New Wave Guide Study

[JonP]

For those with fat wallets Geddes will sell his waveguides including the foam phase plugs for $250ea...

Yeah, that probably is about the "going rate" for whatever way you go. I talked to a few Mech E's here at work, wondering about new 3d model methods nowadays... Yep you can get a part made eaiser and cheaper than having a block of Delrin machined out, but it still would be in the 2-3-400 dollar range per piece.

Is the off the shelf Geddes WG in molded plastic or some such? I know they have a throat adapter plate in the "Bella" Geddes influenced product. From there, it looks like a thick baffle with a shape machined into it... but that's probably way different from this...

[JonP]

Josh, You may not know. A copy was forwarded to Dr. Geddes. His only comment was about the entry angle. So in his own special way, he confirmed it is correct.

My thought (for in the shop) is that it is simple to truncate the throat at a chosen intercept angle. To do so in the spread sheet makes my head hurt....so, in the spirit of your avatar's undying stamina...wear it out big boy!

When I was trying to emulate the Quadratic WG, I found that by lucky coincidence a 5/8" thickness (Baltic Birch I had on hand) with a 3/4" roundover bit, at the right depth, would give you a nearly perfect match from the 90 deg of the throat beginning (at the driver), to the 45 deg of the chamfer bit "layers". That was good for the outer side of the throat. I guess you might be able to calculate how deep on the inner side to put the roundover, so you create a small rounding of a certain angle.

Assuming I'm following things here... of which I'm not entirely sure!

[ThomasW]

Is the off the shelf Geddes WG in molded plastic or some such?

I just glanced into his room during a RMAF, my impression was the WG and baffle are made from fiberglass, or a thermal molded plastic.

[JoshK]

I don't know about his current speaker line coming up and what he is offering to sell to diy'ers but his previous Summa's were fiberglass enclosures, including the WG.

[augerpro]

Exactly. Geddes mentioned the angle of entry for the throat of the Summa was 6 degrees. Earl says the entry angle has a lot to do with the success of a waveguide. He chose the B&C driver for its favorable characteristics. The waveguide in the Summa was built for it.

Did he use 6 degrees strictly because it matched the B&C driver, or for some other reason? I do remember matching the throat entry angle to that of the CD was important.

[Dennis H]

Did he use 6 degrees strictly because it matched the B&C driver

Yeah, that's the way I remember it. But, once the molds were made for his horn, switching to another driver could be a problem because the throat wouldn't match.

Dr. Geddes is a very smart guy but he does tend to get carried away with the theory from time to time. He made it sound like it was hard to calculate the 6 degree thing and only his software could do it. I did some quick calcs in Excel and posted the numbers. He dismissed them because they were off from his numbers by .001". I intentionally hadn't tried to calculate them any closer than that; I could have easily gone for more decimals. I mean c'mon let's get practical, how accurate will the dimensions of a fiberglass horn laid up in a mold be?

[rc white]

os waveguides

If you look at the expansion rate then the os waveguide has a quadratic form of expansion just like the conical horn, the difference being that the os type always has a zero expansion rate at the throat, and the conical always has a finite one.

The quadratic throat type has a curve near the throat that is very close to the os sort and given manufacturing tolerances and the vagaries of different compression drivers in practice there is probably little to choose between them.

The reason for this is that the actual result is dependent upon the actual wavefront entering the waveguide. Compression drivers are traditionally measured on plane wave tubes and in order to be accurate the wave entering the tube must be very close to one.

In fact you can clearly see in plane wave tube plots where the Bessel modes of the tube are being excited, this cannot happen if the waves a truly plane because there is theoretically no coupling coefficient to these modes.

I have a paper by Celestion available on the net that discusses a compression driver specifically designed to produce spherical waves and in the end this is the best way to go, especially for high quality reproduction.
Using this scheme you can drive one of the three section circular arc waveguides with such a compression driver, this type of wave guide has the major advantage that it is not a theoretically infinite device compromised by cutting off and radiating into the outside world, but represents an optimum method of coupling a spherical wave to the outside world.

