More acoustic beamformer questions

Keith Larson <k-larson2@NOSPAM.ti.com> wrote in message news:<3F9E91AD.1010304@NOSPAM.ti.com>...
> Hi Tom, Rune and Fred
> 
> I noticed one thing missing.  A common mistake when summing the signals 
> is that you cant sum power.  Instead you need to sum voltage, or in this 
> case its equivilent (if I remember correctly this is atmospheric pressure).
> 
> Consider the power density at a given radius R from the center
> 
>     P_R = Pin/R^2
> 
> Therefor for Voltage, that you can sum, you need to take the square root
> 
>    V_R = V_in/R
> 
> I ran into this many years ago when I designed a 'line source' array of 
> 16 full range 3" speakers (plus 24 tweeters).  If you think about this 
> for a moment you can visualize that at a given finite distance you will 
> be closer to some speakers than others and that the resulting wavefront 
> will not be spherical (like with one speaker) but a limited length 
> (truncated) cylinder.

The infamous "near field effects"... with bad lick you need to take 
phase fluctuations and local airflow into consideration as well. 
I saw a simulation of a sonar transmitter array where some of the 
elements actually acted as acoustic sinks, transforming the acoustic 
pressure back to electrical current. 

In my applications I have always assumed the "far field approximation",

  1/R_max = 1/R_min

to be true (R_max is the largest and R_min the smallest source-reciever 
distance). 

In a room there is also the problem of normal modes/standing waves and
multiple paths. It's not obvious how a beamformer will work (even if it 
will work at all) in a room.

> Solving for the frequency response for any arbitrary point is an 
> interesting problem.  I did so using calculus (difficult), FFT of the 
> imulse response and a direct computer simulation.  All three matched, 
> but what was interesting was that it gave a 3db/octave rolloff of the 
> high frequencies.  Better yet... it matched the measured response.

Three simulations that not only agreed with each other, but also matched 
the real world? That's not an everyday event. Great work!
 
Rune

Tom wrote:
> I was just wondering if an acoustic beamformer can be made to work in
> reverse. Suppose we have say eight loud speakers, can the sound be
> focused in a narrow 'corridor'? To a certain extent I expect hi-fi
> surround sound is doing something similar but there the speakers
> surround you - here they would be together in an array.I wonder What
> would happen in the limit ifwe could have say 100 small loud speakers or
> similar transducers?
> 
> Tom
> 
> 
Ideally the principle  of reciprocity would apply.  Most of the 
(receiving) beamforming literature assumes that each transducer has no 
effect on the the other transducers around it.  Mechanical impedance is 
  force/velocity.  When you have a group of transducers pushing on the 
same column of air, you have coupling effects that can't be neglected. 
There's a short section in Urick's book "Principle of  Underwater Sound" 
if I recall correctly.  I had an opportunity of taking a class that 
Urick taught and one of his comments was that people fried a lot of amps 
before they figured out what was going on.