Are gravitational waves supposed to be that weak or is it because of the distance between us and those black holes? Do they lose power as they travel through space?
For comparison, the wave that was detected is claimed to be "four one-thousandths of the diameter of a proton". That's about 7e-18 meters, on a baseline arm length of 4 km, so about one part in 6e20 -- about 175,000 times stronger than the waves Earth's orbit produces. And that was about 40x as strong as minimal sensitivity on LIGO, according to the article ("can detect changes in the length of one of those arms as small as one ten-thousandth the diameter of a proton").
Obviously if we were closer to the black hole collision we'd see much stronger waves. But you really do need very massive bodies accelerating very much (or equivalently orbiting very fast) to produce something that's detectable by LIGO over interstellar distances at all. The key part from this article is that the orbital period was about 1/250 of a second at the end; compare to Earth's orbital period. Going back to the formula given in the above Wikipedia entry, the frequency dependence is hiding in the "1/r" factor for the amplitude. 1/r is proportional to w^{2/3} (though it's not clear to me whether that's still true in a general-relativistic treatment; it's true enough for the Earth's orbit), which tells you how the wave amplitude scales with frequency...
Only that in space, it drops even faster: The wavefront carries the same energy, but spread out over ever increasing length/area. For gravitational waves (or radio waves) they form spheres, not circles, and the surface size scales with r^2, not r. (Also water waves are /complicated/)
As others have said, intensity (power per unit area) decreases according to the same inverse square law that governs most effects due to localized sources in three dimensions of space. In this case, you're looking at a distance of over a billion light years, and then squaring it: that's a pretty enormous "per unit area"!
But gravity itself is also a tremendously weak force compared to the others. That may seem surprising at first, but it becomes pretty clear when I point out that a cheap little refrigerator magnet exerts enough force to overcome the gravitational pull of an entire planet right beneath it. Gravitational waves are pretty much just ripples on the top of that already tiny force.
Huh. That sounds entirely sensible and correct, and at the same time it's bugging my physical intuition a bit. I guess they're not trying to do this measurement by absorbing energy, but much more directly by just watching the change in length. I think I believe you: thanks!
Near as I can tell, they're intrinsically extremely weak, so much so that the only thing we've been able to see it all is extreme events like these black hole mergers. In theory, pretty much any time anything moves, some level of gravitational waves should be generated, though no telling if we'd ever be able to detect them.
