  If gravitation is propagated by a massive field, then the velocity of
gravitational waves (gravitons) will depend upon their frequency and the
effective Newtonian potential will have a Yukawa form. In the case of
inspiralling compact binaries, gravitational waves emitted at low frequency
early in the inspiral will travel slightly slower than those emitted at high
frequency later, modifying the phase evolution of the observed inspiral
gravitational waveform, similar to that caused by post-Newtonian corrections to
quadrupole phasing. Matched filtering of the waveforms can bound such
frequency-dependent variations in propagation speed, and thereby bound the
graviton mass. The bound depends on the mass of the source and on noise
characteristics of the detector, but is independent of the distance to the
source, except for weak cosmological redshift effects. For observations of
stellar-mass compact inspiral using ground-based interferometers of the
LIGO/VIRGO type, the bound on the graviton Compton wavelength is of the order
of $6 \times 10^{12}$ km, about double that from solar-system tests of Yukawa
modifications of Newtonian gravity. For observations of super-massive black
hole binary inspiral at cosmological distances using the proposed laser
interferometer space antenna (LISA), the bound can be as large as $6 \times
10^{16}$ km. This is three orders of magnitude weaker than model-dependent
bounds from galactic cluster dynamics.
