Intense terahertz-wave emission in the higher frequency region can result in various applications such as terahertz spectroscopy and ultrafast data communication. In this study, an increase in terahertz waves by the overlap of exciton states in different quantum wells and spectroscopic demonstration are reported. The excitation energy dependence of signal intensity shows the effect of the overlap. The signals measured under the condition of square dependence of intensity on the excitation power indicate interference with the periods corresponding to the laser energy difference. Furthermore, the absorption coefficient of the transparent sheet is obtained at specific frequency. These results indicate that the generation of intense terahertz waves at various frequencies using excitons is possible and that difference frequency mixing is a useful terahertz-wave source.