A different look at horns vs direct radiators???

[jwc]

OK Doc. Here is a quote from Bruce Edgar regarding exponential vs Tractrix for Bass horns. Top secret where I got this.[:'(]

"The explanation goes back to the difference between spherical and plane waves. When the plane waves travel down to the end of the mouth of the exponential horn, suddenly there's a bulge where they exit into space, and that bulge is essentially a discontinuity. So, you have reflections at the mouth, which travel back to the throat and set up a quarter-wavelength resonance condition. With the Tractrix horn, since the waves are spherical going through the horn, they exit the mouth with very few reflections. When I first started building Tractrix horns, I heard this immediately. They didn't have the same horn colorations I'd heard before. I said, "Well, I ought to build all my horns this way," so when I built a 70 Hertz Tractrix Bass Horn (Speaker Builder, 1983), I was in for a surprise. The problem is that the Tractrix is a short horn. If you take the equivalent Tractrix and equivalent exponential horns (same mouths, same throats, same flare rates), the Tractrix horn is shorter. At the low end, the response on any horn is limited by the throat reactance, which peaks at the flare frequency. The exponential horn is long enough that if you can put on a back chamber and resonate it with your loudspeaker at the flare frequency, you can partially cancel out that throat reactance. With a hyperbolic exponential horn, you can cancel it out exactly. With a Tractrix horn, you don't cancel it out at all, so the 70-Hertz horn rolled off at 100 Hertz. It sounded very good, but the problem is that the Tractrix horn response just does not extend to the flare point. There is no way that you can do it, so you have to live with the consequences. Well, for a midrange horn that's not too bad. The 300-Hertz horn that I make turns on at around 400 Hertz, and since its size is not huge, I can build a full-size 300-Hertz horn. It sounds very nice, but it won't turn on until 400 Hertz."

[bodcaw boy]

didn't know that horns were freq band sensitive. this is where bruce and i disagree.

take care,

roy

[jwc]

I sure don't have any evidence to support Bruce's statement. So Doc.......go for the 40Hz Tractrix and let us know what happens.

jc

[ZAKO]

Please elaborate Roy.

[jwc]

Roy, there any compromise with tractrix bass horns?

[Edgar]

If you have Hornresp, you can see it for yourself. Try the following test cases. Note that the only differences are the type of horn (tractrix, exponential, hyperbolic), the horn length (modified as appropriate to keep the same throat and mouth dimensions), and the rear chamber volume (set for appoximately "flattest" response).

Greg

[jwc]

I'm familiar with Hornresp.

I have drawn up and hand calculated several tractrix and exponential bass horns. ON paper and theoretically........look fine.

But curious of the compromise if any to Tractrix bass horns.

jc

[WMcD]

I know that Bruce uses the tractrix equation to make his folded corner horns.

But with the folds and rectangular cross section of the ducts, I expect that no spherical wave fronts develop. Further, he is shortening the mouth end (I'm pretty sure) and it does not reach a 180 degree termination like the full tractrix. I think they don't even get to the equivalent of a trihedral corner. All in all, I think his bass corner horns are missing much of the tractrix effect.

I wonder about Hornrespons and how it is modeling a horn.

For example: I've used a spreadsheet to model the wave fronts of a circular tractix. The important aspect is that (1) the wavefront has the area of a portion of a sphere, so area is greater than a plane wave. Also, it bulges forward from a plane wave and therefore (2) the axial travel is greater. For example, the hemisphere at the mouth has a greater area than a plane wave circle. It bulges forward by an amount equal to the mouth radius.

Does Hornresponse do this?

Once we have the area and incremental distance, we can calculate the equivalent flare rate of an exponential every delta X down the horn. It turns out to be fairly constant even if it wiggles around a bit. Arguably, this means a tractrix has an exponential expansion if we honor the shape of the wavefront!

Gil

[Edgar]

I wonder about Hornrespons and how it is modeling a horn. 

Best person to ask is David McBean himself. I have corresponded with him via email, and he is quite approachable. He hangs out at Audio Asylum and can also be reached through the Hornresp Website.

Greg

[garyrc]

... A purely subjective reaction to horns vs direct radiators:

Between about 1977 and the mid '80s, the better equipped movie theaters (especially 70 mm theaters) slowly changed over from horn loaded bass to direct radiator bass (using large subwoofers). This was before Klipsch was big in the movie business, and I'm aware that there are still some horn loaded bass units in theaters, such as the theater version of the Jube. I paid close attention as S.F. Bay Area theaters made the change, and there was Good News and Bad News.

The Good News was that the subwoofer systems produced a lot more very low bass, down as low as 20 Hz (the old JBL and Altec Horns used in the bigger theaters were generally specified down to 40 Hz in the bass).

The Bad News was that the new systems seemed to lack the extremely clean, sheerly awesome bass impact of the old horns. The horns seemed to have better transients, and seemed to move more air. For example, in the old Coronet theater in S.F., the 70mm 6 track stereo presentation of the crucifixion scene in Ben-Hur had thunder superior to any thunder after the theater changed to direct radiators. With the horns, the thunder caused a formidable puff of wind in the theater whenever it sounded. The same was true for the thunder storm in the Todd-AO presentation of Porgy and Bess, and Disney's Grand Canyon Suite. I realize that there may have been other variables in play, but there seemed to be a clear line drawn in the late 70s, and the thunder was never the same thereafter! Subwoofer thunder seened "floppy" and to lack effortless authority. This was also true for orchestral bass, somewhat less obviously.

