@vzn : a gravitational wave is a quadrupole wave. But if you took a snapshot of it during the horizontal compression, it would look like this:

@JohnDuffield welcome/ thx for dropping by/ info, not familiar with it. do you think the formula has been used wrt the recent black hole pair/ twin mergers? do you know of classical analogies for quadrupole waves? are you saying it would be fundamentally different than a p-wave somehow?

@vzn : I imagine LIGO used the formula to winnow out the noise. A quadrupole wave is a classical wave. It's said to be a transverse wave, but it isn't your typical transverse wave. See this question. It isn't a longitudinal wave like the typical p-wave.

@JohnDuffield ok, reminds me of circular polarization. will have to look into it more. am wondering if s-waves and p-waves are incompatible with circular polarization. not an expert on this. but maybe few experts have looked at the way that waves comparatively vary across different scientific fields. wonder if there are good refs on that somewhere. (am actually working on a "what is a photon" answer at moment)

@vzn : see hyperphysics. It describes circular polarization in terms of two orthogonal transverse electromagnetic waves. That isn't quite right, but it's enough to tell you that s-waves are not incompatible with circular polarization.