Originally Posted by
RMC
Hi Ian,
Re your sept 8 post # 86 with a tricky question about excursion when doubling cone area. I see nobody replied to you 4 days later... For myself I didn't reply since I had already seen part of the answer, and may be told I cheated.
However, If you look at my post # 82 dated sept 4 (4 days before yours) you can see I quoted from Dickason's Cookbook, 5th ed., p. 30-1. On those same Dickason pages I read 4-5 days before your question, a partial or incomplete answer to your question appears. So no real contest. Read below for more.
However again, I'm NOT satisfied with his explanation of driver coupling effect on sensitivity, doesn't seem to make sense, looks like a contradiction or typo made its way in his text. This is why in my sept 4 # 82 post I quoted John Eargle instead for the coupling effect on sensitivity issue, and Dickason on the voltage/impedance issue.
That speaker experts seem to disagree on science (!) is surprising, but does exist. Look at Bullock's book on p. 62 bottom right column where he says + 6 db for two woofers in parallel, and on p. 66 left column from the middle and on where he repeats that, as opposed to Eargle's clear explanation of + 3db for coupling and another possible + 3 db for power handling I quoted in post # 82 (Handbook of Sound System Design, p. 114, and Loudspeaker Handbook, p. 79). Then have a look at Dickason's, 5th ed., p.30 for a confusing explanation of 3 vs 6 db in 1, 2, and 4 woofer formats ...
I tend to give more credibility to Eargle since his manuscript was reviewed before publication by W. J. J. Hoge, another well-known Speaker Engineer, who would normally have picked-up a gross error... JBL's own Sound System Design Reference Manual says the same as Eargle (Authors: Augspurger and Eargle).
Same power input to identical single and double-woofer (in parallel and closely mounted) boxes, gives a 3 db sensitivity advantage to the double-woofer box and cone excursion would be half that of a single woofer box. Dickason stops here, the rest is mine.
This makes sense because a larger cone area can move more air or "take a bigger "bite" at it" and need not go as far (excursion) to reproduce the same sound. If I remember correctly the good old days, the E-V 30" woofer and the Hartley 21" woofer didn't have nor needed a lot of Xmax considering their huge cone area that moved lots of air more efficiently.
But since you mention specifically "for the same output spl" then that would imply a half reduction in input power to the double-woofer box (to get - 3 db) for spl to be equal to that of single woofer box. Logically, lower input also means less excursion and distortion, therefore the answer would be "quarter", if its already half the cone travel at + 3 db as mentioned by Dickason for double-woofer compared to single. Regards,
Richard