Isn't that just a matter of visualization, though? You can visualize (a static snapshot of) a 1-dimensional compression wave as the flattening of a 2 dimension

Isn't that just a matter of visualization, though? You can visualize (a static snapshot of) a 1-dimensional compression wave as the flattening of a 2 dimensional sine wave. More generally, any n-dimensional space with varying "density" can be viewed an n+1 dimensional space, where the extra dimension is the "density" dimension. Maybe a "stretch".