FSP-LA

Danley's comparison is bogus. He fails to mention the fact that line arrays can and do form a smooth and gapless source in the vertical direction, wheras conventional arrays resemble a series of point sources.

Consequently, the diffraction in *either* dimension is much worse in a conventional array. That's why you don't see people trying to use conventional cabinets in line array configuration - you wouldn't get the benefits.

Danley claims manufacturers are profiteering out of line arrays. What he neglects to mention is that he bet his boat on a conventional design called the "unity horn". It arrays like a conventional array and has the same problems. Danley wants to prop up his investment in those speakers rather than admit he was wrong. Yet behind the scenes he licences tech to line array companies - but you wont read about that on his web site.

I'm going to get the popcorn...

Hi



I see he is skeptical, that’s fine.



The sources that form a line array “can” sum coherently into a single
source, but so can the sources that form a multi element point source
(like the old Unity horn and its replacement the Synergy horn), what
governs that is how far apart they are acoustically.



Like with woofer where people are more familiar, the sources must be
about one quarter to one third wavelength apart at most to combine
coherently.

That is the point of the horns I build now, the sources all coherently combine into one source in time and space.

That is also the point of the Paraline waveguide and Synergy horn
alignment used in the “line source” system below, think about how large
the wavelength is at 10 or 20KHz. The purpose of the Paraline is to
form a seamless hf wavefront “as if” the source were a full height
coherent source like a ribbon speaker etc, the synergy alignment takes
over below that..



www.vtcproaudio.com/ technology/index.html



The absence of this coherent summation is why most line sources make
plenty of comb filtering, its just in the Vertical plane and this is
plainly audible IF one moves up and down or lays the system on its
side. Reducing / eliminating that is the purpose of the configuration
above.



He is profoundly incorrect where he says “Danley claims manufacturers
are profiteering out of line arrays. What he neglects to mention is
that he bet his boat on a conventional design called the "unity horn".
It arrays like a conventional array and has the same problems. Danley
wants to prop up his investment in those speakers rather than admit he
was wrong.”



I have “bet my boat” on being able to find better ways to do things and
solve acoustic problems and that is why people buy our products and why
others license a few of the inventions. The absence of the comb
filtering in the arrangement above is immediately audible.



So far as “profiteering” do a “thought experiment”.



Acoustic infinity is a distance much much larger than the line length
where all line array’s revert to point source like spl drop-off with
distance, it is very much like the optical infinity one finds in light.

So imagine a line array set up outdoors and measured at say 1000 feet,
over the surface of a sphere. One has a map of loudness vs angle.

Now, “by magic” lets pretend you could buy a point source system, which
produced the same radiation pattern and intensity at 1000 feet.

Now, at 1000 feet both systems are “equal” but as you walk closer, the
point source increases in loudness faster than the line source. The
desired reduced fall off vs distance the line source exhibits is the
result of nearfield cancellation (incoherent addition due to the
different path lengths to various radiators) and so for a given SPL in
the audience, the line array as built commonly requires many more
sources, amps and so on than a point source of the same audience
loudness.

For the same reason, the line array at a given audience SPL radiates
more energy outside of the audience location than the point source too.
So if you live near an outdoor concert venue, you have a better chance
of hearing the concert too at a given audience SPL.



Just because the other speaker companies weren’t ever able to make
point sources that actually were (a coherent point source like ours)
that is not a reflection on how things work acoustically.

My solution to the distance vs fall off problem is to use a point
source who’s amplitude distribution vs angle is shaded to accommodate
the distance. This avoids the time problem the physical line array has
while retaining a near constant SPL vs distance within the pattern.
The first one of these is the GH-60 shown here, 3rd party measured
data should be done shortly.

www.danleysoundlabs .com/synergy_horn.asp?model=GH%2060



The comparison isn’t “bogus”, its acoustics and its what you actually measure.



Best,

Tom

As far as I can see, Tom makes 2 points:

1. He says the unity/synergy horn acts like a point source in arrays at least as well as a typical line array acts as a line source.

