"Art Ludwig" wrote in message news:O__7d.3313$gk.2647@okepread01...

Hi, Art,

"zigoteau" wrote in message
om...
Bob Cain wrote in message
...

[snips]
Art must like it loud. At 40Hz, let's say the speaker diaphragm has an
rms amplitude of 1e-2 m. Its rms velocity excursion v is 2.4 m.s^-1,
and hence the power flux is Z*v^2 = 2471 W.m^-2. Sound intensities are
normally expressed in dB wrt 1 pW.m^-2. This works out at 154 dB. This
may be compared to the following table from

First off, this is not the example I include on my site. I use a velocity of
1 m/s at 50 Hz, and this is just to generate some convenient numbers which
can easily be scaled. Second, the relationship you use is valid for a
piston in a tube, but for the real world case of a piston in a baffle the
sound output is much less because the real part of the impedance seen by the
diaphragm is much less than your Z. At 50 Hz a 1 m/s velocity corresponds to
a peak displacement of 3 millimeters which is quite realistic for a woofer.
I invite any educated physicist to look at my site and decide for him or her
self if my derivation is valid. It can be seen at

http://www.silcom.com/~aludwig/Physi...on/dopdist.htm

As you pointed out, I assume the linear wave equation in this derivation,
and for very high velocities, or for propagation in a tube, the
non-linearity of air can be important. I have now analyzed the solution to
the nonlinear acoustic equations as well. That analysis is at

http://www.silcom.com/~aludwig/Physi..._acoustics.htm

I hope my response didn't sound too disrespectful, but Bob was
complaining that my formula gave distortion figures which were too
high. My point was that the values plugged in to the formula
correspond to extremely high acoustic intensities, so large distortion
is not unreasonable.

I take your point about the difference between a loudpeaker in a
conventional enclosure and a highly idealized one in a tube.

I am interested if you have managed to solve the nonlinear wave
equations. I haven't got time to digest it just now, but will look at
your website ASAP.

Cheers,

Zigoteau,