Square Pegs

As described in the patents, the Paraline appears to be a way to generate a plane wavefront for applications requiring a "line source", rather than as an impedance matching device. It's what I would call a waveguide rather than a horn. Then I look at Patrick's Proof Of Concept, and I suspect it works differently. I assume his model has a radially expanding first part fed by the drivers, a circular (rather than eye shaped) slot, and a "circular" (sort of square) exit. I keep visualising it as a diverging conical horn capped with a converging conical horn, but this ignores the "two dimensional" nature.

Looking at the patent, Fig. 14, imagine a second "item 30" connected in place of "item 32".That's what Patrick's model looks like to me. I must be missing something basic. (I know it's not my marbles, every morning I look in my toybox and there they are.)
Help...

Edit:
I wonder... if you built a device like Patrick's, and used multiple HF drivers clustered closely together in the centre, would the output at the exit combine into a virtual point source? Would this be the basis for a "layered combiner"?

Don - It would be interesting to know how Patrick did his proof of concept. For the paraline to approximate a conical horn, the wavefront has to keep expanding radially even through the bends. The eye model seems to do this, and I assume that the area of the exit slot is again the next progression up in size from the surface area of the wavefront while still in the slot immediately prior to the exit. The little plug in the exit also seems to me to have a role to play, and of course that is missing from Patrick's model.

Ah, I've just been back through the thread and noticed that Patrick says that he was 'stacking a paraline on a paraline'. And he describes the phase plug in the Danley paraline as being to avoid phase issues between the different edges of the slit. I'm not sure I follow that given that the point of the design was to ensure that all parts of the wavefront hit the exit at the same time (or to allo wfor timing differences deliberately to control the wavefront shape).
 
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Don - It would be interesting to know how Patrick did his proof of concept. For the paraline to approximate a conical horn, the wavefront has to keep expanding radially even through the bends. The eye model seems to do this, and I assume that the area of the exit slot is again the next progression up in size from the surface area of the wavefront while still in the slot immediately prior to the exit. The little plug in the exit also seems to me to have a role to play, and of course that is missing from Patrick's model.

Ah, I've just been back through the thread and noticed that Patrick says that he was 'stacking a paraline on a paraline'. And he describes the phase plug in the Danley paraline as being to avoid phase issues between the different edges of the slit. I'm not sure I follow that given that the point of the design was to ensure that all parts of the wavefront hit the exit at the same time (or to allo wfor timing differences deliberately to control the wavefront shape).

In hindsight, I think there are two problems with a square-exit Paraline:

  • A square exit is not ideal, unless the square is very small.

    There are five layers in a Paraline. It's like a sandwich and it goes like this:
    layer 1 - the bottom. Any thickness will do.
    layer 2 - This has the throat of the horn, in the center. Sound radiates radially in here.
    layer 3 - the middle layer 'slices' the horn in half. Due to this, the shape of the middle layer is critical. In my square exit Paraline, I had a middle layer that includes a measure of error, but I basically ignored it because it was close enough. Total proof of concept really.
    layer 4 - this layer is the second half of the conical horn. It connects to the mouth of the horn.
    layer 5 - this is the mouth of the horn. One problem with a square mouth is that high frequency energy from one edge can interfere with high frequency energy from the other edge. For instance, my square Paraline has a mouth of 2.25" square. So high frequency energy could see comb filtering as low as 1500hz. If you download the measurements of the Paraline from VTC's website, you'll notice some comb filtering, but it's way way higher in frequency than that, likely due to the phase plug at the entrance and the exit.
  • Layer 3 of my square Paraline could use a better shape. On page 1 'Nissep' posted a way to make the shape better, and I recommend trying it yourself if you'd like to build one of these. It works. Here's his comment: http://www.diyaudio.com/forums/multi-way/217298-square-pegs.html#post3117601

The layered combiner in the Jericho horns appears to have a square exit; but I have a hunch that it's not designed to run full-range, like the ones that I'm building are.

 
I really need to get some work done today - so I'll keep this brief.

But last night I stumbled across the solution to a problem which has been vexing me for literally two decades!

Very exciting stuff.

RichardClark-1986GrandNational-4.jpg

The thing that got me into horns, way back in the 90s, was an interview with Richard Clark in Car Audio and Electronics. In that article, Clark talked about how the ideal loudspeaker is a point source that covers 20hz to 20khz. While Clark's car was not perfect, he *did* manage to squeeze about 300hz to 20khz out of a pair of horns with Altec Lansing drivers.

