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I was looking at this question, which contains this animation.

It is my impression that the upper part of the animation is not consistent with the lower part.

In the upper part we see that a piston is displaced forward and returns to its original position. So it should create a compression pulse (or a train of pulses, if the operation is repeated successively), but not a full cyle of compression followed by rarefaction. In fact the animation only shows compression followed by return to ambient pressure, as one could expect.

However, the lower part depicts a pressure wave as a succession of full cycles, where the sequence is equilibrium at atmospheric pressure, a positive peak over that (compression), equilibrium again, a negative peak below atmospheric pressure (rarefaction), return to equilibrium and so on.

I tend to think that the lower picture would be ok if they had not labeled it with 3 heights "max - Patm - min", but instead 2 heights "max - Patm" and maybe if they had placed the curve over the mid-line, i.e. something akin to the typical string pulse.

Am I right or did I miss anything?

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  • $\begingroup$ Maybe start with the piston going left, than you see that there is "rarefication or less pressure than the surrounding air. $\endgroup$
    – trula
    Aug 1, 2022 at 15:09

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I believe they are effectively de-synchronized. When the piston is at the left-most extreme it should be the maximum amplitude of rarefaction (where I define rarefaction as the process in which it begins to lose pressure, that is, after the maximum of compression); as it begins to compress again it should start to increase the pressure. Perhaps you are working with a different concept of compression/rarefaction: you call it compression when the pressure is bigger than the atmospheric one, and rarefaction when it is lower; I am using it as the moment in time when the pressure is increasing (compression) and when it is decreasing (rarefaction)

You wouldn't know if there was more rarefaction than it had in the beginning, after the compressive motion ends, given that you don't know (or haven't mentioned) that it started with the piston in the middle of the cycle or at the left extreme (I assume we are modelling this mathematically as if it has been doing this for eternity).

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    $\begingroup$ There are 2 senses in which to model the oscillation of pressure: (i) pressure wrt ambient (which is separated by pi/2 from displacement wave) and (ii) pressure gradient wrt to other areas of the medium (which goes in phase with displacement). The animation chooses (i) while you seem to have in mind (ii). That is why you see a de-synch but there isn’t if you adopt the (i) view. The problem is not synching but the fact that the picture above paints a pulse (where rarefaction wrt ambient is absent) whereas the one below paints a full cycle (where it is present). $\endgroup$
    – Sierra
    Aug 1, 2022 at 20:23

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