Hi
Both Bill and John have touched on the “bits” but since I have been writing about this and it’s fresh in my mind, I would also reply.
Everyone who has looked at making a bass horn has seen the reference to the ideal mouth size, a daunting 1wl in circumference. If you look at the acoustic radiation resistance curve for a radiator / horn, you see that that point is approximately where the curve goes from slanted up to flat.
This curve has Frequency on the horizontal and resistance on the vertical. The “impedance transformation” part of a horn is the coupling of the large end where the resistance is greatest, to the small end which has very little loading. If one makes the horn mouth that ideal size, one has insured that at any frequency above that, it will always present a constant load (the flat part of the radiation resistance curve). Also, making the horn much larger, has no further effect on loading but can control directivity.
It follows then that at 20KHz where the wavelength is only 5/8 inch, that ALL of the impedance transformation takes place well before reaching even a 1 inch exit.
In a wide band horn, one can picture that the active portion is the entire length at the low cutoff but the “active” region moves towards the compression as the frequency climbs.
Past the active (impedance transformation) portion of the horn is a part where the horn is still confining the radiation angle. Once one is in that region, if you change the horn wall angle or have a discontinuity, it is possible to radiate from that location like with edge diffraction etc. Earl Geddes waveguides are a case where the horn wall angle is changed at a precise rate which avoids that problem.
As you move closer to the horn mouth, you reach a dimension large enough relative to the frequency where the wave can be “launched” free form the horn but still maintain that shape. Don Keele discovered this and through several of his papers (beginning with “what’s so scared about exponential horns) arrived at the “pattern loss frequency” thumb rule. Given the dimensions, the frequency and horn wall angle, one can find the frequency down to which that horn angle will maintain that radiation angle.
So in addition to the acoustic transformation region moving towards the driver as the frequency climbs, so does the pattern control point.
This is why an exponential (normal curved wall horn) has a narrowing radiation angle with increasing frequency.
Also, what you want to avoid is doing anything to the wave front, once it is large enough to have it’s own directivity because that can easily cause a secondary radiation from that point and radiation from more than one point (points more than ¼ wl apart), this produces an interference pattern.
To “fill” out a horn, you do not want a source which already defines the radiation angle, that is what you want the horn to do. So, one can consider how the driver radiates as a simple source before adding the horn to it to make sure that it is the horn, not the driver that is defining the pattern. This plot shows the radiation angle produced by a simple source give different acoustic dimensions.
http://www.soundandcommunications.com/archive_site/audio/images/2005_pics/sc05_09_audio10.gif
On the BMS drivers (Hi Jack), I like these a lot because many radiate an expanding wavefront into the conical horns I use. This makes the acoustic path more like a continuous horn down to a small dimension and then what radiates is as much like a spherical patch as possible. They have other advantages in output and an usually low resonant frequency (more like a TAD) which makes the Synergy crossover easier into 5 in mids.
I use the 1.4 inch coax drivers too, they are really powerful but to be clear, they are projecting a well defined beam at 20Khz due to the dimensions and configuration and it is difficult to make the same phase shift free Synergy horn xover passively. That aside, it is a really powerful and good sounding driver.
Best,
Tom Danley