The synergy horn is a conical horn with focal point inside the cabinet. The top and bottom panels are parallel which means the vertical distance between centres is the entire cabinet height. There's no way two such cabinets one atop the other is behaving like a point source. In the horizontal, the cabinets are strongly trapezoidal, getting the sources to about 6 inches apart. But you have to close stack the boxes to acheive that giving a very wide splay angle meaning 3 cabs is about 180 degrees. Smaller splay angle forces apart the virtual sources. The case for a point source has yet to be made.

Most conventional line arrays by respected companies achieve a HF source separation no bigger than the compression drivers themselves in the vertical direction and of course there's no spacing issue in the horizontal.

I'll just mention that these companies' measurementsconfirm the absence of comb filtering as expected from the physics. If Tom is calling them liars, he's unfortunately outnumbered.

It's simply easier to make a coherant source when you reduce the problem to one dimension instead of two. You can occupy that one dimension with virtually solid compression drivers and still have space for your other drivers to handle lower frequencies. The equivilant in 2 dimensions is a 2-D grid of compression drivers (say on a hexagonal pattern) all driving horns that merge. But where will you put thecone drivers for low mid? There's nowhere you can put them that doesn't obstruct the HF or appear to originate from a significantly different point in space. Synergy is a compromise that makes space by separating the compression drivers. It's an OK compromise if the 2-D array is what you want to do, but the line array is the easier approach.

2. He says the 3dB/doubling of distance rolloff rate in line arrays means they're quieter in the coverage area and hence you need more boxes.

This is very dubious territory. First of all, if you configure a squarish 2-D array to have very wide horizontal coverage and very narrow vertical coverage, you'll get the same rolloff rate over a certain distance range. The idea that 3dB/doubling isa line array thing is one of the many misconceptions about line arrays. You always get behaviour of that kind when the horizontal and verticalfocal points differ.

Secondly, in a typical 2-D array, with substantial curvature in the horizontal, you're*never* even close to an equal distance to all the sources. Not even at infinity.SoTom's assumptions about efficiency of line arrays wouldcast doubt on the efficiency of 2-D arrays too.

In reality, energy tends to be preserved. If the drivers have the same electrical->acoustic power efficiencythen the only factor affecting loudness at the listener is directivity. Line array directivity is a great match for real-world requirements - the 3dB/doubling actually *helps* by balancing out the SPL as does the ability to bend the line at the bottom.

I must concede, in the interests of honesty, that the low frequencyrangeof line arrays suffer a potential efficiency disadvantage compared to 2-D arrays because the narrow line arrangement will result in reduced air loading. But this is easily fixed (just widen the source at frequencies below about 200-300Hz) and anyway we started off talking about small line arrays that would presumably be compared to small conventional arrays- both of which would tend to see a similar airload at low frequencies).

On the other hand, amplitude shading could be said to be a criminal waste of amplifier and loudspeaker power. Unless Tom is selling cost-reduced low power versions of the Synergy horn so customers can recover some of the cost of running a 1600 watt speaker at say 400 watts. And I assume he recommends lower power amps? If not, I not only have to buy/hire the big amps for all cabinets, but I'll need the corresponding big power feed to comply with regs. Ack!

Finally, on the question of noise pollution, I'm sure Tom knows that line arrays degenerate to the usual 6dB/doubling at a distance that gets greater as frequencies go up (because cos(theta) is a first-order approximation to 1.0) and that the air kills off the high stuff over long distances anyway.

He should also know that the biggest problem with noise pollution is reflection off temperature gradients in the atmosphere. This is obviously worse the more energy you launch upwards, and a line array will reject upward radiation better because it is larger in the vertical dimension. Thismay have been a factor in the Glastonbury 2007 fiasco.

PS

Tom, your paraline element is very cool indeed. Compact, flexible and easy to build.
Edited by: jsg

Hi, just acting as a medium here:

/db

Hi Jsg



It is hard to figure how you distilled what I said into what you say I said.



Stacking Synergy horns in the plane where they are not acoustically “array able” does end up producing self interference.

On the other hand one can also use them appropriately for the job in
the array able plane where they don’t interfere and cabinets like the
SH-25 are array able in both planes.

Curiously we have one customer who puts them on top of his large Nexo line array for “far throw.

For the SH-25 a four wide results in about 100 degrees of horizontal coverage.



