The 2003 answer to this referred to the vehicle suspension as being an important aspect of washboard formation, but it seems there only has to be something dragging the loose material and it forms into waves itself.
Where I live, washboard roads are formed by the grader machinery riding up and down the rocks embedded in the gravel. Every so often the municipality would lay down a fresh layer of gravel and the road would be washboard free for the next year or so, until either the rocks bubbled up due to frost, vibration from all the driving or the layer of gravel was graded away.
There may be other causes, but when I look at washboard pretty much every ripple corresponds with a rock visible on the surface.
I’m bringing this to Cecil’s attention. While we don’t normally update Staff Reports, he might want to make a column out of it. I don’t know, I can never predict, I just be sure he sees lots of stuff and then he decides what he’ll do with it (if anything.)