In the past decade there has been much work on the sound generated underwater by a moving laser source. In particular, a great deal of effort has been directed toward understanding the thermoacoustic sound generation process, in which the laser heats the fluid medium and radiates sound as a result of the induced volumetric expansion. Theoretical predictions of the laser generated sound and experimental measurements have been shown to agree well for a wide range of source velocities, and source-receiver geometries. The notable exception to this agreement between theory and experiment is for laser beams which are moved at velocities near Mach one. It was found in earlier experimental studies on moving thermoacoustic sources that transonic motion of the source produces significantly higher sound pressure levels than predicted by linear theory. This report examines some possible explanations of that observation. In particular, we study the effect of non-linearities in the equation of state due to entropy generation, the variation of sound generating efficiency with time for subsonic and transonic sources, and the validity of linear superposition for a moving thermoacoustic source. In Part II of this report we discuss how the sound signal generated by a laser source is affected by various source and receiver parameters.