By writing the complete set of 3 + 1 (ADM) equations for linearized wa
ves, we are able to demonstrate the properties of the initial data and
of the evolution of a wave problem set by Alcubierre and Schutz. We s
how that the gauge modes and constraint error modes arise in a straigh
tforward way in the analysis, and are of a form which will be controll
ed in any well specified convergent computational discretization of th
e differential equations.