As to foam in the waveguide, the foam would be absorbing the high frequencies (depending on how high you use them), and changing the frequency response more or less to your liking. In designing a horn you generally assume smooth wall's as it would not be easy to accurately model horn surfaces with random rough walls. On that note rough walls could be used to ones benefit but would probably take a lot of measurements and trial and error, and theres usually better ways to fix a problem such as rough frequency response than this.

But it does stand to reason.

I think though, that there is some indirect evidence of this fact. Folded horns use straight sections, each one expanding a little more than the one preceding it. This only approximates an exponential flare, yet the performance is similar to what is expected from a purely exponential flare.

The conclusion is easy to draw that the coarseness of the curve has little effect because it is small in relation to wavelength.

Wavelenghth can be scaled down to treble frequencies and horn flares with rough sand-grain texture become similar irregularities. Wavelengths are large compared to the grain of the horn surface, so my assumption is that it doesn't matter in the passband. But I guess a real test might be worth doing, to sand one smooth and compare the difference.

Where there are places in a horn that flare angle changes rapidly, diffraction causes a change of wave propogation. This can be at the throat, the mouth or anywhere in between. If the diffraction causes two wavefronts to be generated and to co-mingle, there can be interactions and possibly destructive interference which cause response irregularities. Even without interactions, rapid changes in directionality cause uneven response due to the fact that the driver's total energy is focused more when DI is high and spread out more when it drops. At the mouth, dispersion control is ultimately lost at some low frequency as the sound bends around it.

There are a variety of methods used to combat these kinds of irregularities, and to reduce anomalies in dispersion and resoponse. Some use radiused transitions. Some use absorbent foam at transitions. Some use hybrid horn shapes. These things are used in an attempt to reduce ripples in response and directivity and other anomalies like pattern flip and astigmatism.

• Diffraction Applet

Agreed to your post. IF the wall roughness is small relative to the wavelength then it will not be much of an effect.

I was thinking more about how one could use a deliberate roughness at the wall to shape the wavefront by creating a boundary layer effect. from my book it is obviuos that one wants the wavefront to diminish at the edges of the waveguide.

Also, please remember that I do not use waveguides or horns at LF. They need to be too big to do any real good. Sure they offer some gain, but remember that I always use big high performance drivers for directional reasons and so gain is not really very important to me. (True unless I am doing a pro sound system, but then the waveguides can be big.) I use waveguides strictly for their directivity qualities, not for their loading ability. SO when I think about horns or waveguides I never think about low frequencies. In essence, if the wavelength is bigger than the waveguide dimensions then the waveguide is no longer a directional control device and I don't really consider it.

Of coarse the foam absorbs high frequencies, but ALL CD devices have to be EQ anyways so I just EQ in this loss. No problem.

I believe that I could model he rough walls. I know that I can model, and have done so, an absorptive wall, as well as an absorbtive internal medium. A rough wall just have a different kind of boundary condition.

You will also have to be more specific about "theres usually better ways to fix a problem such as rough frequency response than this". I am not new to waveguide design and usually know all of the techniques involved, but I am not sure what you are refering to here. If you are refering to the use of the foam, I strongly disagree that there are better ways. If there were then I would use them and not have to "invent" the better solution.