[jwc]

I have been hesitant to make tractrix bass horns for the fear of folding. You just don't hear of it being done and I assumed there was a problem with doing that.

Also....the horn is so short.

Doc and Edgar.......riddle me this....you can churn your software.

scenario:

45Hz Tractrix bass horn 1/4 space. Throat size 135 sq inches.

Now what I get is a mouth that is 1760 sq in and a HORN LENGTH THAT IS ONLY 23.6 INCHES. Is this right? If so....you wouldn't have to fold. What would you expect? Would the curve be "peaky". I was thinking that with exponential bass horns that there was a concern with large throats and short horn lengths causing a "peaky" curve. Is this BS?

A tractrix straight horn that isn't that long gettin down to 45Hz? I mean you would have to add about 10" depth for the woofer chamber. But still....that isn't that "Big".

jc

[Edgar]

45Hz Tractrix bass horn 1/4 space.  Throat size 135 sq inches.

Now what I get is a mouth that is 1760 sq in and a HORN LENGTH THAT IS ONLY 23.6 INCHES.  Is this right?

Here's what Hornresp gives for an answer. The mouth area ("S2", in cm^2) is 7200 square inches, and the length ("Tra", in cm) is 80 inches. "S1" is the throat area and "F12" is the cutoff freq.

Greg

[jwc]

Where do you put in 1/4 space horn?

Is that full space?

[Edgar]

Where do you put in 1/4 space horn?

Is that full space?

I wasn't quite sure what you meant by 1/4 space, so I took a shot and figured that you meant half-Pi space. Hornresp allows you to model 4Pi (no floor or walls), 2Pi (floor mounted), Pi (floor-wall corner), or half-Pi (floor-wall-wall corner, like a Klipschorn). If that is not what you meant, then I can try again, or you can run Hornresp yourself from the parameters that I posted last time.

Greg

[Edgar]

It occurred to me that maybe you actually meant a 1/4-size horn mouth. So I reran Hornresp with a 1/4 mouth instead of a full mouth. This plot shows the 4Pi case (no walls or floor). 1/4-size mouth in black, full mouth in gray. The half-Pi case (floor-wall-wall corner) is much smoother.

Greg

[jwc]

Greg. Thank you. I think I have it figured out. I tinkered with that program a good bit last night.

Your help is greatly appreciated. DOC has been mentioning that program to me for quite some time and your help there with showing the data got me connected with the manual way integrated into that program.

So I'm gonna mess with it some more.

Thanks.........still.......we need to hear more about tractrix bass horns!!!!! Is there a compromise??

jc

[Edgar]

Greg.  Thank you. 

You're welcome.

........still.......we need to hear more about tractrix bass horns!!!!!  Is there a compromise??

I think that there's no doubt that the response of a full-length tractrix horn drops at a higher frequency than that of an exponential or hyperbolic horn. But for less than full-length horns the differences are not as great, because the various horn contours become more similar near the throat. I think that Bruce Edgar said that all horns with the same throat, mouth, and length dimensions respond within ±2 dB of each other, regardless of contour. (David McBean actually showed me a counterexample comparing a conical with a hyperbolic, but the statement is essentially true as long as you don't get too extreme with the contours.) The simulation programs like Hornresp can give you a pretty good indication of the general differences.

Greg

[DrWho]

also don't have the means to reliably predict the polar response, and I can't exactly be building a few dozen prototypes to start figuring out the trends emperically...

Hornresponse's SPL window shows the power response of the horn. It can also give axial SPL at any polar that you select. After you calculate, go to tools, select directivity, then select response. A window will pop up with a place where you can enter the degrees off axis you wish to measure. Note that at 0 deg. the curve given will be the axial SPL, which is what you normally see on a mic'ed response curve of a speaker.

The Hornresponse program is an amazing program with many uses and features.

http://www.diyaudio.com/wiki/index.php?page=Hornresp+Help

This may help in understanding all the features this wonderful program offers.

I knew about that feature, but it makes some assumptions that won't be true in a final build. At the very least, it's only showing you what a circular shaped mouth will do. I also don't think it takes into account how the higher frequencies seem to leave the edge of the horn before the mouth.

Or to put it another way, hornresp is not sufficient to design a horn for an arbitrary polar response...

[DrWho]

OK Doc. Here is a quote from Bruce Edgar regarding exponential vs Tractrix for Bass horns. Top secret where I got this.[:'(]

"The explanation goes back to the difference between spherical and plane waves. When the plane waves travel down to the end of the mouth of the exponential horn, suddenly there's a bulge where they exit into space, and that bulge is essentially a discontinuity. So, you have reflections at the mouth, which travel back to the throat and set up a quarter-wavelength resonance condition. With the Tractrix horn, since the waves are spherical going through the horn, they exit the mouth with very few reflections.

That quote from Edgar doesn't make any sense...

Why would an exponential horn have plane waves and why would the tractrix horn have spherical waves? The way I see it, sound propogates in its own manner and the horn needs to take the sound propogation into account.

The math for the exponential horn makes the assumption that the sound propogation is a plane wave. The assumption is a mathematical simplification - not a description of the real sound propogation through the horn. Same is true for the tractrix (except tractrix assumes spherical).

I see where he's going in terms of the low frequency cutoff, but it seems like he's worrying about losing a trick that you get when you've got a big reflection coming back at the driver - which fundamentally a horn shouldn't be doing in the first place...

[jwc]

Don't know Bentz. This is the only negative I've ever come across for tractrix bass horns. I know of no positive comments either.

So what have you decided to do?

jc