When an acoustoelectric domain in a piezoelectric semiconductor traverses the monochromatic light near the intrinsic absorption edge, absorbed and transmitted optical modulations are observed. In order to reveal the mechanisms, we apply an electric field parallel to the c-axis of the CdS single crystal. In this case the electric field dependences of the off-axis angle are different for a high field domain and an acoustic domain. Comparing the electric field dependence of the off-axis angle of the optical modulation with that of the high field domain or the acoustic domain, we conclude that the transmitted and absorbed optical modulations are caused by the acoustic domain. Further, in order to establish the nature and mechanism of the optical modulation in case of E|| c, we observe the spectral dependences of the absorbed optical modulation and find that there are two kinds of light absorption; one is due to pure shift in the absorption edge and the other is due to broad tail for low energy side. In case of e|| c ( e: polarization of incident light) both types of modulation exist at the same time and in case of e⊥ c only the latter exists. And it is speculated that the transmitted optical modulation is due to the effect of induced birefringence caused by acoustic strain.