zigoteau wrote:

Bob Cain wrote in message ...

Hi, Bob,

Good to see that you're still sticking with it.

I think I got it, finally, and I thank you again for the
fruitful discussion.

For a two tone Vd(t), one at 40 Hz and another at 2 kHz and allowing
a motion of 2 cm (a reasonable Xmax for a two way system) the RMS IM
distortion sidebands about the 2 kHz fundamental near the speaker
face are on the order of .2% of that fundamental. While of some
signifigance compared to other portions of an audio chain, it
probably isn't for a loudspeaker given its other distortion
mechanisms.


I presume that these are the values given by Art Ludwig that I asked
for. Thanks.

Those aren't his. I used the parameters I did because they
more closely relate to real world speakers in enclosures
(even though the analysis is for a plane wave.) The .2%
distortion figure I gave was an error caused by my
accidentally plugging .01 as the velocity rather than the
position magnitude. With that corrected, the distortion
becomes a whopping 25%.

I thought I had posted his for you. Sorry if I failed to do
that (ah, I see that post still in my drafts folder.)

He has recently used 100 Hz, 8000 Hz, .04 m/s, .0004 m/s.
In a plane wave that would be 119 dB SPL and 77 dB SPL in a
tube. That only gives a LF excurison of 6.4 E-5 meters.
The ratio of RMS IM distortion to the HF signal for those
parameters is 0.66%. Even this small amount is signifigant
compared to other factors in the recording/reproduction
chain were it the only source of speaker distortion.


I've improved my value for the acoustic impedance of air, from values
given on

http://hypertextbook.com/facts/2000/RachelChu.shtml and

http://www.rfcafe.com/references/gen..._still_air.htm

The values c=343 m.s^-1 and rho=1.25 kg.m^-3 give Z=429 Pa.m^-1.s

Thank you. I took my approximate values from Pierce's text.
Not sure why he'd have used Z=300 Pa.m^-1.s which is quite
different.


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.

Again, it was I who plugged in that number because it is a
reasonable excursion in real world situations due to poor LF
coupling to the air. I am hardly sure, however, that mixing
apples with oranges by using a plane wave analysis with
nearly point source conditions leads to anything meaningful
so that 25% figure needs be taken with a grain of salt.
I.E. I'm not sure how well LF piston velocity in an
enclosure is coupled to motion of the air immediately in
front of it.


Thanks,

Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein