  We study the effect of compact extra dimensions on the gravitational wave
luminosity and waveform. We consider a toy model, with a compactified fifth
dimension, and matter confined on a brane. We work in the context of five
dimensional ($5d$) general relativity, though we do make connections with the
corresponding Kaluza-Klein effective $4d$ theory. We show that the luminosity
of gravitational waves emitted in $5d$ gravity by a binary with the same
characteristics (same masses and separation distance) as a $4d$ binary is
20.8\% less relative to the $4d$ case, to leading post-Newtonian order. The
phase of the gravitational waveform differs by 26\% relative to the $4d$ case,
to leading post-Newtonian order. Such a correction arises mainly due to the
coupling between matter and dilaton field in the effective $4d$ picture and
agrees with previous calculations when we set black holes' scalar charges to be
those computed from the Kaluza-Klein reduction. The above corrections to the
waveform and the luminosity are inconsistent with the gravitational-wave and
binary pulsar observations and thus they effectively rule out the possibility
of such a simple compactified higher dimensions scenario. We also comment on
how our results change if there are several compactified extra dimensions, and
show that the discrepancy with $4d$ general relativity only increases.
