I'll let this continue as a discussion about steering and beam forming, but let's leave the Danley products out of it.
I too have a fair amount of experience with J1, but enough of the "whatever" vs point source debate.
Hi Doug,
You didn’t leave much wiggle room to answer Yoel’s question or discuss two completely different approaches to beam forming, or the theory behind each.
While I have made loudspeakers since the 70’s, my interest in how sources behave began working with acoustic levitation for space flight hardware in the 80’s, up until then, I never gave much thought to how sound radiates and tended to think of a pa system as something like a bank of lights. That changed working on levitation systems which required a “beam” of very intense sound and where side lobes were very harmful to levitation stability.
One can form a beam two simple ways, one is a horn, with a CD horn producing a near constant beam width over a range of frequencies and the other is with an array of sources as describe in Huygens theory and originally applied to light.
In the latter, the assumption is that there is both constructive and destructive interference “in front” of the sources as the individual radiations combine and cancel depending on their phase in what’s called Vector addition.
While each source is often too large compared to the wavelength to coherently combine or add everywhere, there is a region in front where they do add constructively. This can be used to produce the desired beam and by altering the phase angle between sources, that beam can be steered. This was applied extensively with sound in the early sonar arrays my old boss and acoustician developed back at Mullard labs in WW2.
The unspoken part of that is that there is more than one beam produced and with loudspeaker which cover a vast span of wavelengths, what you get “out front” is also strongly dependant on both the wavelength and size of the array of sources. The other part is while you get a beam, you also have sources more than ¼ wavelength apart and this dictates that they produce an interference pattern, a pattern of lobes and nulls spatially distributed around the array and visible when a high resolution polar plot is made. This spatially dependent interference pattern and not loudness is what limits the usable “throw” of the array approach.
The big sonic difference between this and a CD horn is seen IF one examines the Time aspect and not the steady state view which is normally the only way arrays are examined. With an array of sources, each one has a “vertical beam width” and this beam width is strongly dependant on frequency and below that point, the sources radiate independently and increasingly broadly and follow the Huygens theorem forming the new radiation.
The CD horn on the other hand confines the radiation from a single driver to the angle defined by the horn wall and dimensions, following Don Keele’s “pattern loss frequency” rule of thumb which in inches is 1X10^6 / horn wall angle / horn mouth dimension. That dictates that a 12 inch tall horn with a 10 degree horn wall angle losses pattern control around 8300Hz for example and the angle doubles each octave you go below that frequency, also the pattern loss frequency halves each time the horn wall angle or horn mouth dimension is doubled.
The differences primarily are that above pattern loss F, the horn not producing an interference pattern, generally radiates much less energy above, below and behind the horn than an array for the same beam width.
In large rooms like stadiums etc, this is a good thing and needed to maximize intelligibility and musical articulation and can be seen in the Hopkins Stryker equation where N is the number of sources and Q being the directivity of the source (the difference between the energy radiated in the desired pattern vs the rest radiated outside the pattern)
http://www.acousticworx.com/sound%20system%20design%20hopkins%20stryker%20formula.htmlSecondly, out front in the time domain, the full range horn is a single source and produces one arrival in time, a single finger snap arrives as a single sonic event while the array of separately radiating sources delivers one arrival for each source, each separated in time and at a level depending on frequency, beam width at that frequency and distance to each individual source.
In this regard, for a given identical beam width, the single source is much more like the input signal than the array which is inherently dispersive in the time domain due to the extended size of the radiation area. An Energy vs Time measurement shows this very clearly.
Since we hear not only amplitude but also much of music and voice especially IS TIME VARIANT this part is a key but often forgotten element in this kind of discussion.
Hopefully this was helpful and more scientific than marketing.
Best,
Tom Danley