My whole journey down the rabbit hole started back then, and I'm not exaggerating when I say that I've been searching 20 years for something that will get close to that goal of 20hz to 20khz off of one driver.


As I see it, the Synergy horns are about as close as we can get right now. While there are nine drivers in the horn, it 'looks' like one driver due to the way the wavefront expands in the horn.

Second best to a Synergy horn is a plain ol' fullrange, but the problem with a fullrange is that it can't do 20hz to 20khz with any real authority. (IE it don't get loud.)

Coaxials have intrigued me also, but I *really* like it loud, and I've never heard a coaxial tweeter that can do real SPL.

Last night I came up with something new:

photo%2520%25285%2529.JPG

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What you're looking at is a Paraline, but with a 'Smiley' shaped exit. I actually invented this to solve a completely different problem, and then it occured to me that the 'Smiley' exit allows you to stack the woofer and the tweeter face to face!

This puts the woofer and the tweeter within one quarter wavelength at the crossover frequency, a level of coupling that's nearly impossible to do without buying a coaxial.

If you're into Unity or Synergy horns, this solves a whole pile o' problems for those of us that want Synergy horns in the home or car:

  • The Unity and Synergy horns use about nine drivers to get the job done. That's great if you have the space for a speaker that's the size of refrigerator, but I'm really sick of big boxes. The 'Smiley' Paraline has just two drivers.
  • The on-axis SPL of a horn is related to it's directivity index. To put it simply, narrow directivity horns are louder on axis than wide directivity horns. And the Paraline is a VERY narrow directivity horn. Therefore, my 'Smiley' Paraline gets exceptionally loud.
  • Clamping the drivers together makes a surprising reduction in distortion.
  • The 'Smiley' Paraline enables the use of a lot more midranges. For instance, I think it should be possible to go up to an 8" midrange, or perhaps even a 10" midrange. This wasn't possible in a Unity or Synergy horn, as the use of large midranges would drive the xover point down to 500hz or so, due to the very specific spacing requirements of the crossover filters. (The VTC Paraline gets away with the use of 8" and 10" drivers by using a digital delay.)
  • If you peruse the main Unity horn thread on this forum, you'll see that people have literally spent *years* trying to find a suitable midrange that will meet up with the tweeter. Basically there are only a handful of drivers that will play high enough. If you don't get everything perfect, you get a gap between the midrange and the tweeter, right in a frequency band where problems are very noticeable - about 1500hz. My 'smiley' shaped Paraline gets the midrange and the tweeter very very very close together. I believe that part of the reason that there is a gap in a conventional Unity horn is due to the spacing from side-to-side of the midranges. The 'Smiley' Paraline solves that.

The last advantage of the 'Smiley' Paraline is the whole reason I built it in the first place. You can bend the wavefront.

marten-bending-ply.jpg

In the Danley Paraline that's used in the Genesis horn, Danley bends the wavefront via a delay inside of the Paraline. But it occurred to me that you could also bend the wavefront by bending the whole device! (Picture how plywood is bent like the pic above.)

So my original goal with bending the Paraline was simply to get a curved wavefront, but then it occurred to me that I could stack the drivers.

An externally hosted image should be here but it was not working when we last tested it.

My Smiley Paraline will be mated with a conical horn, a la the Image Dynamics HLCDs.

Smiley - YouTube

Here's a video of the Smiley Paraline. It's pretty rough - there's just one cap on the compression driver. But you get the general idea - full range sound off of a 15cm long (566hz) conical horn folded into a Paraline.

 
Patrick - thanks for sharing that. Interesting! How did you make sure that the wave fronts from the tweeter and midrange both hit the smiley slot at the same time, or is the delay between them part of your desire to bend the wavefront (although I'd assumed that that was what the smile was for)? I've thought of a couple of other ways to do the same thing - I'll try to draw them up.
 
I think I see what Patrick's done - the smiley mouth isn't to make the wavefront curved, it's so that he can mount a second driver where the slot would have otherwise been. Remember the "piece of string" video? Patrick has pulled the drivers "off centre". This would result in unequal path lengths in the horn, but he has also pulled the slot "off centre" to equalise the path lengths again. Imagine the horn with a lot of strings tied between the driver opening and the corresponding parts of the slot - if you pull the driver one way, the slot must move the other way to keep all the strings the same length.

