In this report, a dispersion relation for sound wave in a uniform, low ionization plasma is derived from the plasma hydrodynamic equations. From this relation, the properties of a shock wave travelling in a glow discharge are evaluated and compared with previous experimental results. The present results show that a small acoustic dispersion can cause the broadening of the shock wave and the formation of a complex density structure downstream of the wave. The calculations of the density distribution in front of and behind a shock wave are in good qualitative agreemenwt ith that previously measured across a shock wave travellmg through a glow discharge.