Jsg said;

“I'll just mention that these companies' measurements confirm the
absence of comb filtering as expected from the physics. If Tom is
calling them liars, he's unfortunately outnumbered.”



That is fine if you haven’t taken a Synaudcon class, studied acoustics or actually measured many of them in detail yourself.

I have not seen any high-resolution measurements for commercial line
arrays, just “pretty” color displays, which can’t show the unpleasant
details one see’s with a TEF machine..

Also, it is not out of unfamiliarity I say what I do about them.

I have built many line source drivers as well as line source speaker systems.

Consider the “virtual array” line source patent here, which precedes
even the Vdosc patent. I have been aware of how they work
acoustically for some time.



www.google.com/patents ?q=Thomas+Danley&btnG=Search+Patents



Jsg said;

“It's simply easier to make a coherant source when you reduce the
problem to one dimension instead of two. You can occupy that one
dimension with virtually solid compression drivers and still have space
for your other drivers to handle lower frequencies. The equivilant in 2
dimensions is a 2-D grid of compression drivers (say on a hexagonal
pattern) all driving horns that merge. But where will you put the cone
drivers for low mid?”



Again, how the sources sum is not based on how it looks or mfr’s claims
but rather the acoustic spacing, “Coherent” means something specific,
the sources need to be less than about ¼ wl apart, just like with
woofers.

A 2 d grid of compression drivers takes you back to a source with
self-interference and is not coherent and so like a line array also has
a reduced change in SPL vs distance while in the interference zone..

RE point #2







“On the other hand, amplitude shading could be said to be a criminal
waste of amplifier and loudspeaker power. Unless Tom is selling
cost-reduced low power versions of the Synergy horn so customers can
recover some of the cost of running a 1600 watt speaker at say 400
watts. And I assume he recommends lower power amps? If not, I not only
have to buy/hire the big amps for all cabinets, but I'll need the
corresponding big power feed to comply with regs. Ack!”



I don’t think you have a clue about what the Shaded Amplitude approach is.



"Finally, on the question of noise pollution, I'm sure Tom knows that
line arrays degenerate to the usual 6dB/doubling at a distance that
gets greater as frequencies go up (because cos(theta) is a first-order
approximation to 1.0) and that the air kills off the high stuff over
long distances anyway."



Well I do agree that a line source reverts to point source fall off of
SPL when you approach acoustic infinity, which is acoustic fact, which
results from the distances to all sources approaching equality.. The
line array becomes a “point source” at that distance (aspect ratio). As
is known in acoustics, a line source can only be accurately measured in
two places, acoustic infinity and at zero distance. Everywhere else,
the response you get is a function of distance as a result of self
cancellation.



My point in the thought experiment was that if one configured a real
acoustic point source with the same SPL at infinity but without the
“line source” effect from near field self-cancellation, the SPL would
continue to increase 6 dB each time you halved the distance to the
source.

The flip side is that for a given acoustic intensity (SPL) in the
audience who is much closer than acoustic infintiy, a real point source
produces less SPL at infinity and requires fewer sources with less
power.

This is how we are able to sell speakers for large installations when the choice was made based on side by side comparisons.



The line source has a slower increase of SPL because of self
cancellation in the near field, this is why when you are less than
about ½ line length away, the SPL stops increasing altogether as you
move closer..

I know marketing has “taught” people how the line source “works”, its just that physics and marketing don’t agree here.

If you have any doubt what so ever, get a large ribbon speaker, a
source, which is homogeneous, top to bottom and carefully measure it.

Be skeptical here, draw conclusions from acoustic theory and measurements not marketing or popularity .

Best,

Tom Danley

Tom seems to believe interference is an issue with line arrays, where the sources are less then 6 inches apart and individual source elements radiate withless than10 degree vertical beam width, but not with a 2-D array where elements are more like 12-18 inches apart with a 40-60 degree beamwidth. The case for this upside-down view of things has yet to be made.

Tom doesn't say why he thinks I don't understand Amplitude Shading. Perhaps the confusion arose because I saw the SH-50 ratedat 1600 watts on Tom's website. Upon opening the PDF data sheet it's actually an 800 watt cabinet.

Tom is really determined to make the 3dB/doubling effectseem like a bad thing, but he ignores my comments about HF absorbtion in air and reflection off the thermal gradient. Does his thought experiement stand up to years of experience at the Glasonbury main stage?

