Cardinal Meadowhawks lay eggs while the males and females hover in tandem—this is how the male guards "his" female in this species. Here's a photo of a pair of Cardinal Meadowhawks hovering in tandem over an egg-laying site:
They hover for a second or two as the female gets ready to lay one or more eggs. They then dip down and drop off the eggs. The wingbeat frequency during this process is approximately 48 beats per second—that is, five frames at 240 frames per second.
In addition, it's possible to see how the wing beats of the male and female are related to one another. One might think they flap in sync with one another, but that's not the case. Alternatively, one might think they flap independently, but again, this is not the case. What they do is the following:
(1) The female's hindwings flap first.
(2) After 2/5 of a cycle, that is 144˚ of phase later, the female's forewings flap in unison with the
male's hindwings. This is the key aspect of the hovering flight.
(3) The male's forewings flap 1/5 of a cycle (72˚) later.
(4) Finally, 2/5 of a cycle (144˚) later the female's hindwings flap for the next cycle.
There's a definite relationship between how the male and female flap, it's just not what one might imagine.
Here's a plot that shows the wing positions for both the male and female as a function of time for two cycles:
This same type of phase relationship between the male and female has been seen in Red-veined Meadowhawks and Autumn Meadowhawks. It will be interesting to see how widespread this behavior is among other species.
For a bit more detail, let's take a look at frame-by-frame screenshots for a typical cycle:
Here's frame 1 of the cycle. In this frame, the female's hindwings are up.
Next, frame 2 (recall that the frames are taken at 240 frames per second).
Frame 3 shows the female's forewings and male's hindwings in the up position.
Frame 4 shows the male's forewings up.
Frame 5 ends the cycle.
Frame 6 starts the next cycle, with the female's hindwings up again.
Very interesting phasing between the male and the female.