[JoshK]

Dr. Geddes is a very smart guy but he does tend to get carried away with the theory from time to time. He made it sound like it was hard to calculate the 6 degree thing and only his software could do it. I did some quick calcs in Excel and posted the numbers. He dismissed them because they were off from his numbers by .001". I intentionally hadn't tried to calculate them any closer than that; I could have easily gone for more decimals. I mean c'mon let's get practical, how accurate will the dimensions of a fiberglass horn laid up in a mold be?

That was my take too. I think it is a common pitfall of smart people to assume others aren't.

[augerpro]

Mr White do you have links to this paper? Also any Excel based spreadsheet for your formula's? Thanks.

[JonP]

The reason for this is that the actual result is dependent upon the actual wavefront entering the waveguide. Compression drivers are traditionally measured on plane wave tubes and in order to be accurate the wave entering the tube must be very close to one.

I have a paper by Celestion available on the net that discusses a compression driver specifically designed to produce spherical waves and in the end this is the best way to go, especially for high quality reproduction.

I was wondering how the wave off a dome tweeter compares to an average compression driver, or this special, spherical wave type. Would one of the discussed horn types be a good match? I imagine the throat to dome area match would be highly influential, and there's always some "dead area" in the neigborhood of the surround and faceplate, which will vary from tweeter to tweeter... But here's hoping that it isn't too bad for those of us wanting to "roll our own" out of off the shelf drivers...

[augerpro]

I wonder if the relatively flat dome of the Visiton KE25 is more suitable to WGs than other conventional domes? Assuming WG should are really all that usefull for these type of tweeters at all.

[rc white]

links

http://professional.celestion.com/pro/rd/pdfs/AESPAPER.pdf

link to convex compression driver

https://web.archive.org/web/20071014131131/http://www.kef.com/kefamerica/technology/uniq/qwpcoaxial.asp

link to waveguide and dome geometry

I do not use spread sheets but a 20 year old programmable calculator.
rcw

[kevmurray]

Spreadsheet waveguide application?

Ed, Josh,

Forgive me if this question has been answered before but what is the intended application for the spreadsheet waveguide? Compression drivers?

[JoshK]

Kevin, yeah, its intended for CDs but I guess you could use it for domes...maybe. I am not sure though that the OS profile is ideal for domes.

[EdL]

Kevin, I agree with Josh. Earl has stressed the importance of coupling the driver to the guide. Even at that, I'm dogged by my curiosity...Why not?

A secondary use for myself...I respond well (depend on it, actually) to the visual...to see it is to understand it better.

[kevmurray]

Kevin, I agree with Josh. Earl has stressed the importance of coupling the driver to the guide. Even at that, I'm dogged by my curiosity...Why not?

Me too. I think the ring radiators might work best but I'm curious what changes could be made to accommodate a dome. My first concern is that domes produce a spherical wave and might have multi-modal behavior in a waveguide that starts to flare at the throat.

A secondary use for myself...I respond well (depend on it, actually) to the visual...to see it is to understand it better.

Again, me too. I've finally fixed the math in my own spread sheet for the constant directivity waveguide. Seems page two on the ESP pages does have an error (I think). My spread sheet math finally agrees with what AutoCAD gives me, without the visual from the cad I'd have been lost.

I have access to a lathe so hopefully I'll have time to play with various designs during the Christmas holidays. Hardest part is going to be preparing a test setup for radiation patterns. If anyone could offer help or advice in this it would be welcomed.

[rc white]

matching

If you have a flat wavefront being "bent" into a spherical one you get scattering.

Depending upon the exact nature and extent of this higher modes are produced, most being "evenascent", that decay exponentially and don't propagate below the cut of frequency locally.

The types of waveguide I described have less scattering than the os type since they are essentially not bending the wavefront, or at least not much.

If for instance your dome is too flat then there is at least theoretical benefit in making an os waveguide with this dome angle at its entry and the required directive angle at its output, this seems to be the a scheme adopted by jbl in its application of os waveguides, but as already mentioned a suitable circular radius will do just as well.