As part of his insistence that interference is only an issue for line arrays, he suggests that the lower SPL close-up is a result of interference. At these distances, the beam-width is wider relative to a point source - so the acoustic power is the same.However, Ican see how talk of losing SPL due to interferencemight "put the frighteners" onpotential customers.

Tom's claim that a line array reverts to constant SPL below half the line length is wrong. It stays at 3dB per doubling until the half-wavelength matches the source width for each frequency, thensmoothly dropsto 0dB. Tom may be thinking of a 2-dimensional surface source, which would behave as he described.

Finally, there are too many accusations of incompetance levied at myself and the industry in general. It's not good enough to ignore points, misread points, and respond to points with substanceless arguments.
Edited by: jsg

If one is going to be pedantic enough to claim that a line array can only be measured at zero distance and infinity, one should be consistent. No conventional loudspeaker behaves as a point source. A point source is small compared with the wavelength being produced and radiates omni directionally. The only real loudspeakers that come close to being a point source are single small sub-woofers.

So imagine a line array set up outdoors and measured at say 1000 feet, over the surface of a sphere. One has a map of loudness vs angle. Now, “by magic” lets pretend you could buy a point source system, which produced the same radiation pattern and intensity at 1000 feet. Now, at 1000 feet both systems are “equal” but as you walk closer, the point source increases in loudness faster than the line source.

This is wrong. The reason the sound level of a point source drops off at a rate of 6dB per distance doubling is because it is radiating spherically. As you move away from the sound source, the total energy is spread over an increasing area. For a sphere the area quadruples as the radius doubles. The power density therefore decreases by a factor of 4 which corresponds to a 6dB reduction. With an ideal line source the radiation pattern is cylindrical. As the radius doubles so does the surface area, resulting in a halving of the power density; hence the 3dB rate of decrease

If you have two sound sources that have the same radiation pattern and match the levels at a given distance then the power density will increase or decrease at the same rate as you move either towards or away from the source.

Meanwhile back in the real world we will agree that although a line array is only an approximation of a true line source it exhibits some of the characteristics of the real thing, namely it radiates cylindrically. We will also agree that a point source loudspeaker is not a point source but it too exhibits some of the properties of the real thing. That is, it approximates a small segment of the radiation pattern of a point source and the radiation pattern is spherical. This now creates a problem with the thought experiment above. If you create an array that has the radiation characteristics of a line array it doesn't keep the characteristics of a point source. Just like trying to fit a square peg into a round hole you can't have a point source array that has the same radiation characteristics of a line array.

Hi,

A reply for John and an invitation.

Tom:


Jsg said;



“Tom seems to believe interference is an issue with line arrays, where
the sources are less then 6 inches apart and individual source elements
radiate with less than 10 degree vertical beam width, but not with a
2-D array where elements are more like 12-18 inches apart with a 40-60
degree beamwidth. The case for this upside-down view of things has yet
to be made.”



Maybe there is a language issue here, I will try again.

What governs “IF” two sources add coherently is the acoustic distance
relative to the wavelength. For example, when two woofers are less than
¼ wl apart, they combine coherently, each feel the radiation pressure
of the other and the efficiency is increased

3 DB.

Try the applets on this page and think wavelength not inches or feet.



www.falstad.com/mathphysics .html





“Tom doesn't say why he thinks I don't understand Amplitude Shading.
Perhaps the confusion arose because I saw the SH-50 rated at 1600 watts
on Tom's website. Upon opening the PDF data sheet it's actually an 800
watt cabinet.”



The SH-50 is not an amplitude shaded cabinet, maybe that in addition to
the fact there is no explanation for how it works posted up yet is part
of the confusion.



Power rating and loudness is to some degree a game in Pro-sound, to
reduce that marketing exaggeration problem, we have a third party Lab
measure our cabinets.

Here, the 800 W “Rating” is for the power level where the frequency
response has changed 3dB from the 1 Watt response shape, a very
conservative method..

The signal used for that rating has a 6 dB peak to average ratio so the actual peaks involved were 4X 800W or 3200W.



