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Figure 18-5

*b*shows an oscillating element of air of cross-sectional area A and thickness [itex]\Delta x[/itex], with its center displaced from its equilibrium position by a distance

*s*.

From Eq. 18-2 we can write, for the pressure variation in the displaced element,

(18-16)

[tex]\Delta p = - B \frac{\Delta V}{V}[/tex]

The quantity V in Eq. 18-16 is the volume of the element, given by

(18-17)

[tex]V = A ~ \Delta x[/tex]

The quantity [itex]\Delta V[/itex] in Eq. 18-16 is the change in volume that occurs when the element is displaced. This volume change comes about because the displacements of the two faces of the element are not quite the same, differing by some amount [itex]\Delta s[/itex]. Thus, we can write the change in volume as

(18-18)

[tex]\Delta V = A ~ \Delta s[/tex]

...

They go on to make some substitutions and take partial derivatives to find some stuff. If that text would be helpful, just ask and I'll copy it into a post. My question, however, is this: Why aren't [itex]\Delta x[/itex] and [itex]\Delta s[/itex] the

*exact same thing?*How is the "difference between the displacements of the two faces of the element" different from the "thickness" of the element?