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The feedback between mechanical and chemical signals plays a key role in controlling many biological processes and collective cell behavior. Here we focus on the emergence of spatiotemporal density waves in a one-dimensional “cell train.” Combining a minimal theoretical model with experiments on MDCK epithelial cells confined to a linear pattern, we examine the spontaneous oscillations driven by feedback between myosin activation and mechanical deformations, as well as their effect on the response of the tissue to externally applied deformations. We show that the nature and frequency of spontaneous oscillations is controlled by the size of the cell train, with a transition from size-dependent standing waves to intrinsic spontaneous waves at the natural frequency of the tissue. The response to external boundary perturbations exhibits a resonance at this natural frequency, providing a possible venue for inferring the mechanochemical couplings that control the tissue behavior from rheological experiments.