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by DICK CRAWFORD
THERE IS AN INNATE appeal in the use of multiple speakers. It is difficult to dispel the notion that many of a kind are better than one. And why not, for that's the principle of democracy, is it not? What, then, are the advantages of democratic speaker systems? G. A. Briggs, in his 3rd edition of Sound Reproduction (pp. 58-61), discusses some of the characteristics of a system using nine 8-inch speakers. Both good and bad results were noted. Among the former was the ability to produce sound at 30 Hz without doubling, and among the latter was a good deal of boominess. Improvement was gained by being less democratic and replacing two of the 8-inch units with more conservative 10-inch speakers.
Of a more recent vintage is the Sweet Sixteen speaker system, in which sixteen small, low-cost speakers were used. Opinions vary, but many claim improved bass response from this array.
Even more recently we have the Bose speaker system. This unit also has nine speakers, but arranged so as to achieve a large percentage of reflected sound. The reviews of this system are generally excellent. Having listened to this system, I must say that it has much better bass than one would expect from a group of small speakers. I don't care how much the bass is boosted, it is difficult to achieve decent bass much below the resonant frequency of the speakers.
Then, too, we have the example of some speaker manufacturers who make top-of the-line speaker systems using several of their best speakers in parallel (acoustically speaking). For example, I have always had a liking for the large Bozak systems that use four 12-inch speakers for the bass, and Bozak makes it clear that they believe these larger systems to be superior. Now why is that?
Many reasons have been given for the superiority of multiple speaker systems, but the one I wish to dwell on is the superior bass response. This is partly because I like lots of low bass and partly because of my limited test facilities. On to the experiments!
I measured the impedance characteristics of four identical low-cost ($15) 12 inch speakers. The indicated resonance was 38 Hz and varied only by 1 Hz, and the impedance at resonance varied only by a few ohms between the four speakers. The results for one of the four are plotted in Fig. 1.
The four speakers were then mounted in a simple corner enclosure ( which we will discuss later) and the impedance of the single speaker was again measured. As can be seen from Fig. 1, there is some effect due to the combination of the cabinet and the corner placement. The speaker was slightly better damped, and the resonant frequency was lowered by two or three Hz.
Finally all four of the speakers were phased, and then wired in a series parallel combination, so as to achieve nominally the same impedance as the single speaker. The results (see Fig. 1) are gratifying! The resonance has been moved down to 27.5 Hz.
What has happened? Mutual coupling. When several speakers are connected in phase and not too far apart physically, the reactive and resistive components of the air loading at low frequencies are increased. Mr. Knowles has a good discussion of this effect in Keith Henney's Radio Engineering Handbook, 4th Ed. (pp. 741-744). For four speakers the radiation resistance, which is that part of the air loading to which the speaker can deliver acoustic power, is multiplied by four. This is somewhat offset by the increase in radiation reactance, but, as Mr. Knowles points out, a typical speaker system will gain about 5 decibels in bass response by using four similar speakers.
There is more. If we place the same four speakers in a corner we gain another factor of four in radiation resistance. So we achieve another 5 decibels bass boost, for a total of 10.
Does it really happen? A microphone and a.f. voltmeter were used to measure the bass response. With the same 100 Hz signal level the four in the corner were found to produce 5 decibels more output than the single speaker in the corner. At 40 Hz the increase was 12 decibels. That is as low as my microphone goes. I believe that at 30 Hz the increase is more like 15 decibels, but I cannot prove it.
This is mostly in agreement with the theory, although there is more bass increase at 40 Hz than would be predicted. Of course, room acoustics and microphone placement may explain the differences. Incidentally, 10 decibels is not peanuts; it is the difference between a 20-watt amplifier and a 60-watt unit.
But what about that lowering of the resonant frequency? Well, there is the increase of reactive air loading that we mentioned. The resonant frequency of the speaker is determined by the compliance of the speaker, the mass of the speaker cone and voice coil, and the equivalent mass of the reactive air loading. As the air loading increases due to mutual coupling effects, the equivalent mass of the air load also increases, and this lowers the resonant frequency. At this point we need to know more about the speakers in order to calculate the effects of the increased air loading, but we can make a few assumptions and see if the results seem reasonable. From Olson's book Elements of Acoustical Engineering, 2nd Ed., pp. 126, we see that the mass of the speaker cone is approximately equal to the mass of the air loading for representative speakers.
If we then assume that the air mass, due to the twin effects of four speakers and corner placement, is doubled at low frequencies (as seems reasonable from Mr. Knowles curves), we arrive at the conclusion that the total mass is increased by a factor of 1.5, giving a new resonant frequency 1/1.24 that of than the original. Since the measured new resonant frequency is 1/1.27 times the original, either we made compensating errors in our assumptions, or we are very close to being right.
What about damping? Since the resistive part of the air load at low frequencies has increased more than the reactive part, we would expect better damping. A glance at Fig. 1 shows that the impedance of the four in the corner is lower than the single unmounted speaker, so that the damping is apparently improved.
What sort of enclosure was used in these tests? Not much. Fig. 2 shows the design. The top and bottom are made of a 24-inch square piece of %-inch plywood sawn diagonally. The front is 32 x 48 inches, also of 3-inch plywood. A 2 x 4 is used at the rear to space the top and bottom. All are screwed and glued together. The speakers are mounted, phased, and the whole is jammed into a corner. Foam weather-stripping is used to seal the inevitable gaps around the top. The weatherstripping also prevents rattles. There is about a 1-inch gap along both sides which becomes a port. Thus this is a bass reflex cabinet. The main purpose of this port is to avoid the necessity of achieving a seal along the edges. The area of the port is too small in relation to the total cone size to give much radiation. Furthermore, its high periphery-to-area ratio is such as to damp the port radiation rather well. However, the port undoubtedly does some radiating, and it lowers the speaker impedance as well. The volume of the cabinet is just under eight cubic feet. The cabinet does not rattle, but for those interested in making their own cabinets I recommend the advice of Mr. Briggs ( cited earlier ). There you have it, a little curiosity, a simple cabinet, a few simple measurements, and a little theory. How does it sound? Clean. Good opera recordings are very clear, without boominess. Beethoven really growls.
What are the conclusions? Simply that theory and experiment both conclude that multiple speaker systems can give both lower resonant frequencies and more bass.
"Another word on multiple speakers" by John Ward, Audio December, 1962 "Mutual acoustic impedance between radiators in an infinite rigid plane" by R. Pritchard, J. Acous Soc. Am. 32, No. 6, 1960
"An open-baffle parallel-series array" by R. Oakley, Audio December, 1963 Loudspeakers, by Gilbert Briggs (Cahners Publishing Co., 221 Columbus Ave., Boston, Mass. 02116)
(Audio magazine, Nov. 1970)
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