The subtlety is this: Imagine you are in the weightlessness of space, and you measure distances by taking a ruler and placing unconnected beads 10 cms apart.

The subtlety is this: Imagine you are in the weightlessness of space, and you measure distances by taking a ruler and placing unconnected beads 10 cms apart. Now a gravitational wave passes through, what do you see? Nothing. The beads don't move. The intervals you use to measure the distance are stretched in the same way as the space you want to measure in the first place. So what you can do is, every milisecond or so you lay a new string of beads into empty space. And now when a gravitational wave passes through you'll see that when you lay the string of beads at the moment the gravitational wave passes it doesn't line up with the previous ones. That you can measure. And by observing the miniscule misalignment of the beads you can see stretching that is much smaller than the 10cm intervals. So the strings of beads are light rays, and their intervals are the wavelength. The difference is that they don't last, but if there is a light ray in there right as the tube is stretched, it get's stretched along with the tube and you would not see a difference with that, whereas the light that's coming right after it will place new beads/amplitude peaks and actually see the stretched distance.