(I assume that the tweeter extends through the "top" plate so that the sound from the driver enters the horn in the "rear" chamber directly opposite the midrange.)
 
I think I see what Patrick's done - the smiley mouth isn't to make the wavefront curved, it's so that he can mount a second driver where the slot would have otherwise been. Remember the "piece of string" video? Patrick has pulled the drivers "off centre". This would result in unequal path lengths in the horn, but he has also pulled the slot "off centre" to equalise the path lengths again. Imagine the horn with a lot of strings tied between the driver opening and the corresponding parts of the slot - if you pull the driver one way, the slot must move the other way to keep all the strings the same length.

(I assume that the tweeter extends through the "top" plate so that the sound from the driver enters the horn in the "rear" chamber directly opposite the midrange.)

That's correct.

Here's what you do:

1. Take the eye-shaped configuration that's in the Paraline patent
2. Move the ENTRANCE off center by one inch
3. Move the EXIT off center by one inch
4. As long as the the change is balanced, path lengths stay equal. For instance, move the horn exit to the left by 1" and the horn entrance to the right by 1". Path length is same.
5. As Don noted, the tweeter fires THROUGH the center plate.

paraline.jpg

The eye shape ends up looking a little droopy, bcuz the widest point of the Paraline (aka A1) moves along with the entrance.
 
To anyone trying this: Remember to keep the space at the junction of the driver(s) with the horn as small as possible. If the space is significantly larger than the width of the eye cavity, it will form a throat chamber which will act as a low pass filter. The ideal configuration for a tweeter/midrange pair would be a "naked" dome tweeter / compression driver with the dome protruding into the cavity formed by the cone of the midrange driver.

I do worry a little about possible interaction between the two drivers placed so close together, with the horn load increasing the interaction.
 
Ah! My response was lost. Never mind. Don/Patrick - thanks. The offset wasn't troubling me, but you've cleared up that the tweeter was protruding through into the back layer. I should have realised.

Patrick - out of interest, this is for your car?

NB: I'm more interested in using the paraline as a way to make horns shorter (in order to use compression drivers not cones). I live in Hong Kong and don't have much space in my sitting room (and my wife won't allow the speakers too far into the room anyway ...) I actually took a day off work today to go to the HK Hifi show. So, many of the rooms had 'big' speakers out in the middle of the rooms - it made you wonder whether they've actually been to any of the typical listening spaces that we have to live in here. I can't say that there was a huge amount that I was interested in, although I did buy quite a few records and a small tube amp ...
 
I think the correct descriptor for this device is simple- it's a method for making phaseplugs with various wavefronts.

Pretty slick stuff but no getting around the challenges of that 180 degree turn in the real world. It could be mitigated by softening the transition and using some damping a la geddes, but then you're getting into a more complex construction and deeper assembly. But 2" of depth added to allow this transition to happen in a smooth fashion may be a very worthwhile tradeoff for sound quality apps.
 
I think the correct descriptor for this device is simple- it's a method for making phaseplugs with various wavefronts.

Pretty slick stuff but no getting around the challenges of that 180 degree turn in the real world. It could be mitigated by softening the transition and using some damping a la geddes, but then you're getting into a more complex construction and deeper assembly. But 2" of depth added to allow this transition to happen in a smooth fashion may be a very worthwhile tradeoff for sound quality apps.

IMHO, you are half right. This *is* a phaseplug. It's a device designed to equalize the pathlengths of wavefront.

Where we disagree is whether the bends are a problem. IMHO, high order modes, diffraction, and reflections cannot form below 18khz. (assuming a maximum height of 1/4".)

The wavefronts simply cannot form; the dimensions will not allow it. For instance, if you took a block of aluminum, then drilled a hole through the aluminum that was one micron wide, you would not be able to see through the aluminum. The hole is simply too small. You wouldn't be able to see through that hole until it's diameter was sufficiently large to allow light to pass.

That's what's going on in the Paraline. There is air in the Paraline, but there is not sound, at least not below 18khz. The sound does not form until the duct is large enough to allow it to form. Until the duct is large enough, it's just a bunch of air molecules squirting through the device with no waves formed.


