[sdiy] inductors, B fields, and confusion

[Don Tillman]

   > From: <rkmoore at memphis.edu>
   > Date: Fri, 11 Jun 2004 22:27:51 -0500
   > 
   > I've got a bit of a physics question that applies to an electroacoustic 
   > project that I'm trying.  It's not exactly this, but this is the best 
   > analogy of the problem without going into details:

I figured.  :-)

   > Which will sound louder, an amp driving a speaker cabinet with two 16 
   > ohm speakers wired parallel, or the same amp driving two 4 ohm speakers 
   > wired in series?  In both cases the amp is running at an 8 ohm load.  
   > The assumptions to take into account are that the voice coils of the 
   > speakers have the same diameter for all of the speakers and the gauge 
   > of the voice coil wire is all the same.  Also, the magnet weights are 
   > the same.  Consequently, there should be four times as many turns of 
   > wire in the voice coils of the 16 ohm speakers than in the 4 ohm ones.  
   > Does this mean that the magnetic field strength for the 16ohm speakers 
   > will be stronger for a given current than the B field generated in the 
   > 4 ohm speakers?  
   > 
   > Does this mean that the 16 ohm speakers would be louder or am I 
   > skipping something?  Is there some sort of physical saturation point 
   > that I'm ignoring? 

I believe so.

The bible on this is the original Neville Thiele article
"Loudspeakers in Vented Boxes", parts 1 and 2.  Also the Richard
Small articles.  These are nicely reprinted in the Loudspeakers
Anthologies available from the Journal of the Audio Engineering
Society.  

(I haven't looked at these for a while, so it's entirely possible I'm
missing something here.)

Thiele states that the efficiency of a speaker is:
  eff = (rho/4 pi c) (B^2 l^2 Sd^2 / Re Mm^2)

(details in the article)

The interesting parts here are Re, the dc resistance of the voice
coil, and l, the length of wire in the magnetic field.  The 16 ohm
speakers will be louder because they have some many more windings in
the magnetic field.

  -- Don

-- 
Don Tillman
Palo Alto, California
don at till.com
http://www.till.com