"Bob Cain" wrote in message
...


Karl Uppiano wrote:


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 )

It is the piston velocity v(t) that follows this for equal sound pressure
at all frequencies.

Hmmm... what is the equation for x( t ) then?


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 )

That would be the acceleration a(t) which has no acoustic consequences.

Isn't velocity the first derivative of position? Isn't acceleration the
first derivative of velocity? It seems that acceleration (if we cared about
it) would be

a( t ) = - ( w1^2 A sin( w1 t ) + w2^2 B sin( w2 t ) )

However, all three equations only differ by a constant. So I believe you
could get the same physical consequences by simply adjusting A and B
accordingly.

I'm too tired right now to follow those corrections all the way through
the rest of your welcome attempt to quantify this but would you consider
working them through to the conclusion you can reach?

My end result would differ by a constant (i.e., it would have a different
magnitude), as I mentioned above, but I believe the phenomenon would be the
same.

Thanks,

Bob
--

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

A. Einstein