A major difficulty with compression drivers is if the spigot section does not fit properly to the horn flare and you get a sharp discontinuity that causes diffraction, the major problem is that this is usually asymetric and causes a severe impedance anomaly inside the horn that can be seen in its electrical impedance curve.
The double blind testing referd to in my article found several cases of this type of mismatch and it was clearly audible in the double blind trial.

As mentioned before the shallow dimensions of these waveguides mean that except at the highest frequencies they operate in the near field of a spherical wave.
Unlike plane waves spherical waves have a complex impedance that is a function of curvature such that the real and imaginary parts become equal at a "kr" of unity.
A major advantage of this type of operation is that it allows us to use progressive decoupling.

In an exponential horn decoupling also occurs but exactly where it does is constrained by the need for a specific flare rate.
The decoupling occurs because the real part of the impedance starts to dominate and the acoustic field takes on the characteristics of a classical potential field that has no curvature.
At lower wavenumbers where kr is around one or a bit more the potential field also has stream functions that describe at set of stream lines that follow the wall, the wavefront "leaving the wall" at a point where the stream functions amplitude is diminished sufficiently.
The wavefronts can't leave the wall if the wall has no curvature and this is what happens in the conical horn and os type of waveguide, and since unfortunately we must cut the waveguide art some point to let the sound out and all of our troubles with matching the waveguide to the outside world begin.
The shallow waveguide has a much more gentle impedance transition than a far field horn, giving much less mouth reflection, and progressive decoupling means that the wavefront leaves the wall before and higher order modes with coupling coefficients to the mouth region Bessel modes are excited.
rcw

[noah katz]

Robert,

Thanks for sharing your very interesting work.

I really like the extension of directivity control down to lower freq than the OS types.

But I'm puzzled how this is achieved w/o being much bigger.

Or is it? What are the dimensions of the mid/high section?

I'm also most curious as to how it sounds. Could you say a few (or many) words about that? What have you compared it with?

It seems like there might be issues with reflections from the 5", with so much of its area blocked by the tweeter.

Also, wouldn't there be some ill effects from the discontuity at the corners where the horizontal/vertical sections of the WG meet?
Thanks

[rc white]

Happy to share what I have learned about these devices Noah.

the general impression I and most people get of the coaxial waveguide speakers is that they have the effortless quality one also finds in large format monitors. They can play loud with no audible distress, and have a very solid stereo image.
Overall on all types of music compared with a set of small monitoring quality speakers, (with a small bbc dip), they lack accuracy on solo violins and unaccompanied female voices etc. and recording faults clearly audible in the monitors are glossed over to a certain extent.

At 450 x 295mm. to the extreme of the flare the directivity is around that predicted by Keele.
It is true that the driver could be a better fit to the throat, but since the crossover occurs at around 2.5kHz. the actual throat and small waveguide dimensions are small compared with that wavelength, and the area behind the tweeter waveguide and the corners give approximately equal and opposite scattering amplitudes, the overall result being a wavefront that is a fair approximation to a flattened spherical cap with minimum abherations.

The mouth area starts to reach its diffraction limit above 5kHz., an octave above the crossover frequency, and above around 4kHz. the tweeter does not illuminate the larger waveguide.

The overall aim of that system is to see what could be done with cheap readily available drivers, with the size restraint removed. The bass section is accordingly a qb5II box that gives the best efficiency for what is a cheap car subwoofer, people are particularly impressed by the bass which is tight and articulate, this is also helped by the fact that the room they are in is being driven at the quarter quarter wavelength points of its two shortest dimensions.
rcw

[noah katz]

Robert,

How deep is the WG?

If I wanted narrower dispersion horizontally as well as vertically, would a cone at the same angle as the vertical work, with the same depth?

Thanks

[kevmurray]

Rob, just a heads up that I sent you a PM last week. Says "unread" on my end so I thought I'd let you know in case you didn't know it's there.

[rc white]

The overall depth is 155mm. from the baffle to the driver mounting plate front.
I just used Keeles expression to calculate mouth width at a given angle, then cut the cone where the driver fits, the depth being variable.

I suspect a 60x30 horn is around the practical lower limit.