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
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.
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 $R$.
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.