“Tom is really determined to make the 3dB/doubling effect seem like a
bad thing, but he ignores my comments about HF absorbtion in air and
reflection off the thermal gradient. Does his thought experiement stand
up to years of experience at the Glasonbury main stage?”



No, actually that reduced fall off is the main advantage the line array
offers, in the process it adds several other acoustic problems however
and these are not marketed or mentioned..

The shaded amplitude horn I mentioned solves that issue without the
self interference by “aiming” much less energy at the front row than
the back row.

Yes, I am familiar with atmospheric absorption and thermal gradients,
those are “air” effects independent of what kind of speaker is used..
Also, while I wasn’t at Glasonbury, I am pretty sure that isn’t the
first or only time a large concert was ever held outdoors.





“As part of his insistence that interference is only an issue for line
arrays, he suggests that the lower SPL close-up is a result of
interference. At these distances, the beam-width is wider relative to a
point source - so the acoustic power is the same. However, I can see
how talk of losing SPL due to interference might "put the frighteners"
on potential customers.



Actually given the popularity of line arrays most of our customers are
skeptical about a point source initially but also, most of our
customers do a side by side comparison “to see / hear” before buying.

It is what they hear and not the marketing argument that swings most over.

Why would say Imax choose our boxes over everything else available for
the refurbishment of the large Navy Pier Theater in Chicago, re-opened
last month?



“Tom's claim that a line array reverts to constant SPL below half the
line length is wrong. It stays at 3dB per doubling until the
half-wavelength matches the source width for each frequency, then
smoothly drops to 0dB. Tom may be thinking of a 2-dimensional surface
source, which would behave as he described.”



Actually, when you measure a real homogeneous line source one finds
that there are no “knee’s” that the slopes change gradually from 6 dB
to 3 dB to zero dB per doubling, at least on all of them I have
measured.



“Finally, there are too many accusations of incompetance levied at
myself and the industry in general. It's not good enough to ignore
points, misread points, and respond to points with substanceless
arguments.”



Well I missed those posts I guess and perhaps given our respective
jobs, we have a very different view of acoustics and marketing both.

If your going to this, say Hi, maybe we can talk further;

www.aes.org/events/125/ livesoundseminars/session.cfm?code=L2



Best,



Tom Danley

Tom Danley wrote: Well I missed those posts I guess and perhaps given our respective jobs, we have a very different view of acoustics and marketing both.
If your going to this, say Hi, maybe we can talk further;
www.aes.org/events/125/livesoundseminars/session.cfm?code=L2

I'd love to come, but I can't justify flying to Frisco for one convention. I notice you'll be accompanied by at least one of the worlds best line array designers - perhaps you'll be more willing to believe them...

PS I know interference depends on wavelength, but we're talking about sources that play the same range of frequencies, about 100-20K, so the wavelengths are in the same range (3.4m to 1.7cm).

jsg, I have sent that to Tom.



Steve, here:




Hi Steve





“f one is going to be pedantic enough to claim that a line array can
only be measured at zero distance and infinity, one should be
consistent. No conventional loudspeaker behaves as a point source. A
point source is small compared with the wavelength being produced and
radiates omni directionally. The only real loudspeakers that come close
to being a point source are single small sub-woofers.”





It is true that the ideal line source only radiates into one plane, a
plane wave in that axis, it is the mechanism that causes it that is the
key.


At any point “out front” the pressure one measures is a summation of
all the radiated pressures and phases arriving at that point in space.


In the region where one has the “line effect” the summation is from
many different path lengths, some of which add constructively and
others destructively, the latter lowers the pressure compared to fully
constructive summation.


In the near field, the pressure is less than one would expect from
sources of the same total acoustic power but arranged not to have
destructive interference, originating at one point.





As you move closer to acoustic infinity, the line array reverts to
spherical radiation on axis, a point source, because all the path
lengths to each source become closer to being identical and there is no
longer any cancellation and all the paths add constructively at
infinity.


For that reason, a measurement that doesn’t include this cancellation
must be done at acoustic infinity (where all the paths are acoustically
the same) or at “zero” where the far end of the line is very very far
down from the close region. If you try to measure a ribbon speaker you
will find the result is highly variable with distance unless your very
close or very far.


