  When a gravitational wave (GW) from a distant source propagates through the
universe, its amplitude and phase change due to gravitational lensing by the
inhomogeneous mass distribution. We derive the amplitude and phase
fluctuations, and calculate these variances in the limit of a weak
gravitational field of density perturbation. If the scale of the perturbation
is smaller than the Fresnel scale $\sim 100 {pc} (f/{mHz})^{-1/2}$ ($f$ is the
GW frequency), the GW is not magnified due to the diffraction effect. The rms
amplitude fluctuation is $1-10 %$ for $f > 10^{-10}$ Hz, but it is reduced less
than 5% for a very low frequency of $f < 10^{-12}$ Hz. The rms phase
fluctuation in the chirp signal is $\sim 10^{-3}$ radian at LISA frequency band
($10^{-5} - 10^{-1}$ Hz). Measurements of these fluctuations will provide
information about the matter power spectrum on the Fresnel scale $\sim 100$ pc.

Astrophysics;General Relativity and Quantum Cosmology