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My teacher told me that pressure variation is maximum at mean position in a sound wave. Though by proof of pressure wave and displacement wave, I am convinced but in understanding the physical meaning I am facing a problem as I have a counter argument. According to me pressure variation should be maximum there at extreme position because pressure is maximum due to the fact that density is maximum as all particles come closest to each other due to compression.Hence by this argument the claim that pressure variation is maximum at mean position contradicts my understanding. please help

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There are two ways to describe a sound wave.
One is in terms of the displacement of the medium and the other is in terms of the pressure variation from atmospheric.
This simple diagram of a sound wave, a "photograph" of a sound wave at an instant of time, shows that the two descriptions are $90^\circ$ out of phase with one another.

enter image description here

According to me pressure variation should be maximum there at extreme position because pressure is maximum due to the fact that density is maximum as all particles come closest to each other due to compression

In a region where there is a compression $C$, the increase in pressure above atmospheric is a maximum and the displacement of the particle is zero.
The same is true at a rarefaction $R$.

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  • $\begingroup$ can u answer as to exactly why what Mathomania said about the extremum position is wrong? $\endgroup$ Sep 2, 2019 at 8:16
  • $\begingroup$ @SchwarzKugelblitz What exactly did Mathomania say? $\endgroup$
    – Farcher
    Sep 2, 2019 at 11:14
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    $\begingroup$ Well he said that because the density is maximum at extreme so pressure should be max there.Why is this wrong? $\endgroup$ Sep 2, 2019 at 11:17
  • $\begingroup$ @SchwarzKugelblitz Who said it was wrong? Please look carefully at my graph which tries to shown that the displacement of the particles is $90^\circ$ out of phase with the variation of pressure. $\endgroup$
    – Farcher
    Sep 2, 2019 at 11:20
  • $\begingroup$ And pressure is minimum at mean position right? $\endgroup$ Sep 2, 2019 at 11:22
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If you want a physical picture of it, you can think of it this way: a depleted region or minimum pressure region is created because particles are moving away in opposite directions from this region. Hence, at the exact center of this region the particle displacement changes its sign: it is null. The same reasoning would hold for a maximum pressure region.I hope this helps.

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I know the pain as i been through the same in understanding why at max pressure the displacement is zero and at max displacement the pressure is normal.but don't worry just imagine what i will tell you and it will be fine.

enter image description here

In the particle displacement curve there are points where particles don't move. These are the points where you get max pressure. Treat these points like nodes of a standing wave. As time passes surrounding particles around these point gather and form commpression at that area. When these particles move away they form rarefaction.enter image description here

The first image shows rarefaction while the second one shows compression .

According to me pressure variation should be maximum there at extreme position because pressure is maximum due to the fact that density is maximum as all particles come closest to each other due to compression.

Your intuition is correct as you can see pressure maxima are there where displacement is max and also as your teacher said the displacement is zero where pressure is max. Its just that you both are trying to express the same thing by two different particles having phase difference of π/2. You have chosen the particles which are moving towards the area that will make rarefaction or compression while your teacher has chosen the ones which are at the place of compression and rarefaction and thus the confusion.

I hope everything is clear now.

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