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The response of cell populations to external stimuli plays a central role in biological phenomena such as epithelial wound healing and developmental morphogenesis. Wave propagation of a protein signal has been shown to direct collective migration in one direction, but this mechanism based on active matter under a traveling wave is not fully understood. To elucidate how the traveling wave of the protein signal directs collective migration, we study the mechanics of the epithelial cell monolayer, taking into account the signal-dependent coordination of contractile stress and cellular orientation. By constructing an optogenetically controlled experimental cell model, we found that local signal activation induces changes in cell density and orientation with the direction of propagation, increasing the net motion relative to the wave. In addition, the migration exhibits an optimal speed with the propagation speed of the signal. This occurs because the mechanical deformation is not fully relaxed for rapid signal activation, resulting in an optimal signal propagation speed. The presented mechanical model can also be extended to wound healing, providing a versatile model for understanding the interplay between mechanics and signaling in active matter., Comment: 11 pages, 5 figures