Do several small Vb's equal one larger Vb?
 

I'm designing a line array but I don't want to use a lot of stuffing, so I'm avoiding the transmission line approach. The whole line is about 5'7" long. My plan is to use two shorter cabinets instead of one long one, and keep the cabs no more than twice as high as they are wide, and to either put partitions between every couple speakers or just shelf bracing between every couple with off-set holes so there is no continuous straight-shot hole from the top of one cab to the other. And thus avoid building an organ pipe.

I've been doing acoustic power and efficiency calculations from Small's paper on vented boxes. I see that the efficiency kp is directly proportional to Vb.
So, with the two cabs I have two volumes that equal a volume twice as large. I also have twice as many speakers as in one cabinet alone, and they are all adjacent in line array style. So if I calculate acoustic power and efficiency based on the total of the speakers and the total volume, I get much higher numbers than I do calculate each (identical) cab separately. Does this really happen? Will it be as if I had the whole number of speakers in one big cabinet?

Might I actually get all the acoustic power benefit and efficiency benefit of the one big cab, but at the lesser enclosure losses that Small associates with smaller cabinets?

It seems that these issues would be quite the same with partitioned off sub-volumes in a single cabinet.

The other issue that comes up is the vent requirements for several small volumes vs. one big volume. Each volume gets its own vent. I'm trying to have as much duct cross-sectional area as possible to minimize vent compression. I get more area with the same duct length from one big volume (or two big volumes, with the two cabs) than I do from one small one.

Or, if I don't subdivide the cab, but use multiple vents, do I use the total Vb of the cab to calculate the vent area?

First off, you don't need a straight shot to create a pipe - the wavelengths are too long to care about little impediments, they just flow around them. That's why folded horns and TLs work.

Beware Small's comments on efficiency, they only apply to the bass, and were to some degree recanted in later papers. Each driver wants a certain volume, and with multiple drivers it really doesn't matter if that volume is separate or combined, except that with several drivers combined in one large cab you get longer standing waves, which in a vertical array brings on the pipe effects you want to avoid. So yes, I think you're on the right track with the idea of separate partitions.

As far as vents go, there are problems at either extreme, so aim for the middle. If you make the vent too big, you end up with a TL*. ;)



* To acknowledge a recent thread, not a "proper" transmission line, but a 1/4 wave resonator, to be more precise. Of course this can work, Augspurger did some work on coupling chamber loaded pipes, while King did the reverse, adding a duct to the termination end of the line. There's lots of ways to skin a cat (as long as the ASPCA isn't watching).

"As far as vents go, there are problems at either extreme, so aim for the middle. If you make the vent too big, you end up with a TL*. ;)"

This would be with too long a duct, right?

Small is recommending .8FsVd for a vent area that keeps the velocity under 5% of the speed of sound. At 343 m/s, that's 17 m/s, and Salvatti et al are citing 10 m/s as the speed where trouble really kicks in inside a duct, so I'm thinking my vent area ought to be significantly bigger than Small's recommendation. With the shelves and so on, I can manage almost half again as big as Small's minimum area with a duct length of 1/12 the wavelength of the speaker resonance, but then I get an organ pipe, however kinky...

I'm off to look into Ausberger.

Do several small Vb's equal one larger Vb?

I have always found several small ones to my liking!!!

Adam

I guess another way of putting it would be- do any number of bottles ever really equal a keg?