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K-402 in wood!


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Tractrix curve construction. Note the second half of the construction Dennis...it's pretty important...

 

Tractrixtry.gif

 

 

Constructing a catenary from a tractrix curve (i.e., inversely, the tractrix curve is a involute of a catenary):

 

Evolute2.gif

 

An involute of a circle is the tooth profile for typical gears (having almost no sliding motion as the gear teeth mesh ---heel to toe)

 

Involute_wheel.gif

 

All the animated gifs from Wikipedia.

Edited by Chris A
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Remember that it's an area expansion formula.
 

Roy will need to plug his ears, but that's a point that I disagree on....and you answered exactly as I hoped....

 

Webster's one-dimensional solution to the wave equation doesn't allow you to bend the central axis of the horn. It's a fundamental assumption behind the equation. The wavefront must propagate in one axial direction, or I'm totally misinterpreting the setup of the equation. The whole point was to make a 3-D problem a 1-D problem. Curving the horn requires at least a 2-D solution...have fun cranking through that nasty math. The 1-D solution is already hard enough.

 

I totally agree with Roy when he says that the area expansion dominates the acoustic coupling provided you bend it correctly. However, all of the polar response predictions go out the window - and Roy has pointed that out on the folded bass bins, so I don't think I'm off my rocker here. I personally place a greater emphasis on the 'constant coverage' (to borrow Roy's delineation) because it keeps the on-axis and off-axis tonally balanced. Unlike PWK, I'd be willing to give up some efficiency to improve the polars (PWK loved collapsing verticals so I'm not alone there either).

 

All that to say, you may get similar acoustic coupling when the area expansion is similar, but the polar response does not follow the prediction. If I'm looking for polar response performance, then I need to find new ways to model the "curved conical horn".

 

 

Nothing here is terribly surprising or controversial in today's acoustic horn design world. 

 

Geddes in fact says that efficiency isn't important at all, and calls his horns "waveguides"--a point that I believe that he's gone astray on.  Efficiency IS important when talking about certain forms of distortion, of the type that Geddes doesn't talk about--and denies is important.

 

Modeling horns of curving and other shapes nowadays really isn't difficult--at least not like the difficulty that PWK faced without the tools to do it.  I think that the folded horn designs for bass bins were mostly empirically developed - and therefore slow going in terms of improvements.  He could get away with non-controlled-coverage bass bins because of the peculiarities of the human hearing system (including the brain) that forgive inconsistent coverage in front of the bass bins - a point that almost everyone misses today.

 

Having efficiency in a bass bin IS important, in order to minimize AM (and to a much lesser extent-FM) distortion.  Horns reduce driver diaphragm motion by over a factor of five, and that difference or disadvantage is one of direct radiators -- no matter how well you think that you've designed your drivers to be more linear: that advantage will never go away. PWK was one of the first of a very small group of engineers to realize that, I believe.  That group is still very small, indeed, but that doesn't mean they don't have the right answer.  Witness the enthusiast following here that prefer the "Klipsch sound" (actually the sound of music being reproduced with very low AM, FM and compression distortion and the resulting loudspeaker designs with half the number of crossover disturbances to control FM distortion). 

 

It's interesting to me that a couple of poorly done "memeplex" articles in the 1970s by a couple of audio engineers that got that subject wrong still seem to hold peoples' attention today (and they had a vested interest to get it wrong, I might add).  I look at it like low-carb diets: someone long ago decided that they were "bad" and that (incorrect) notion still hangs on, but now the "experts admit that it's actually the best diet--except if you already have heart disease" (...see how the old memeplexes refuse to leave?...).

 

Chris

Edited by Chris A
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I think where I differ from Geddes is I still maintain that efficiency is important...and my reasons include all the Doppler distortion reasons you point out. I am very grateful PWK stuck to his guns on that one because there are some fundamental insights there.

I think where I differ from the classic Klipsch approach is that I always hear some unwanted artifact in the folded bass bins. It's annoying enough that I prefer the distortion of the direct radiator, and then I can further justify that by the monitors used in the creation of the music I enjoy.