As for Geddes, he wrote a patent on optimum phase plugs. Yet on this very forum he's stated that he did not pursue it because the differences were not audible. Perhaps there's a connection?

(Note to self - I should probably be careful about misquoting Geddes, he could make me look really dumb in a hurry, since he knows way more about this stuff than I do :) )

Here's Geddes patent on optimum phase plugs:

Patent US20040156519 - Phase plug with optimum aperture shapes - Google Patents
 
To anyone trying this: Remember to keep the space at the junction of the driver(s) with the horn as small as possible. If the space is significantly larger than the width of the eye cavity, it will form a throat chamber which will act as a low pass filter. The ideal configuration for a tweeter/midrange pair would be a "naked" dome tweeter / compression driver with the dome protruding into the cavity formed by the cone of the midrange driver.

I do worry a little about possible interaction between the two drivers placed so close together, with the horn load increasing the interaction.

Don, this is a good point.

photo%2520%25286%2529.JPG

Here's a measurement of two of the Goldwood cone tweeters in a Squaraline. (The Squaraline is the first one that I built, which has a video here: http://www.youtube.com/watch?v=z1ECVZ0LPOc&feature=plcp) The measurement is kinda crummy, but I've been too busy building Paralines to do proper measurements. This iPad program is about 80% as good as the results that I get from Arta, so it's better than nothing.

What we notice with the Goldwood tweeters are a few things:
  • The high frequency response of the Goldwood tweeters in a Paraline is almost more extended than on a flat baffle. If it wasn't for the peak at 4khz, I'll bet you could run the Squaraline to 10khz using cone tweeters. I believe that the peak at 4khz is due to geometry. I've found that you must have the tweeter centered in the Paraline to get flat response at high frequency. It's simply cannot be off-center.
  • As I understand it, the driver that we want for a Paraline is flat, to match with the surface of the line. If not flat, it should produce a flat wavefront at the driver exit, like a compression driver. Also, this is still a horn, and horns are impedance transformers. Therefore, we should watch out for drivers with a high VAS, as they'll need a larger air load. I'd imagine that if you used a driver with a large VAS, it would be peaky, just as it is in a horn. This doesn't necessarily mean that you need a driver with a large motor. But if it *doesn't* have a large motor, you probably want one with a light cone. It's a bit of a catch 22, because drivers with a large motor kinda defeat the purpose of a Paraline, which is it's incredibly shallow depth.

    At this point, arguably the best results in the midrange have been found with cone tweeters and with planar magnetics. (Goldwood GT-25 and BG Neo 8, respectively.) The best results at high frequency have been compression drivers. Admittedly, I've only tried one ribbon and no domes. So still lots of testing to be done.
 
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IMHO, you are half right. This *is* a phaseplug. It's a device designed to equalize the pathlengths of wavefront.

Where we disagree is whether the bends are a problem. IMHO, high order modes, diffraction, and reflections cannot form below 18khz. (assuming a maximum height of 1/4".)

The wavefronts simply cannot form; the dimensions will not allow it. For instance, if you took a block of aluminum, then drilled a hole through the aluminum that was one micron wide, you would not be able to see through the aluminum. The hole is simply too small. You wouldn't be able to see through that hole until it's diameter was sufficiently large to allow light to pass.

That's what's going on in the Paraline. There is air in the Paraline, but there is not sound, at least not below 18khz. The sound does not form until the duct is large enough to allow it to form. Until the duct is large enough, it's just a bunch of air molecules squirting through the device with no waves formed.


As for Geddes, he wrote a patent on optimum phase plugs. Yet on this very forum he's stated that he did not pursue it because the differences were not audible. Perhaps there's a connection?

(Note to self - I should probably be careful about misquoting Geddes, he could make me look really dumb in a hurry, since he knows way more about this stuff than I do :) )

Here's Geddes patent on optimum phase plugs:

Patent US20040156519 - Phase plug with optimum aperture shapes - Google Patents


Patrick - sorry, I'm slightly confused by some of the above. Given that sound is just a series of compression/rarefactions in air and this must be happening inside the paraline here because otherwise we wouldn't get any sound out, there must be sound 'inside' the paraline? What I thought Tom Danley had said was that if you kept the slit narrow then you didn't get waves bouncing off the parallel walls of the paraline, because there wasn't enough space for a wave below 18khz to form as between the walls. That doesn't mean a wave isn't formed in the direction of travel out along the radial path. However, the distance out to the first bend is more than a few mm, and so don't we get problems arising at that point with reflections back from the edge of the 'eye' back to the driver? But as I previously posted, maybe it's not enough to be a problem. Does anyone know where I might read some more on this please?

