Tom, where would be a good place to look for this info? Know of any charts or perhaps software that would show this?
Hi Pano
There are a lot of things about horns that I have not seen written anywhere, this limitation being one of them.
You can model MANY things with AKABAK which deal with the actual dimensions and not the theoretical perfect case. While sort of pain to learn (and I only use part of what it can do), it is free and there are tutorials out there.
Remember the old days when they used to say a 30Hz bass horn would have a mouth about 10 feet in diameter or that the low cutoff was approximately where the mouth was 1 wavelength in circumference?
The reason is that at about 1 wl in circumference, one has reached the knee in the radiation resistance curve for a horn.
Beyond that point, making the horn mouth larger and larger offers no improvement in efficiency (but can confine the radiation angle which can appear to be gain in efficiency but isn’t).
But what that curve didn’t say was that there was no point or gain from having a mouth smaller than that.
A generalized curve from the interweb;
http://www.cummingsdesign.com/Benwin/images/Figure1.jpg
The unspoken thing in that curve is that at the upper frequency end, there is no additional horn loading once the radiator is already large enough to have reached that knee.
The importance of this became crystal clear trying different sized drivers in the Unity and Synergy horns, here, a 5 inch cone driver can efficiently drive a horn up to about 1000-1200Hz or so. Size matters when playing with these acoustic resistances.
The real point of a horn (so far as efficiency goes) is to couple the acoustically small driver far to the left of center of that graph to the big end’s constant radiation resistance to the right side.
As a result, it is entirely possible to “horn load” a cone driver and get little or no increase in electro-acoustic efficiency and the same thing is what (one of the things) governs the efficient band of most compression drivers.
I was asked to write about loudspeakers a good while back, in a book I have had past editions of for ages. I wouldn’t have accepted otherwise (I am not a writer) and even with Doug’s help, it was something like passing a watermelon through ones colon when finished.
The past edition had a superb, very encompassing chapter on loudspeaker’s so I tried to explain more and spent some extra time things like back emf and on horns if interested (and I did write about this issue as I recall). Anyway, it’s the 5th edition of “Handbook for Sound Engineers”
Best,
Tom
What’s new out your way?