  We consider the phase shift in the gravitational wave signal induced by fast
oscillations of scalar dark matter surrounding binary systems, which could be
probed by the future experiments LISA and DECIGO. This effect depends on the
local matter density and the mass of the dark matter particle. We compare it to
the phase shift due to a standard dynamical friction term, which should
generically be present. We find that the effect associated with the
oscillations only dominates over the dynamical friction for dark matter masses
below $10^{-21}$ eV, with masses below $10^{-23}$ eV implying cloud sizes that
are too large to be realistic. Moreover, for masses of the order of $10^{-21}$
eV, LISA and DECIGO would only detect this effect for dark matter densities
greater than that in the solar system by a factor $10^5$ or $10^4$
respectively. We conclude that this signal can be ignored for most dark matter
scenarios unless very dense clouds of very light dark matter are created early
in the Universe at a redshift $z\sim 10^4$.
