The primary mode of wave propagation in conical tubes is spherical and along the central axis of the tube. An infinite horn has no termination, and so no mouth diffraction. An extended horn with a large mouth tends to approach this as far as I can tell.

Maybe what you are talking about are high order modes. Geddes has made that a special focus, and he uses a aborbant foam in his horns to reduce them. While the principle mode of radiation is along the central axis, high order modes also exist that traverse from side to side. He explains that his solution attenuates the high order modes more than the primary mode because they have to bounce through more absorbent material.

That's what I have understood from talking with Earl, but beyond that, I should probably allow him to elaborate. Perhaps he'll chime in and discuss it further.

"This is my understanding, and please correct me, if I am wrong. There are (at least) two consequences associated with the transition from the boundary formed by a horn or a cone driver.

A transition from the boundary constrained space to a 2 pi (if mounted on a baffle) or 4 pi (if radiating to free space), which is characterized by impedance mismatch, reflections, and resulting standing waves (ripples)."

Yes I think we are saying the same things. A couple of minor additional points.

First, you don't need a baffle to have a baffle step. The physical size of the driver or the mouth of a front loaded horn like the Oris will also produce a baffle step. The source diameter is in effect a baffle. So when I simulate something like an Oris horn or the mouth of a back loaded horn which is "framed" by an enclosure structure I still calculate a baffle step response.

Second, I don't think the ripples are a result of standing waves. I believe they occur at frequencies for which the path lengths from all of the edge sources produce reinforcement (arrive in phase) or cancellation (arrive out of phase) of the summed response from the individual pressures from each source. If a standing wave response occured, I would expect these ripples to be more like sharp tall peaks and deep narrow nulls.

"The second is diffraction on the edge of the boundary. Invoking Huygens'principle, the wave emanating from the boundary restricted space will interfere with the wave emanating from the edge of the boundary."

Yes.

"I have an idea how to deal with the first one. Whether I am correct is to be seen. However, I am at loss how to deal with the other one, if I esclude various rules of a thumb. I understand that I am making a heuristic argument here, but it appears to me, that by a "proper" shape of the edge of the boundary, the interference could be minimized."

What I should have stated clearly before is that my thoughts are primarily for full range drivers and in particular my collection of Lowther drivers. For a tweeter or small horn my thinking would be different, if I had done any thinking at all. At the frequencies where ripples contributed by the edge of a baffle, as seen in the EDGE program, the driver is becoming very directional. For larger horn mouths the directivity is even more pronounced. I am not sure that the ripple produced by different edge conditions, sharp or rounded, is the biggest problem to be solved. I guess I would consider edge treatments as a tweak and something to be experimented with on the completed speaker and probably not something I would include in the initial design calculations. Adding a radius porbably would not hurt the response but I would not highlight it as a feature in the design of the enclosure. As you may have already guessed, I don't have a calculation for a rounded edge on a baffle .......... yet.

Martin

you wrote:

"Second, I don't think the ripples are a result of standing waves. I believe they occur at frequencies for which the path lengths from all of the edge sources produce reinforcement (arrive in phase) or cancellation (arrive out of phase) of the summed response from the individual pressures from each source. If a standing wave response occured, I would expect these ripples to be more like sharp tall peaks and deep narrow nulls."

Excellent observation in the last sentence. Let me think about it and see if I can desing an experiment that would confirm this.

I do trully hope that you will find a way to make your invaluable spread-sheets available without them being missused, although, sadly I have no idea how you could do that. ;-( But then again, I am not as smart as you are.;-)

M

"I do trully hope that you will find a way to make your invaluable spread-sheets available without them being missused, although, sadly I have no idea how you could do that. ;-("

I have been struggling with this problem for a while, I would like to make more stuff available. The feedback, continued discussion, and new design ideas that result accelerate me towards the next round of upgrades. Having people using the worksheets and commenting is extremely efficient.

"But then again, I am not as smart as you are.;-)"

You only see the stuff I get almost right, nobody sees the stuff I screw up. This produces an illusion that I might have more answers then questions.

Martin

you wrote: "I have been struggling with this problem for a while, I would like to make more stuff available."

Yes, from my discussion from some people I understood that you were almost ready to give up on shariong your work. I, for one am exremaly pleased to sense this new attitude.

M

To my knowledge no one but me has ever considered mouth diffraction in a theoretical sense. That was what my earler papers were about. There are two aspects to consider here. One relates to the cross-sectional shape - the shape normal to the wave propagation - and the other the shape in a plane of the wave propagation. The later one determines the amount of diffraction, while the cross-sectional shape has an influence on the axial and polar aspects.

Let me first say that NO diffraction is best, so its best to first worry about the in-plane shape. Here the answer is simple, radius the junction of the waveguide with the baffle as large as possible. This will minimize the diffraction and if done correctly will make it small enough that the other shape question is mute.

But it is often the case that one cannot radius the edge enough to yield no diffraction and the cross-sectional shape enters into the problem in a subtle way. A circular shape turns out not to be ideal since on axis the diffraction effects all add up in phase to yield a "hole" on axis at some frequency. This can be clearly seen in the Summas polar response. An elliptical section minimizes this hole, smearing it in frequency. But an ellipse has other problems like non-axi-symmetric polar response. Woofers usually have axi-symmetric polar responses. In the Summas, I don't recommend listening on-axis so this hole is not a big problem.

Beyond the circle and the ellipse, every other shape has basically these same characteristics.

But don't forget the Golden Rule here. NO diffraction is best, and no shape can compensate for a poorly diffracting waveguide mouth.

Hope this helps.