Recently it has been possible to perform computer calculations with sufficiently high resolution to obtain the response of the gas in galaxies to a tightly wound spiral potential due to a stellar density wave. Previously for pitch angles ~ 10° the problem had to be simplified using the tightly wound approximation, with gradients parallel to the arms neglected compared to perpendicular gradients, yielding a quasi-1-dimensional calculation. This paper reports the early results of a 2-dimensional calculation, and compares them with the 1-dimensional results.