Suppose a tractoid horn is flush-mounted to an infinite baffle. And suppose spherical sound waves travel down the horn. Then, when they leave the horn, they should be hemispherical in shape and omnidirectional. In fact, they should disperse perfectly in all directions. See the "orthogonal to circles" diagram at,

www.xahlee.org/SpecialPlaneCurves_dir/Tractrix_dir/tractrix.html

The only flies in the ointment that I understand are,

1) The compression driver may not produce spherical waves, so the value of the tractoid geometry is negated (why, then, load this driver with a tractoid??), or

2) The geometry of the tractoid, along with the laws of fluid dynamics, does not maintain the spherical shape of the sound waves as they travel down the horn, so they leave the horn focused. (Again, then, why use a tractoid?)

3) The absence of the infinite baffle completely mucks up everthing. (Same question.)

4) Perhaps the Oris horns do not flare out to their asymtotic ends; but this would not explain the issue for other tractoids or "tractrix horns."

Can someone explain why these would beam?

Is there a good, modern book on Acoustics where one can study these things? I bought Collom's "High Performance Loudspeakers," but it has been little help so far. Maybe I need to read more of it...

But here are some references you can download to get you started. Check out George Augspurger's "Sound System Design Reference Manual." Chapter 3 is about directionality, and it touches on the subject of narrowing directivity. Polar plots are used to illustrate coverage at various frequencies. Also see the AES paper called "Improvements in Monitor Loudspeaker Systems," by David Smith, Don Keele and John Eargle. It discusses directivity as well.

I called the publisher (Customer Service) this morning, and they have the book and are sending me one to arrive in a few days (from Iowa). $60 plus tax plus shipping. (About $72 for me.)

Thought that I would pass this along in case anyone else is interested. They say that the book uses math. thru calculus plus complex numbers.

Leach also has a link to errata for all the editions, so if anyone here has an earlier version and wants the corrections, they are there.