It is rather well understood that a finite aperture of a horn/wave-guide causes diffraction effects, [1]. However, neither this reference nor another paper [2], which at least tangentially touches on this issue, gives any insight on computation of a mouth shape that would give an optimal (whatever the criteria) diffraction.

I am also aware of the work of Jean Michel Le Cleac'h [3], but this appears to be concerned with the entire horn contour, and not only the mouth shape. As such, it appears inapplicable to a situations, where a horn contour is pre-determined, e.g., constant directivity.

I would appreciate if anyone, who aware of any theory/papers/software dealing with this issue, could post references.

Thank you,

M

[1] Geddes, E., R.: "Sound Radiation from Acoustic Apertures." JAES., vol. 41, pp. 214-23 (April 1993)
[2] Henwood, D.J.: "The Boundary element method and Horn Design, JAES, vol. 41, pp. 485-496 (June 1993)
[3] http://ndaviden.club.fr/pavillon/lecleach.htm

Maybe I've over-simplified the problem, but I've always been of the opinion that an oversized horn is a solution because the mouth is larger than the wavelengths involved. Of course, this is an impossible proposition in many cases, or at least an impractical one. But for home hifi use, where room boundaries can be exploited, you can take advantage of the walls as flare extenders if you can get the mouths close enough. So for LF and MF frequencies where size matters, the expansion from a corner can reduce edge diffraction by effectively extending the flare. And for HF frequencies, the wavelengths are small enough that you can make the horn large enough to reduce edge diffraction.

I include diffraction around the perimeter of the horn's mouth in both of my latest front and back loaded horn MathCad worksheets. These worksheet are not the ones currently available for downloading form my site. It is a similar calculation that is done by the EDGE program with one exception. When the bottom edge of the horn is in contact with the floor, then it bcomes both a diffraction and a reflection problem. Some typical results can be seen in my advanced back loaded horn design documentation. I am still working on the technique so I expect further revisions will be coming.

Martin

• Quarter Wavelength Loudspeaker Design

thank you for your time replying.

The problem with an oversized horn, as I understand it, is that the frequency of the on axis "hole" moves down. Because it is a phenomenon with harmonics, this results in more of these "holes" in the passband.

M

thank you for your time replying.

I am well aware of your "released" MathCad worksheets. I am also familiar with EDGE, but I am unaware of its ability to model other than a flat baffle. If you understand, how to do that, could you please give me a hint?

I am wondering if I could be your "guinea pig" for your diffraction solution, either by letting me have the MathCad worksheets or calculate a solution for me, which I would reciprocate by providing you with measurements.

If my suggestion is unreasonable, please cheerfully ignore it. As an Intellectual Property practitioner, I understand your ownership concerns; otherwise, please contact me at mefistofelez_at_hotmail_dot_com.

Thank you,

M

[1] Geddes, E., R.: "Acoustic Waveguide Theory revisited." JAES., vol. 41, pp. 452-461 (June 1993). See Section 3.5. The equation introduced there and its implication are treated in:

[2] Geddes, E., R.: "Sound Radiation from Acoustic Apertures." JAES., vol. 41, pp. 214-23 (April 1993). See in particular Section 6; the conclusion in the first paragraph.

M

Looking at the EDGE again I think I was in error. My MathCad worksheets use the same basic math as the EDGE but can handle both rectangular and circular sources and baffles. So modelling a round or rectanguler horn mouth and baffle is easily done. I don't think the EDGE will do those combinations. I used the EDGE as a double check of my algorithm using sample problems.

As far as rounded edges on baffles, I do not believe that exact modelling of this is needed. There are two effects from the baffle, the baffle step as the sound radiated transitions from 4 pi to 2 pi and the sound "scattering" at the edge itself. The second effect produces small wiggles in the SPL plot. I do not believe that these small wiggles are as significant as room effects or the baffle step response. Maybe this is because I use full range drivers that are starting to beam at these same frequencies so the impact of the edge sharpness/radius is minimal.

Thanks for the offer of help with the horn worksheets. At this time I am pursuing a design and test of my own and have decided to hold onto the worksheets and the test results until I decide what I want to make available.

Martin

you wrote:

"As far as rounded edges on baffles, I do not believe that exact modelling of this is needed. There are two effects from the baffle, the baffle step as the sound radiated transitions from 4 pi to 2 pi and the sound "scattering" at the edge itself. The second effect produces small wiggles in the SPL plot. I do not believe that these small wiggles are as significant as room effects or the baffle step response. Maybe this is because I use full range drivers that are starting to beam at these same frequencies so the impact of the edge sharpness/radius is minimal."

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).

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.

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.

You wrote:

"Thanks for the offer of help with the horn worksheets."

ROTFLMAO. You are very polite, you know, where my motivation was comming from.

You wrote:

". . . and have decided to hold onto the worksheets and the test results until I decide what I want to make available."

No problem at all, see my previous post. I would like to nominate myself as a beta tester, though.

M

I have completely forgotten to add that the second phenomenon of my message is eloquently described in your "Design of a Front Loaded Exponential Horn" paper, p. 7, last two paragraphs.

M