"ruffrecords" wrote in message
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Karl Uppiano wrote:
"ruffrecords" wrote in message
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Karl Uppiano wrote:

The flaw in this argument is that this set up assumes it is the same as
the linear superposition of the of the two signals in a single
transducer. it is not.


A single loudspeaker reproducing the linear sum of two different
frequencies. The higher frequency "riding" back and forth on the lower
frequency. Will that not affect the wavelength of the higher frequency
as a function motion of the diaphragm due to the lower frequency,
assuming the speed of sound in air remains constant under these
conditions?




Go look in a good text book for the words 'linear' and 'sum'


Why don't you just answer my question, and forego the superior attitude?
I'm sure you can figure out what I meant.

OK. No, otherwise it would not be a linear sum. Hence my reading
suggestion.

I understand what "linear" and "sum" mean. When modulated by two sinusoids,
the x position of the diaphragm as a function of time is defined by

x( t ) = A sin( w1 t ) + B sin( w2 t )

Where A and B are the amplitudes of the two frequencies, and w2 and w2 are
the frequencies in radians per second of the two frequencies. Let's call w1
the low frequency and w2 the high frequency. There are no non-linear terms
in this equation, so we won't get harmonic or IM distortion. I understand
that.

Since Doppler shift is based on the velocity, not the position of the
diaphragm, we must differentiate this equation. The velocity of the
diaphragm as a function of time is then

v( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t )

The formula for Doppler shift is

ls = lo ( 1 - ( vs / c ) )

where

ls = the resulting wavelength (lambda shifted)

lo = the original wavelength of the higher frequency (lambda original)

vs = the velocity of the source (diaphragm velocity)

c = is the speed of sound in air

therefore, substituting v(t) for vs,

ls( t ) = lo ( 1 - ( ( w1 A cos( w1 t ) + w2 B cos( w2 t ) ) / c ) )

which appears to my eye as a time-varying wavelength based on the diaphragm
velocity. What am I doing wrong?