For a wave on a string, a transverse wave, the snapshot graph is literally a picture of the wave. Not so for a longitudinal wave, where the particles in the medium are displaced parallel to the direction in which the wave is traveling. Thus the displacement is $\text{Δ}x$ rather than $\text{Δ}y$, and a snapshot graph is a graph of $\text{Δ}x$ versus x.

FIGURE 16.9a is a snapshot graph of a longitudinal wave, such as a sound wave. It’s purposefully drawn to have the same shape as the string wave in Example 16.2. Without practice, it’s not clear what this graph tells us about the particles in the medium.

FIGURE 16.9 Visualizing a longitudinal wave.

Full Alternative Text

To help you find out, FIGURE 16.9b provides a tool for visualizing longitudinal waves. In the second row, we’ve used information from the graph to displace the particles in the medium to the right or to the left of their equilibrium positions. For example, the particle at $x=1.0\text{cm}$ has been displaced 0.5 cm to the right because the snapshot graph shows $\text{Δ}x=0.5\text{cm}$ at $x=1.0\text{cm}$. We now have a picture of the longitudinal wave pulse at $t_1=0\text{s}$. You can see that the medium is compressed to higher density at the center of the pulse and, to compensate, expanded to lower density at the leading and trailing edges. Two more lines show the medium at $t_2=1\text{s}$ and $t_3=2\text{s}$ so that you can see the wave propagating through the medium at $1.0\text{cm}\text{/}\text{s}$.