Thanks
 
... However, the distance out to the first bend is more than a few mm, and so don't we get problems arising at that point with reflections back from the edge of the 'eye' back to the driver? But as I previously posted, maybe it's not enough to be a problem. Does anyone know where I might read some more on this please?

Thanks

There is no reflection problem, because the width of the passage is much smaller than the wavelength of the sound. The sound "flows like a fluid", rather than bouncing off the walls. It's the same reason why you don't have reflections at the folds in a tapped horn within its designed operating bandwidth. Tom Danley has pointed this out in several posts. The best explanation I have seen is in his patent application - Fig 13 and its description.
Patent US20090323997 - Horn-loaded acoustic line source - Google Patents
 
Patrick - sorry, I'm slightly confused by some of the above. Given that sound is just a series of compression/rarefactions in air and this must be happening inside the paraline here because otherwise we wouldn't get any sound out, there must be sound 'inside' the paraline?

Thanks

There's no sound inside the Paraline, because the duct is too small for the soundwave to fit inside of it.

This applies to all speakers - horns, transmission lines, ribbons, domes, whatever.

What happens in this situation is that the waveform is formed when the duct is large enough for the wave to form.


Here's a hypothetical example:

Get a piece of PVC pipe that's a mile long and 2" in diameter. Now put a speaker on one end of the pipe and play a sound that's 10khz. If you put your ear on the other end of the pipe, it will sound like the sound is a mile away, because 10khz is just 1.35" in diameter. So 10khz fits in the pipe easily. You'll also notice that the sound is hollow, due to a mile's worth of reflections.

Now have that speaker play 100hz. The sound will seem to emanate from the mouth of the pipe. This is because 100hz is 135" long. So it can't fit in the pipe at all. When your speaker plays 100hz, all it's doing is pushing the air molecules through the pipe, like they're a liquid. YES, it's still 100hz, and it will be 100hz when it exits the pipe, but inside of the pipe it's just air being pumped at 100 cycles in a second... there is no wavefront and the wave does not exist until those air molecues exit the pipe, where they enter a duct that's big enough to allow the wave to form.


If you imagine sound as light it's easier to grok; make a hole big enough and the light will exit, but as long as the hole is too small for the light to exit, it won't.
 
There's no sound inside the Paraline, because the duct is too small for the soundwave to fit inside of it.

This applies to all speakers - horns, transmission lines, ribbons, domes, whatever.

What happens in this situation is that the waveform is formed when the duct is large enough for the wave to form.
Patrick,

There is sound inside of a Paraline or any horn, and the sound pressure varies inversely with the distance from the driver. Sound waves are made as soon as the diaphragm or cone moves.

For example, here are the dB (A scale) measurements of a conical horn crossed at 1250 Hz, using pink noise:
110 2 meters from mouth
115.2 1 meter
119.7 .5 meter (19.5 inches)
122.5 .25 meter (9.75 inches)
124.2 .125 meter (4.875 inches)
126.3 at horn mouth, 26 inches from driver throat screen
131.7 13 inches from screen
136.8 6.5 inches from screen
141.0 3.25 inches from screen
143.7 at screen (144+ dB SPL on impulse, flat)
149.1 at screen, xover output turned up to +11 (+6.5 dB over last test)

The pink noise had basically the same frequency response at each distance.
If you were to use a very small microphone in a Paraline you would find the same sort of inverse distance increase in level.


Have you compared your "Squarealine" output to the same speaker with no horn?

Other than a more narrow pattern at upper frequencies boosting on axis response, is the sensitivity increased broadband?

Art
 
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Patrick,

There is sound inside of a Paraline or any horn, and the sound pressure varies inversely with the distance from the driver. Sound waves are made as soon as the diaphragm or cone moves.