With a TEF machine looking at Energy vs Time, one can see the entire
arrival corresponding to the closest portion first and farthest portion
last, all spread out in time.





The explanation of this line source measurement quandary is an a good
Acoustic Society of America paper I have around here somewhere.





What is a point source?





A point source radiates spherically, into both X and Y planes from the
same origin point, an acoustically small woofer is a good example.


In that case, the source is small enough not to have any directivity on its own and nature takes care of the spherical pattern.


Also though, a conical horn driven by an acoustically small source can
be a point source as well, it radiates a spherical segment or patch
instead, just like the half sphere of the woofer on the ground or
partial sphere of the woofer by a wall or in a corner..


The key is in both planes the origin is the same place defined by the radius and curvature of the radiated wave front.





It is true that a multiway speaker is generally not a true point source
but an array of point sources that interfere with each other and a
typical pile of concert boxes much more so. I don't know of any big
name concert array boxes where measurements for two or more "arrayed"
were shown, its just not pretty.





That driver to driver or box to box interference is revealed in a polar
of spherical measurement of the speaker which shows lobes and or other
self interference anomalies.


It is that same “self interference” which is mostly limited to the
vertical plane in the popular line arrays, that plane is not the one
where it is easy to walk back and forth and hear it but if you lay a
line array down, then it is audible something like “old days” concert
arrays.


The advantage the Paraline has in the VTC array is that it makes a
continuous source which has a 5 degree arc of curvature to it so the
source to source problem is greatly reduced. The driver to driver
mounting and spacing prevents driver to driver interference.





A point source can also has astigmatic distortion too, that is
exhibited by the radiation in one plane having a different effective
origin than the other.


A diffraction horn is one example of this done deliberately, one origin
behind the other but so too is a finite length line array, its origin
in the vertical plane is FAR behind (instead of at infinity for a
theory line array) the origin the Horizontal plane.





On the other hand, it is possible to make horns which are point
sources, it is possible to make a multi way speaker without crossover
related lobes or interference or even crossover phase shift too.


Down load the CLF file for the SH-50 and viewer and look at the
spherical plot for the speaker. One can move the viewing angle around
as well as changing the Frequency.


www.danleysoundlabs .com/technical%20downloads.html





While very few other companies provide this level of detail, it is only possible because these approach an ideal source.





Also, what no one else does (that I know of) is give independently
measured data for this stuff and predicted and measured results for
more than one cabinet too.


Go down to page 7 and 8 here


www.danleysoundlabs .com/pdf/danley_tapped.pdf





Now, so far as the thought experiment, making a point source with the
same radiation pattern would be difficult in the real world, it would
require a fantastically large and deep horn and producing an asymmetric
radiation pattern is more problematic.


Considering the devices directivity Q is maybe a better object.





The key point is though that as long as one is within the pattern
control range of the conical (CD) horn, the sound pressure always falls
at the inverse square as you move away or increases 6 dB per doubling
as you move closer.





Where as with the line array, even a very long ribbon speaker is
treated as many small slices, each a point source, each summed
according to distance.





Consider that in one case you have a 100 acoustic Watt point source and
in the other a 50 foot tall line source which radiates 100 Acoustic
watts.


Both have a directivity Q of 30 for frequency X.


Both will produce the same SPL at Frequency X on axis at a very large distance as they have the same power and Q.


Now, what happens as you walk up to each?





Best,


Tom



PS




Something to add to the post,





www.meyersound.com/ support/papers/line_array_theory.htm

Tom Danley wrote: Consider that in one case you have a 100 acoustic Watt point source and in the other a 50 foot tall line source which radiates 100 Acoustic watts.
Both have a directivity Q of 30 for frequency X.
Both will produce the same SPL at Frequency X on axis at a very large distance as they have the same power and Q.
Now, what happens as you walk up to each?

Tom, I'm sure both Steve and I have addressed this. The beam cross-section falls more slowly for the line array than for the point source. Energy is preserved and there's no loss to interferance as you suggest.

I really want to encourage you to think in terms of energy conservation. It's impossible for any source to radiate more power at a larger distance than it does at a shorter distance. The fact that interferance -a phasor/amplitude phenomenon - and energy conservation are both true even when they appear to disagree is one of the fascinatingenigmas ofphysics.

