From: gt0869a@prism.gatech.EDU (WATERS,CLYDE GORDON)
Newsgroups: rec.audio.car
Subject: Re: 2 subs vs. 4
Date: 5 Oct 92 13:49:36 GMT
Organization: Georgia Institute of Technology

In article <1anki8INNlgd@usenet.INS.CWRU.Edu> kmr4@po.CWRU.Edu (Keith M. Ryan) writes:
>In a previous article, gt0869a@prism.gatech.EDU (WATERS,CLYDE GORDON) says:
>>No, the output from the 4 10" woofers will in theory be 3 dB louder. 
>>This is from mutual coupling- every time you double the # of drivers,


>	When you add additional speakers, if the total power in remains
>constant, then the total acoustical power out will remain fairly constant.

Not when you include mutual coupling effects! The efficiency (which starts
out like less than 1%) typically DOES increase when multiple drivers are 
used in conjunction! This can easily be proved to work for low frequencies
by basic acoustic radiation theory- the acoustic impedance changes in such
a way that the transfer of energy from the speakers to the air is more 
effective, irregardless of the power input. However, this ONLY works for 
speakers operating in the uniform source mode- usually below 200 Hz or so
for average woofer baffle areas. Higher frequencies operate in either 
hemispherical or more directional radiation modes, so this does not have
any effect at HF. 
 
 
>( you will have some lobing effects which will increase volume in certain
>areas though ) However, if when two speakers are hooked up, the amplifier
>delivers more total power ( let's say double the power into 2 ohms ), then
>adding speakers will increase accousitcal power output.

Yes it will; if you double the power by adding the speakers, you will get 
_6 dB_ more output, not 3 dB. You will get 3 dB from the extra power, 3 dB
from the coupling effects, almost always.

  
>1 watt and you get 90 db's. If you add another woofer, with 1 watt
>total in, you do not get 93 db's out. [ argh, that really is not the
>right terminology, one should deal with the total acoustical energy ]
>if that were so, then we could add another woofer, and get 96 dB's for
>only 1 watt. But then we could add another one.... till finally we
>have 12 woofers, 1 watt in with a total output of 133 dB's! Come on, 

Not quite correct- every time you DOUBLE the # of woofers, you WILL get
approximately 3 dB more sensitivity in near field! So, if 1==90 dB, 
then 2==93 dB, 4==96 dB, 8==99 dB, etc!! This has been verified!!
This works until you get to sizes so big that one woofer cannot couple
with all of the other woofers( which would prohibit using 50 woofers, 
I guess :-). 

>>to losses, bad placement, etc- it does work to more or less extent in
>>all multiple driver systems. I have both calculated (I wish I could find

>	Probably was a localized increase ( and a subsequence decrease in
>another local ) or the power input was not held constant.

Don't know about far field energy, but this has been verified for near field. 
Power measurements have been taken vs. output level, as well as verification 
by theory. For reference, look up Dr. W. Marshall Leach's articles on
woofer enclosure design, or his Georgia Tech EE4026 Audio Engineering
class notes, for all the equations, theory, etc. behind this.
It's all there in the theory!!

Regards,
Gordon.
 
-- 
WATERS,CLYDE GORDON-Georgia Institute of Technology Atlanta Ga 30332 
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