Bob Cain wrote in message ...

Hi, Bob,

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


Since you failed to mention prior work on this problem, or acknowledge its
validity, I will simply state that the -15dB sideband level is in good
agreement with the prediction of Art Ludwig's prior analysis of Doppler
distortion in a tube.

Presuming it built on them, I had not gone past the
unmotivated equations 4) and 5) in his note to see that he
had proposed something similar for two sinusoids as an
approximation further on without regard to those equations.
What I wrote was determined without refering to anything
in that note following equations 4) and 5). The discussion
in sci.physics with Zigoteau was invaluable in leading me to
the answer and that discussion is on the record if not
crossposted to every group in which the discussion found itself.

extracted from previous post

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.

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

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
http://www.nidcd.nih.gov/health/educ...cibel_text.asp

Decibel level What we hear
10 dB Normal breathing
20 dB Rustling leaves, mosquito
30 dB Whisper
40 dB Stream, refrigerator humming
50-60 dB Quiet office
50-65 dB Normal conversation
60-65 dB Laughter
70 dB Vacuum cleaner, hair dryer
75 dB Dishwasher
78 dB Washing machine
80 dB Garbage disposal, city traffic noise
Prolonged exposure to any noise above 90 dB can cause gradual hearing
loss.
84 dB Diesel truck
70-90 dB Recreational vehicle
88 dB Subway, motorcycle
85-90 dB Lawnmower
100 dB Train, garbage truck
97 dB Newspaper press
98 dB Farm tractor
Regular exposure of more than 1 minute risks permanent hearing loss.
103 dB Jet flyover at 100 feet
105 dB Snowmobile
110 dB Jackhammer, power saw, symphony orchestra
120 dB Thunderclap, discotheque/boom box
110-125 dB Stereo
110-140 dB Rock concerts
130 dB Jet takeoff, shotgun firing
145 dB Boom cars

Cheers,

Zigoteau.