Here's another thought experiment. Compare (a) a point source such as yours, radiating 100 watts spherically, with (b) a solid sphere, diameter 1 metre,on which are a number of point sources, say 3mm apart (less than 1/4 wavelength at 20KHz).

The sources on the sphere could radiatespherically except that being on the surface of the sphere they cannot radiate into the sphere (the sphere reflects the incoming wave).

Now you'll agree that the sources are coherant and will radiate a spherical wave. It has a single point of origin, and so resembles a point source.

If we assume the total output of all the sources is 100 wattsthen the question is, how loud at near, middle and far distances compared to the point source?

Well,we've produced 100 watts of acoustic power and by symmetry it must emerge as a spherical wave. It must therefore sound the same as a single point source at all distances.

But unlike the single point source, we have interferance. All the sources on the half of the sphere you can see are radiating towards you, and the distances vary by 50cm from nearest to farthest (or just under if you're close up). But this system *must* achieve the same efficiency as the point source, *in spite* of the cancellation. Conservation of energy demands it.

Here's another thought experiment, now at a particular frequency, say 1KHz:

Taking two point sources close together, less than 1/4 wave, makes them couple. You expect to see a 6dB (ish) increase in output compared to just one source. But that'sfour timesthe power! How come? Well, as I'm sure you know, each is seeing twice the radiation impedance, and if we assume each source fixes its volume velocity output. So the impedance match got better and the sources got more efficient.

In practice, speakers are not perfect volume velocity sources and so you get less than 6dB. Furthermore, if the sources were already close 100% efficient, then we would predict nearly 200% for a pair, which is physically impossible. Therefore, sources close to 100% efficient cannot resemble the perfect volume velocity sources we so often assume. This is important!

OK, so now lets try changing the experiment by moving the sources apart. At say 10 metres seperation we'll get a nice rich interferance pattern. The output from each source will have attenuated somewhat by the time it reaches the other, so they are largely independent. Each sees the same air load impedance they would see if there were no other source, so their volume velocity output is not reduced due to there being two sources.

The interference pattern is calculated using simple geometry and as I mentioned it's about amplitude. The amplitude at a ridge (say, half way between the sources, or on an equilateral triangle or at infinity on the perpendicular - you choose) is the sum of the amplitudes of the outputs of each source. But lo, that's 6dB or four times the power again. We cannot have more than two times the power of a single source since we haven't changed the loading at the sources (and this time, they could be close to 100% efficient anyway).

Of course, the explaination for this is that at the nulls, we get approaching -infinity dB or zero power. In fact, if you place a sphere around both sources, and add up the power levels corresponding to the amplitudes on the sphere, you'll find the total is exactly as expected from the two sources. So interferance actually gives you gain in some directions which are then cancelled by attenuation in other directions.

The point is, the presence of interferance isn't necessarily a bad thing. Maybe the word diffraction should be used instead - it's the more concise term and lacks the FUD-like overtones of the other word.

Considering diffraction in cojunction with preservation of energy leads us to see it not as a method of wasting or losing power, but merely steering a constant amount of power through a certain spacial geometry.

That line arrays have spherical(ish) wavefronts, and the -3dB/doubling function, and the astigmatism with its differing horizontal and vertical origins doesn't change any of the above. It's just another example of the same therory and the same preservation of power is obtained.

My feeling, and the basis for my original comment about smooth and gapless sources, is that the astigmatism doesn't matter. There's nothing scary about it. Conversely, there's nothing special about a point source that makes it better than an astigmatic but coherant wave front.

Of course we do care about incoherancy due to gaps in the source, causing a messy diffraction pattern at the listener, but a line array lets you put the HF units close together and it lets you use narrow dispersion sources, such as the 10 degree flares commonly used or indeed your own paraline eleemnt (which I think is great, by the way). This narrow directivity makes the sources audible only close to the perpendicular where the path length differences are a small fraction of the physical spacing. So a spacing of a few inches can result in a much smaller path length variation.

By insisting on attacking the problem of coherance in a 2D array, which is the harder problem, you're just making a rod for your own back. Meanwhile companies like l'Acoustics and Martin audio are making very very good sounding line arrays the easy way and then going home to f**k the prom queen as Sean Connery might say.