Geddes on Waveguides

Patrick Bateman said:
The thing that's a bummer is that I'll bet a number of people have bought the XT1086 and assumed it's a substitute for an OS waveguide, based on how the mouth looks. But the throat diverges from OS by quite a bit.

...

Note that the throat is muuuuuch longer than the OS waveguide, even though their coverage angles are comparable. The OS is 108x72, the XT1086 is 80x60.

So the XT1086 could be described as a Continuous Diffraction device? (AKA CD Waveguide) 🙂


Patrick Bateman said:
Anyone have volumes 1-3? I can't decided if any of them are worth buying. They're $32 each at the moment.

http://www.aes.org/publications/anthologies/

I have volumes 1 & 2. What would you like to know?
 
soongsc said:

I think it is possible to get consistent results with molding once the mold shape is properly designed. The thoat really needs to be designed for a specific driver.

Yes ofcourse, but still no easy

Mold will change and be slightly different from proto

Then the items done in the mold will once again be slightly different from the mold

All in all you will end with something different from the proto

And it may even be hard to measure
Changes could be anything
Even a slight change in shape

And if not very careful even each molding could be different from one another
Many factors like the accurate % of hardener
Moisture, heat, production time etc
 
Keele’s Asymptotic Model

Dr. Geddes,

There is an article at Elliot Sound Products (ESP) discussing DIY wave guides. I know there may be several things in which you might not agree with, but I want to narrow our focus on wave guide directivity vs. frequency behavior. On the ESP web site it references Keele’s Asymptotic Model. As I understand it, it allows us to calculate at what frequency a CD wave guide exhibits constant directivity behavior. Below this frequency, there is a narrowing of directivity to 2/3 of the wave guide’s included angle.

Link to ESP wave guide page: http://sound.westhost.com/articles/waveguides1.htm

The formula is given as: F = Kk / á * w Where á = included wall angle, Kk = 25.306 x 10^3 and w = mouth width (meters). This is for rectangular wave guides. For an axis-symmetrical circular wave guide, the Kk constant is given as 29.707 x 10^3. This is the frequency at which the wave guide will exhibit constant directivity.
To find the frequency where directivity narrows to 2/3 of the wall angle the formula: 10^ ( Log ( f ) - 0.176) is given; “f” being the frequency at which the wave guide exhibits constant directivity.
1.) Are the above formulas valid from your experience?
2.) At what frequency do you place the crossover? Do you place is before the dip in directivity, at the lowest dip in directivity, or only after constant directivity behavior begins?
3.) What is the ideal place to crossover to the wave guide in the example below?

Rgs, JLH



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Re: Keele’s Asymptotic Model

JLH said:
Dr. Geddes,

There is an article at Elliot Sound Products (ESP) discussing DIY wave guides. I know there may be several things in which you might not agree with, but I want to narrow our focus on wave guide directivity vs. frequency behavior.


The author of that paper is a member of diyaudio, using the moniker "rcw." Here are 31 posts; there may be more:

http://www.google.com/search?hl=en&safe=off&num=50&q=site:diyaudio.com+gedlee+rcw
 
Re: Keele’s Asymptotic Model

JLH said:
Dr. Geddes,

There is an article at Elliot Sound Products (ESP) discussing DIY wave guides. I know there may be several things in which you might not agree with, but I want to narrow our focus on wave guide directivity vs. frequency behavior. On the ESP web site it references Keele’s Asymptotic Model. As I understand it, it allows us to calculate at what frequency a CD wave guide exhibits constant directivity behavior. Below this frequency, there is a narrowing of directivity to 2/3 of the wave guide’s included angle.

The formula is given as: F = Kk / á * w Where á = included wall angle, Kk = 25.306 x 10^3 and w = mouth width (meters). This is for rectangular wave guides. For an axis-symmetrical circular wave guide, the Kk constant is given as 29.707 x 10^3. This is the frequency at which the wave guide will exhibit constant directivity.
To find the frequency where directivity narrows to 2/3 of the wall angle the formula: 10^ ( Log ( f ) - 0.176) is given; “f” being the frequency at which the wave guide exhibits constant directivity.
1.) Are the above formulas valid from your experience?
2.) At what frequency do you place the crossover? Do you place is before the dip in directivity, at the lowest dip in directivity, or only after constant directivity behavior begins?
3.) What is the ideal place to crossover to the wave guide in the example below?

Rgs, JLH

Hi JLH

That this effect occurs is quite true. Don did a lot of good work in this area for its time, but that was some time ago. His methods were somewhat rough as well as his capabilities somewhat limited so, at best, we have to assume his formulas to be approximations. How good are these approximations? I don't have a good feeling for that especially as applied to a symmetric waveguide like I use.

My crossovers tend to be below the dip in directivity, but very close to the dip.

Ideally one would want to crossover above 850 Hz in your example. But that example is far more optimistic than I have found to be the case in practice. On a 15" 90 degree included angle the dip in directivity is about 1 kHz or a little bit higher. This would imply that the Keele formula that you show is quite optimistic for a waveguide, which is not at all surprising since Keele used diffraction devices in all his work. A diffraction device has a much more controllable and predictable polar pattern. Its just that it also has a lot of diffraction and standing waves to achieve this predictable control. Control versus sound quality, thats the tradeoff.

Hence while I would love to always work above the "dip" it is not feasible in my designs (which prioritize sound quality for nice plots), I have to deal with the dip and do the best that I can to minimize its effects.
 
The ideal wavefront for the OS waveguide is flat. This is precisely what a flat disk source provides. As long as the throat of the waveguide matches the diaphragm no phase plug is required or desired. This is of course NOT a compression driver in that case, but thats not really critical.

My first experiments with the OS waveguide used a Panasonic 1" flat honeycomb disk tweeter. It was an excellent device in this application.

Except for the thermal aspects, i.e. the smaller 1" voice coil will not be as thermally tollerant as the larger VC in a compression driver, this would be the source that I would use. I may in fact order some to try and the flat piston honeycomb is a very good source. The compression driver, with its larger diaphragm and VC does require a phase plug, which has its own set of problems to be sure.
 
4" will have trouble controlling directivity above about 5KHz. Modal vibration will cause additional reflections in the wave guide. This would be eveident if you take the raw driver and measure off-axis response within 60deg.
The tradeoff of using a driver modal response is slightly smear in focus, the sound will not be as crisp.