How Does the Geometry of Space Affect Gravitational Wave Amplitude?

[Prairie]

Have a question related to this quote from Wikipedia:
"The amplitude of a spherical wave will fall off as the inverse square of the distance from the source."

Is it correct to think that the energy of the whole of the wave is maintained but that it's the disbursement of the wave which results in a reduction in amplitude rather than it actually "losing steam", so-to-speak? Also, is its speed maintained over the course of its travels? Thanks.

 

[sophiecentaur]

It's simply a consequence of the geometry involved. As you go further away from a source / explosion / mass, the effect / flux / energy flow gets spread over a bigger and bigger area - as the area is proportional to the square of the distance you get an inverse square relationship. If you want to talk in terms of photons, the individual photon energy doesn't change; there are just fewer of them entering your window as you go further away.

Needless to say, this only applies over a scale where space is isotropic and linear and the geometry is well behaved.