Now is the time for the tricky details. Let's take 'em one at a time. When it strikes an object, this wave initially compresses it horizontally and stretches it vertically. Then it reverses the treatment and stretches horizontally and compresses vertically. It alternately stretches and compresses in perpendicular directions.
Nothing happens along the two diagonal directions.
This is traditionally called the plus polarization. This diagonal axis oscillation is traditionally called the cross polarization. S o, you see, the two waves are similar in that they both affect stuff perpendicular to the direction in which the wave is going. They are also similar in that the electric and magnetic fields are perpendicular to one another, just as the compression and expansion are also perpendicular to one another. I am cheating on this section because I'm only going to introduce the fundamental particle of the gravitational wave.