Care to explain the "very old approach" or the math involved?
Hi Corey, Guys
I am sorry I couldn’t answer this earlier but I have been out of town, but think I can explain the “very old approach” without using any names.
If you measure a vertical axis polar plot of a well behaved single horn loudspeaker, what you see is a single “lobe” or sort of an ellipse which is the equal loudness contour or a line which represents the same loudness.
At the first Synaudcon meeting I went to in the late 80’s, Don talked about the fact one could use the bottom of that contour to make a point source to produce a near constant SPL over a large distance.
The idea was that one aims the lobe at the farthest seat and then mounts the speaker up in the air so that the bottom of that lobe presents the seating plane with a much more constant SPL than the “on axis” spl with always falls off at the inverse square (-6dB per doubling of distance).
This worked great IF one only needed the frequency range a single horn could produce but there are potential flies in the ointment. The polar plots one sees are shown at ONE frequency and if one is producing a range of frequencies, then one finds the shape of that balloon can change with frequency and then the assumption this is based on goes out the window. For example, curved wall horns normally produce a narrower pattern up high vs low and all horns have a “pattern loss:” frequency related to size and wall angle.
For this to work over a range of frequencies requires the lobe shape to be “constant” over that band and if it’s not, then the frequency response changes as a function of listening position and frequency. This is one of the things which drove the development of the constant directivity horn, the desire to have the same spl and have it sound as close to the same over the listening area, over a range of frequencies.
For musical reproduction, the frequency span is far larger than what a single driver can cover and also the acoustic power that is needed is often larger than a single driver can produce which then requires multiple sources.
As John Murrays paper on line arrays discusses to a degree, an array of sources produces a Huygens summation into a new wave front but less understood is they also they continue to radiate as individual sources with their individual directivity and so in addition to the desired result , they also radiate a great deal of energy (lobes) in “other “ directions like up down to the sides and rear, directions you do not want the sound to go if one wants to use this old time approach.
Also with the arrays of sources, one finds a strongly frequency dependant behavior and so what you measure / hear changes a great deal with the position and distance. Also, that configuration radiating as individual sources produces a complex interference pattern which is a problem if the wind starts to blow, the interference from individual sources is so dense it isn’t noticeable as a discrete effect until there is wind or movement, or one measured the time aspect when the individual arrivals spread out any impulsive / transient information..
On the other hand “IF” there was a way to produce a wide bandwidth horn that had constant directivity, then the old time approach becomes a very powerful tool in large scale sound for music.
“IF” there was a way to make one of these powerful enough for a large space, then one can use it here as well.
By radiating as a single acoustic source and not radiating a complex interference pattern, then the effect of wind is also greatly reduced and the “time variable” part of musical information is also preserved.
The degree these things effect large scale sound is not generally appreciated and the directivity behavior is what normally limits the effective working distance of loudspeakers and is why systems often need delay rings etc. Conversely, if the sources are horn loaded and close enough to combine coherently such that they act like one source, it takes far fewer drivers and power to do a given job.
Here are a couple video examples of such an approach in action in a large space I was just at. These were from a handheld video recorder and taken at several distances. Note the one with my daughter showing that if one is not radiating an interference pattern, even a strong wind has a minimal effect. Try headphones.
https://www.dropbox.com/sh/lvtdlbna0fj47vz/JLcYLguKTeThe shaded amplitude sources are a way to alter or shape the underside of that radiation lobe to produce an even more constant spl over distance but like all horns, there is a pattern loss frequency where the radiation pattern is not constant with frequency. The upshot of Don Keele’s pattern loss formula is that the large the horn mouth is and/or the wider the horn angle is, the lower the pattern loss frequency is. The best, most constant results are from the largest horn possible for whatever the needed angle is.
Best,
Tom Danley
