I took an hour today to read your horn theory papers, and I was really impressed. That's not nearly enough time to study the papers properly, more like just a brief scan. But I printed the documents and can spend more time with them in the days to come.

One of the things I was most impressed with was your study of horns with circular mouths and of rectangular mouths having various aspect ratios, in particular of their acoustic impedance. I am anxious to focus on your derivations when I have more time.

You also describe the radiation pattern, both at high frequency where the horn has good control of directionality and at low frequency where it doesn't. I didn't see any mention of the transition range in between, which is of particular interest. Single slot diffraction is often cited as a reason for dispersion behavior in the transition region, which makes a great deal of sense. But I did see that you mentioned length differences at different angles, and perhaps alluded to dispersion behavior in the transition region. So I may have missed it in my first pass.

Your work in this field is really outstanding, Martin. You contribute so much of your time, and so much work of value. I can't tell you enough how impressed I am with the work you've done in loudspeakers, made available for all to understand and digest. It's one thing to write papers like this for advancement in university, to defend a thesis or something. It's another thing to write for puplication in peer-reviewed journals. But it is another thing altogether to make such works available to all, and for the benefit of all. The goodwill that you generate is outstanding.

Thanks,

Wayne

• Martin King Horn Theory Article