For example, here are the dB (A scale) measurements of a conical horn crossed at 1250 Hz, using pink noise:
110 2 meters from mouth
115.2 1 meter
119.7 .5 meter (19.5 inches)
122.5 .25 meter (9.75 inches)
124.2 .125 meter (4.875 inches)
126.3 at horn mouth, 26 inches from driver throat screen
131.7 13 inches from screen
136.8 6.5 inches from screen
141.0 3.25 inches from screen
143.7 at screen (144+ dB SPL on impulse, flat)
149.1 at screen, xover output turned up to +11 (+6.5 dB over last test)

The pink noise had basically the same frequency response at each distance.
If you were to use a very small microphone in a Paraline you would find the same sort of inverse distance increase in level.


Have you compared your "Squarealine" output to the same speaker with no horn?

Other than a more narrow pattern at upper frequencies boosting on axis response, is the sensitivity increased broadband?

Art

I wish I had time to make some illustrations of why I do not believe that a wavefront can form in the Paraline. (Well, a wave can form, but not below 18000hz.)

If anyone is interested in reading the stuff that's brought me to this hypothesis, please review these two posts. I know Art's reviewed the first one, because Art's project inspired my project, and the following post is a response from Tom to Art :)

ProSoundWeb Community - Index

"hen the wavelength is short enough (frequency high enough) the sound that went to the pointy end, bounces back and arrives out of phase with the driver pressure.
One finds (as you raise the frequency) that you eventually have a BIG cancellation notch when that “driver to dead end” distance is about 1/4 wl.
The two low pass filter effects strongly attenuate above band energy from the cone drivers and helps make the distortion especially low.
It was that notch, or pondering that notch that made me wonder about and then try what became the Tapped horn.
I thought what happens if I substitute a source of the opposite phase for that reflection? (a source which was present in the back side of the radiator), then they add instead of cancel. Some considerable fiddling in the computer eventually resulted in boxes that work better than similar sized normal bass horns using this new principal.

Anyway, up to now, the only function a phase plug has is to occupy an excess air volume that would have other wise made the acoustic “low pass filter” too low in frequency.

Once one is dealing with a radiator who’s dimensions are approaching the wavelength size, then the other function of a phase plug comes in handy.
The speed of sound governs how a pressure disturbance radiates away from its source.
If one has a radiator that is “large” acoustically and also has a single exit point, one finds that just like in the Synergy and Unity horns, one gets a deep cancellation notch when the difference in the two paths is 1 / 2 wl. The range of coherent summation is limited to the frequencies BELOW the region where cancellation begins.
This is like a pile of subwoofers, when the array is less than about 1/4 wl across, they all add together and feel “mutual radiation pressure” while a significantly larger spacing produces directivity and then lobes.

Here, a phase plug can be shaped so that the acoustic passages all have the same length or have a length appropriate to the desired exit wave front shape.
One big difference in the sound of compression drivers (IMO) after being eq’d flat is that many have a phase plug that produces a converging wavefront at the summation, while what one needs at the throat of a horn is a diverging wavefront. That “clash” can cause diffraction or interference, which produces Higher Order Modes that Earl Geddes describes.

So far as the Paraline as used in the VTC array and GH-60, this is an acoustic device which can be shaped to provide an exit wavefront that can be flat, a line source or diverge or converge, an astigmatic point source with positive or negative focal point..
It works by allowing the sound to expand radially between two plate that are too close together to support any reflected modes between them so only radial expansion takes place.

A correction slot who’s shape defines the exit wave front shape and who’s dimensions are small enough to allow the sound to bend around the corners, is placed in the radial path. The sound passes through the slot and what emerges on the other side is a wave that travels to the center from each side, bends around a corner and exist at a center slot having entered at a center hole at the rear. The VTC site had a nice graphic of the one they are using.

It probably sounds weird to suggest that you can bend sound without ill effect but you can when the acoustic dimensions are small enough. The difference as it is in the examples above is that keeping the difference in path lengths less than about 1/4 wl at the highest frequency of interest..
I used to work with 21KHz levitation sound sources and needed to place a microphone in the levitation furnace to monitor the source sound level.
Well, very very few things are “happy” at 1500 degrees C but I found that a Zirconium / Alumina tube with a 1/16 inch bore passed 20KHz sound out of the furnace to an external microphone with no problem.

Funny, the external microphone’s heatsink wasn’t large enough on the first one and the microphone melted.
Later fooling around (research) showed that a 3 foot long, 1/16 inch bore copper tube could be wound around a small coffee cup and not effect the sound passing to the microphone.

