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Let me be quantitative.
1) I am treating the source disk (the source of the field at x=0) as
it were a point particle of mass M. The detector is at the distance x
from the source. Therefore the field intensity, g, at any given
distance from the source‚ is given by Newton's law:
g=G*M/x^2, where G is the universal gravitational constant.
2) The distance x is time dependent, due to some unspecified process.
That is why g is also time dependent.
3) Te frequency of longitudinal gravitational waves (in my gedanken
setup) is the same as the frequency at which the x is changing.
4) What is wrong with this classical reasoning?