One of these days I'll finish a 3-way system using a straight horn below a K402. Right now I've chosen to pick up racing instead since I get burned out on audio at work. And really my next speaker project should probably be replacing our nasty diffraction slots at church.

Edited by DrWho
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Allison and Villchur on the audibility of modulation distortion.  The article link here is excellent in discussing the history of realization and the audible effects of FM (i.e., Doppler) distortion, but note that the author apparently didn't know about AM distortion, a subject that Klippel sorts out very well for both bass and treble distortion contributions.

Edited by Chris A
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Right now I've chosen to pick up racing instead since I get burned out on audio at work.

 

I certainly understand that. I used to really get into the subject of systems architecting (I'm still interested but I see that human memeplexes and ego-driven behaviors are the problem that get in the way of better architecting).  Before that, mechanical design, and before that: music-formal music education. 

 

It's easy to get burned out if you're not careful.  Work has a way of feeding you Spam (...the pork product...not the internet meaning) until you can't stand to look at it anymore. 

 

Chris

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Btw, which articles did you have in mind? I'm not familiar with any memes here?

 

You are kidding right, Dr. Who???   ;)  LOL

 

http://en.wikipedia.org/wiki/Meme

 

 

lol, I know what a meme is, haha :P

 

I thought Chris was alluding to memes that ignore doppler distortion? Or maybe they were getting on about something else?

 

a couple of poorly done "memeplex" articles in the 1970s by a couple of audio engineers that got that subject wrong still seem to hold peoples' attention today

 

I've not come across any articles like this, and I wasn't around in the 70's to experience it...I think I would have enjoyed the hippy era, but I'm glad I wasn't an engineer back then. Those guys had to be crazy awesome to overcome the limitations of their tools.

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  • Moderators

 

 

Btw, which articles did you have in mind? I'm not familiar with any memes here?

 

You are kidding right, Dr. Who???   ;)  LOL

 

http://en.wikipedia.org/wiki/Meme

 

 

lol, I know what a meme is, haha :P

 

I thought Chris was alluding to memes that ignore doppler distortion? Or maybe they were getting on about something else?

 

 

 

a couple of poorly done "memeplex" articles in the 1970s by a couple of audio engineers that got that subject wrong still seem to hold peoples' attention today

 

I've not come across any articles like this, and I wasn't around in the 70's to experience it...I think I would have enjoyed the hippy era, but I'm glad I wasn't an engineer back then. Those guys had to be crazy awesome to overcome the limitations of their tools.

 

 

 

I am sure that was the reference Chris was making, I just couldn't resist!!!!  :)

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I think where I differ from the classic Klipsch approach is that I always hear some unwanted artifact in the folded bass bins. It's annoying enough that I prefer the distortion of the direct radiator, and then I can further justify that by the monitors used in the creation of the music I enjoy.

 

Remember that the bass bins that you listened to in Hope were basically not EQed to remove the rather significant frequency response peaks in the 40-250 Hz band, and there are some really big peaks there that need taming (just like the Khorn bass bin). 

 

I'm not sure why those bass bins were not EQed out since so much effort was spent EQing the K-69-A/K-402, K-69-A/K-510, and TAD TD-4002/K-402 combinations to within +/- 1.5 dB.  Do that to the bass bins and you'll hear something completely different--albeit preserving some rising LF response below the room's Schroeder frequency.  At least one of the group there voiced a preference for "having that extra energy in the mid-bass region", an opinion that I didn't share, and have since found that taming it really changes the listening experience.

 

Chris

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I wonder if the 402 could be veneered in wood? 

 

A lot of work - expensive to do right, I'd think, at least in time expended.  Work in the throat area would have to be done extremely well in order to not affect the FR/polars.  We're talking a few thousandths of an inch form factor accuracy.

 

Chris

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I wonder if the 402 could be veneered in wood? 

 

Greg

 

That was my idea as well, Greg. Thin veneer is typically around 0.025", from what I could just find on the Internet. Once beyond the critical throat area, that extra thickness should have negligible effect upon the horn. In fact, it's probably on the same order as production tolerances.

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