  We calculate the low temperature quasi-particle contribution to the
ultrasonic attenuation rate in the mixed state of d-wave superconductors. Our
calculation is performed within the semi-classical approximation using
quasi-particle energies that are Doppler shifted, with respect to their values
in the Meissner phase, by the supercurrent associated with the vortices. We
find that the attenuation at low temperatures and at fields $ H_{c1} \leq H \ll
H_{c2}$ has a temperature independent contribution which is proportional to
$\surd H$ where $H$ is the applied magnetic field. We indicate how our result
in combination with the zero-field result for ultrasonic attenuation can be
used to calculate one of the parameters $v_F$, $H_{c2}$ or $\xi$ given the
values for any two of them.
