"Bob Cain" wrote in message
...

1. The piston will move exactly in step with the motion of
the air molecules as the pulse passes by it.

Disclaimer: I am *not* stating anything here as an expert in this field.
Other than being a musician and doing some recording at home, my only other
"experience" in mathematical acoustics was building my own bass cabinet
years ago. I used some formulas from a book to cut in the proper port for
this particular woofer and cabinet volume. I'm just trying to use logic and
imagination.

With that said, I respectfully disagree with #1. :-)

First, the piston will stop moving at some point and return to its starting
position. The air molecules will keep moving until they run out of energy.

Second, think about there being two pulses. If the second pulse arrives
after the piston returns to its starting position, then the duration between
the pulses will be exactly known. Therefore, the frequency of the pulses is
exactly known. If the second pulse arrives while the piston is still moving
forward with the first pulse, then the second pulse strikes the piston while
it's in a different position than when the first pulse struck it. That pulse
has traveled farther than in our first scenario. If you were to measure the
duration between the pulses in this scenario, it would be greater.
Therefore, a form of distortion is introduced.

Another way to imagine this is if the piston did *not* return to its
starting point. Assume at some known point in relation to the energy of the
wave that the wave can no longer push the piston. The piston then becomes
stationary at that new position. The next pulse that came along would strike
it at some distance X from where the first pulse struck it. This pulse in
turn would carry it some distance. Then the next pulse and so forth. No one
would argue that such a piston would accurately reflect the frequency of the
pulses. That would be Doppler in its truest form, right?

Let's resolve this premise before we move on.