While inspecting the intermediate rough of Kentucky bluegrass along a newly established Kentucky bluegrass fairway, you notice several important differences between the fairway and rough turfs maintained at mowing heights of one and two inches, respectively. After using your knife to extract samples from these turfs, you notice some additional differences in visual and functional quality. First, what are these differences? Second, what are the implications with respect to the cultural requirements of these turfs? Finally, as some of the fairway turf exhibits a wavy (washboard) pattern with the ridges running perpendicular to the direction of mowing, what does this indicate (be sure to explain its mathematical basis and influence on turf quality)?