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We present the analysis of time-resolved, high resolution spectra of the coolwhite dwarf pulsator, G29-38. From measuring the Doppler shifts of the H-alphacore, we detect velocity changes as large as 16.5 km/s and conclude that theyare due to the horizontal motions associated with the g-mode pulsations on thestar. We detect seven pulsation modes from the velocity time-series andidentify the same modes in the flux variations. We discuss the properties ofthese modes and use the advantage of having both velocity and flux measurementsof the pulsations to test the convective driving theory proposed for DAV stars.Our data show limited agreement with the expected relationships between theamplitude and phases of the velocity and flux modes. Unexpectedly, the velocitycurve shows evidence for harmonic distortion, in the form of a peak in theFourier transform whose frequency is the exact sum of the two largestfrequencies. Combination frequencies are a characteristic feature of theFourier transforms of light curves of G29-38, but before now have not beendetected in the velocities, nor does published theory predict that they shouldexist. We compare our velocity combination frequency to combination frequenciesfound in the analysis of light curves of G29-38, and discuss what might accountfor the existence of velocity combinations with the properties we observe.  We also use our high-resolution spectra to determine if either rotation orpulsation can explain the truncated shape observed for the DAV star's linecore. We are able to eliminate both mechanisms: the average spectrum does notfit the rotationally broadened model and the time-series of spectra providesproof that the pulsations do not significantly truncate the line.Comment: 24 pages, 9 figures, Accepted for publication in ApJ (June

High‐Resolution Spectroscopy of the Pulsating White Dwarf G29‐38