  Super-Alfv\'enic shock waves associated with coronal mass ejections (CMEs)
can produce radio emission known as Type II bursts. In the absence of direct
imaging, accurate estimates of coronal electron densities, magnetic field
strengths and Alfv\'en speeds are required in order to calculate the kinematics
of shocks. To date, 1D radial models have been used, but these are not
appropriate for shocks propagating in non-radial directions. Here, we study a
coronal shock wave associated with a CME and Type II radio burst using 2D
electron density and Alfv\'en speed maps to determine the locations that shocks
are excited as the CME expands through the corona. Coronal density maps were
obtained from emission measures derived from the Atmospheric Imaging Assembly
(AIA) on board the Solar Dynamic Observatory (SDO) and polarized brightness
measurements from the Large Angle and Spectrometric Coronagraph (LASCO) on
board the Solar and Heliospheric Observatory (SOHO). Alfv\'en speed maps were
calculated using these density maps and magnetic field extrapolations from the
Helioseismic and Magnetic Imager (SDO/HMI). The computed density and Alfv\'en
speed maps were then used to calculate the shock kinematics in non-radial
directions. Using the kinematics of the Type II burst and associated shock, we
find our observations to be consistent with the formation of a shock located at
the CME flanks where the Alfv\'en speed has a local minimum. 1D density models
are not appropriate for shocks that propagate non-radially along the flanks of
a CME. Rather, the 2D density, magnetic field and Alfv\'en speed maps described
here give a more accurate method for determining the fundamental properties of
shocks and their relation to CMEs.