A constantly re-occurring theme in much of what I do is that many things depend on how large X is compared to the wavelength.
Anyway, I hope that makes some sense.
"


aaaand this one:

Plane Wave Tube Construction

"rho = density of air
c = speed of sound
d = diameter
Upper limit = 1,22 * c / d
lower imit = c / 4 / length of tube

Now let's talk about horns driven by compression drivers. One of the handy pieces of information that used to be included with compression drivers (but is not always now) is the plane wave tube response. A plane wave tube is a tube the same size as the exit of the driver (or smaller or larger and including an adaptor to have a smooth transition from the driver's throat to the size of the tube). There is absorbing material in the tube which is designed to provide a certain load to the driver - a load of rho * c * diameter of the tube, where rho is the density of air and c is the speed of sound. This is usually called a "rho c" load; rho * c is the specific impedance of air. This load is supposed to be constant at all frequencies and allow easy comparison of different drivers, but in reality the size of the tube determines the frequency range measurements are useful in. The upper limit of the tube is set by the diameter. 1.22 * c / d is usually given as the upper limit. There will typically be a notch at this frequency and other notches above it. The lower limit is c / 4 / length of the tube. So only the response between these frequencies should really be looked at. With high frequency horns, you can typically build them large enough to obtain a rho * c * some constant input impedance that is relatively flat above the cutoff frequency (depending on the type of horn). This means in theory the frequency response on the horn will be the same as on the plane wave tube (although the sensitivity will be different - compression drivers' sensitivity on a PWT is very high). The only caveat here is that many high frequency horns have a polar response that varies with frequency. In other words, at low frequencies the horn is not big enough to the control the sound radiated by it, so the sound spreads out over a wide angle. At high frequencies, the horn becomes acoustically large compared to the sound waves being radiated, and the sound is confined into a narrower angle. This means that at higher frequencies more power is concentrated over a given area, so the sound pressure level is higher in that area (but lower outside it). This is effectively an acoustic equalizer, so this effect needs to be added to the plane wave tube response to come up with the on-axis response of the horn / driver combination. This also explains why typical horn design programs do not predict the on axis response of high frequency horns very well - they don't typically include this factor.
"
 
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Dipoles are all the rage here right?

Well how about a dipole paraline?

The extremely shallow depth of the BG drivers makes this do-able. I made some sloppy measurements with RTA Lite, and found that the response of the NEO 8 was one of the flattest of all the drivers I tried. On the downside, the horn filters out a lot of the high frequencies.

I'd have to run some polars, but I'm guessing that the paraline reduces high frequency energy similar to the way that a constant directivity horn does. Basically that the high frequencies are spread across a larger coverage angle, so the overall SPL level is lower than if you listened to a planar on-axis.
 
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There is no reflection problem, because the width of the passage is much smaller than the wavelength of the sound. The sound "flows like a fluid", rather than bouncing off the walls. It's the same reason why you don't have reflections at the folds in a tapped horn within its designed operating bandwidth. Tom Danley has pointed this out in several posts. The best explanation I have seen is in his patent application - Fig 13 and its description.
Patent US20090323997 - Horn-loaded acoustic line source - Google Patents

This would only hold if the pathlength were small relative to the wavelength. The parallel surfaces aren't the problem- the abrupt bend that is on the order of 1/4 wave at 1kHz, is a meaningful concern. Any one dimension that is meaningful in size is sufficient to create disruption.

In a tapped horn, the waves are long relative to the length of the segments with the bends.

That's not true with a several inch pathlength producing treble.
 
This would only hold if the pathlength were small relative to the wavelength. The parallel surfaces aren't the problem- the abrupt bend that is on the order of 1/4 wave at 1kHz, is a meaningful concern. Any one dimension that is meaningful in size is sufficient to create disruption.

In a tapped horn, the waves are long relative to the length of the segments with the bends.

That's not true with a several inch pathlength producing treble.

It doesn't matter how long the wave has to travel to get to a bend, it is the dimensions of the bend itself that matter. In a "properly" designed paraline that bend is acoustically invisible to the wave front. The acoustical image size the bend presents is too small to effect the wave front traveling around it. However, almost everything you have stated holds true for frequencies above 18KHz in a 1/4" sized paraline.
 
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