This article provides a rigorous mathematical analysis of acoustic wave scattering induced by a high-contrast subwavelength resonator whose material density is periodically modulated in time, with a modulation frequency significantly larger than the incident wave frequency. The analysis reveals that, generally, the effect of the fast modulation is averaged over time, and the system behaves as an unmodulated resonator with an apparent effective density. However, under a specific tuning of the modulation, which aligns temporal Sturm-Liouville eigenvalues with spatial Neumann eigenvalues, the low-frequency incident wave becomes capable of exciting high-frequency modes in the resonator. This phenomenon leads to the generation of scattered waves carrying high-frequency components in the far field and the existence of exponentially growing outgoing modes. The findings suggest that such time-modulated systems could serve as spontaneously radiating devices or high harmonic generators. The paper includes a detailed mathematical formulation, analysis of subwavelength resonances, and a discussion on the effective medium theory for time-modulated metamaterials.This article provides a rigorous mathematical analysis of acoustic wave scattering induced by a high-contrast subwavelength resonator whose material density is periodically modulated in time, with a modulation frequency significantly larger than the incident wave frequency. The analysis reveals that, generally, the effect of the fast modulation is averaged over time, and the system behaves as an unmodulated resonator with an apparent effective density. However, under a specific tuning of the modulation, which aligns temporal Sturm-Liouville eigenvalues with spatial Neumann eigenvalues, the low-frequency incident wave becomes capable of exciting high-frequency modes in the resonator. This phenomenon leads to the generation of scattered waves carrying high-frequency components in the far field and the existence of exponentially growing outgoing modes. The findings suggest that such time-modulated systems could serve as spontaneously radiating devices or high harmonic generators. The paper includes a detailed mathematical formulation, analysis of subwavelength resonances, and a discussion on the effective medium theory for time-modulated metamaterials.