I asked a very knowledgeable friend, who actually designs real systems for large venues, to please explain the Inverse Square Law and how it may apply to the Bose system:

"Inverse Square Law is actually very simple. I hope the graphic shows up with this email. But in general, from a point of origin, sound will disperse over an increasingly large area as it spreads out. The same energy that might produce 100dB SPL at 10 feet, will only produce 94 dB at 20 feet from the source. This is because the same amount of sound energy is now, at twice the distance, spread over 4 times the area. So, at any point within that area, the sound pressure level or SPL is now 6dB less.

So, Inverse Square Law is stated as: Sound Intensity is inversely proportional to the square of the distance. Or, more simply that sound pressure decreases 6 dB for every doubling of distance. Of course it works backwards too, so sound pressure increases 6dB for each halving of distance. That is, if you get closer to the source by half the distance, the pressure goes up 6 dB.

This phenomenon is important, but can be overcome somewhat by using line arrays or line sources such as your Bose. For the frequencies above where the line is a multiple of a wavelength, it will focus the vertical wave plane and reduce inverse square to approximately 3dB. This can be important in a reverberant room, minimizing reflections off the ceiling, and energizing the reverberant field a bit less. My guess is that the Boos functions as a true line source somewhere above
1 or 2 KHz. This is not a new idea, and has been used in sound reinforcement for many decades. Remember the old Shure Vocalmaster or the JBL Cabaret Line Array? Those were line sources as well.

This effect of line array systems is the reason why they are used so successfully in high level sound reinforcement. It takes very careful design of the full range box or system, that is then stacked or hung in a vertical array of usually identical boxes. The horizontal dispersion angle remains constant, but the vertical angle can be manipulated by curving the array. Make the top of the array almost straight, (but never completely, or problems occur) say 1 or 2 degree angles between boxes, then make the angle progressively larger so that the array is more curved toward the bottom. That way the maximum focus is toward the rear of the venue, and the array decouples and becomes broader in the vertical for near coverage. With careful aiming it is possible to get very even SPL over the entire arena.

This is what has been done at the Hollywood Bowl, Greek Theater, etc. In practice, though this seems elegant, it can introduce other problems. Just because we can make the rear of the venue almost as loud as the front doesn't mean that we should in all circumstances. This is a vastly simplified explanation. If you would like more technical details, check out the JBLPro.com website for some technical papers. Look for Vertec. I've used a number of those systems in large arrays and they are very predictable in their coverage.

So, your Bose is a simple line source above a certain frequency, and serves to collapse or narrow the vertical coverage, while maintaining an even horizontal coverage for that range of frequencies..

That's probably more than you wanted to know, but there's a lot more than that! We can discuss acoustics when I am in town next."

Hi Joseph,

You have a good friend, who has written a thoughtful explanation.

I would like to add a few things:

I would describe the reduction in reverberant field differently. It is a large difference that lay people can readily hear and appreciate. It is not at all subtle.

About the only similarity between the Cylindrical Radiator(r) speaker and column speakers is drivers in a row. The number of differences are enormous. A good read of our white paper I think would suffice to enumerate these differences.

The narrowing your friend correctly describes goes WAY below 1-2 kHz. To predict the narrowing, one should consider that the speaker is located on the ground, and so the effective height is 4 meters not 2. Interestingly, the effect of doubling the length of the source (from 2 to 4) QUADRUPLES the effect acoustically. Said another way, if a source 2m long has a certain narrowing at frequency x, then a 4m source will have that same narrowing at x/4!!!

Neat, huh?

With best regards,

Ken

Wow, I never realized that the inverse square law applied to sound waves. It is a standard in radiation physics; if you double your distance from a radioactive point source, you receive 4 times less radiation exposure. I guess it must apply to any waveform source (sound, radiation, visible light).
Having walked away from our old 18" mains at many venues (especially outdoor gigs), the dropoff in sound certainly confirms the inverse square law with a 3 tiered setup. The PAS system is a stark contrast in this regard.
Thanks Joseph and Ken for helping put things in perspective.

Jeff
http://www.theunmentionables.com

quote:

Originally posted by Ken-at-Bose:
To predict the narrowing, one should consider that the speaker is located on the ground, and so the effective height is 4 meters not 2. Interestingly, the effect of doubling the length of the source (from 2 to 4) QUADRUPLES the effect acoustically.

Ken,

This is interesting. What happens when we use the Bose Personalized System in a low ceiling enviroment with the L1 nearly as close to the ceiling as the floor? Do we get 6 or 8 times the effect acoustically?

Thanks, Oldghm

Jeff,

The inverse squared law applies to "point sources" (that are creating waves). As you know this is a nic-name for the formula 1/r^2.

A line source follows the 1/r formual and a planar source has no drop in power over distance or basically 1/1.

Now keep in mind all of this is an approximation and is "proven" in the lab where conditions are ideal, but in the real world we can get "close enough" to experience these behaviors, and in the case of the Cylidrical Radiator(r) speaker, enjoy the benefits of the cylidrical wavefront as well.

Steve

Joseph,

No need for my reply. Ken (he's the Bose guy, I would guess, and I
probably know him) is correct about the mirror image created by ground
plane. But it is not necessarily uniform. It might be on a large flat
surface, but consider the typical club with many
obstructions that are larger than a wavelength at mid and high
Frequencies. That is one reason why big sound systems are flown
(better coverage is another, fewer seats "killed" by sightline
obstructions is another) .

This is also why woofers are usually on the ground. They benefit from
this mirror or ground plane effect. It is called boundary
reinforcement, and can give you as much as 9dB boost below say 150 Hz
depending on your placement.

As I said, my explanation was very much simplified, and in the real
world, nothing is ever simple.

At any rate, this could go on for decades and probably will! I'll opt
out while the opting is good...

Have fun!