Ao/(4pi*r*c)] * [1 + 1/(jkr)] * exp[j(wt - kr)]

From which we define :

Near-field : kr < 1
- particle velocity varies as 1/(r^2)
- particle velocity is in phase quadrature with pressure

Far-field : kr > 1
- particle velocity varies as 1/(r)
- particle velocity is in phase with pressure

(one can readily confirm that our original "pressure equation" can be found by taking the first derivative wrt "time" of the Velocity Potential, multiplied by -(rho) ... and that the Particle Velocity can be found by taking the gradient, or first derivative wrt "r", of the Velocity Potential)

Now i think it really is time to abandon our Point Source, and develop the "pressure response" for an Infinite Line Source :)
 
I want to clarify something because I have seen this misquoted very often. The definition of near/far field given above is only valid for a fictional point source - real point sources do not exist. For a real transducer like a piston the near field transition is at r = k*a^2, which is quite different than the point source. The near field definitions differ for every type of source and using k*r = 1 as the transition in all cases is incorrect.
 
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Just coming to this topic, maybe I can help : if you give me the number of (ideal) loudspeakers of the array (16 max or 784 max for continuous arrays), distances/positions (x y z or type like J, CBT,...) and/or delays between each source, I can show the simulated global frequency response at 10 listening positions, so you may compare ie nearfied and farfield responses.

here is an example of arrays for different angles
keele410.png


or other arrays at different distances
bmr10.jpg


I can also send the impulse responses so with any convolution soft, you could even listen to results.
 
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