@deadbeat the nexo reference was regarding their high frequency horn which is basically folded. The only relevance to this thread is that if they can get very high frequency sounds round a fold, then it should be posible to do the same with a bass horn
Nexo uses what they call a Hyperbolic Reflective Wavesource which consists of an acoustical reflector (i.e. mathematically calculated hyperboloid acoustic mirror, derived from rigorous geometrical transformations) this creates path lengths from the virtual and real sources,
to the horn mouths that are identical at the coupling points. Where the two wavefronts touch they will therefore be in phase because the pressure wave takes the same amount of time to travel an identical path length to the coupling point, regardless of where its real source is located in relation to that coupling point .
With some rigorous head scratching, trying to remember my A level maths I believe that the equation for a hyperbola is:
x^2 / a^2 - y^2 / b^2 = 1
Obviously deriving a curved reflector from that equation makes all the difference.
For my version, I shall use the more impressive looking equation of an ellipse:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
The fact is that any surface will act as a reflector. Changing the rate of curvature just changes the focal length Saying that one particular curve is optimum is a bit like saying that there is an ideal pair of glasses that will work for everyone with impaired eye sight. It is still a folded horn and having a curved back section won't eliminate the problems associated with folded horns.
Also the idea that if the sound sources all emanate from the same virtual acoustic centre all will be well is wrong. If you had a row of say four of these horns and stood directly in front of one then if you are in the coverage area of the other horns the path length will be different. The problem is that the path difference after the sound comes out of the horn is the problem.
What has all this got to do with bass cabinets. Simple, stop worrying about the design and concentrate on the marketing.
Meanwhile, back with the ported horn.....
Consider collapsing the mouth of the horn down so that it is a simple tube. Drilling a hole in the side of the tube and connecting a chamber to it with a short pipe will create an acoustic notch filter. Moving away from the resonant frequency the attenuation reduces to zero. As I said before, if the port is to increase efficiency below the operating range of the horn, it, the horn, won't increase the gain of the sound radiating from the port. It will to some extent alter the tuning of the port so conventional calculations used for tuning may be wrong.
If you have not seen it already, there is some interesting reading on horns at Martin King's web site.
<a href="www.quarter-wave.com/Horns/Horn_Theory.html" target="_blank">
www.quarter-wave.com/Horns/Horn_Theory.html
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