Low Mach number shock waves propagating through a low pressure, nonequilibrium positive column gas discharge have been observed to experience dispersion and velocity changes. It is shown that these effects depend on discharge polarity. Optical and electrical measurements are described which show further polarity-dependent effects in discharge light emission and changes in electrical properties. Using two types of probes, electrical measurements were made of both the global changes in discharge voltage and current and time resolved local electric field changes. The measured behaviors of discharge and shock wave point to very localized triple or quadruple layer electric sheaths connected with the propagating shock wave, which provide local enhanced ionization at the shock front which can sustain the discharge, at least during the short shock propagation time. The postulated density gradient driven large local recirculation current in the potential minimum near this sheath [H. S. Maciel and J. E. Allen, J. Plasma Phys. 42, 321 (1989)] at the shock front will result in large local Joule heating, causing the shock dispersion and shock speed increase, which have been observed in many experiments. Thus, the conclusion is that the effects are due to highly localized gas heating which is facilitated by the response of the positive column plasma to the acoustic shock.