We investigate the evolution of cosmological scalar perturbations in the case where the background radiation is weakly coupled to a light scalar field 𝜙. The light scalar 𝜙 is a homogeneous background field with a large initial value. In the radiation-dominated Universe, the coupling term introduces an effective mass to 𝜙 and the background ultrarelativistic particles. The oscillations of 𝜙 result in the periodic change of the equation-of-state parameter and the sound speed, which provides a novel mechanism to amplify subhorizon scalar perturbations through parametric resonance. The amplification of scalar perturbations leads to a stochastic gravitational-wave background (SGWB) expected to be observed by multiband gravitational-wave observers. The observation of the SGWB helps to determine the initial value of 𝜙 and the coupling strength of the interaction. This mechanism is generally applicable to the interactions that introduce an effective mass, and we take the interaction between 𝜙 and electrons as a concrete example to illustrate the result. We find that under the condition that the coupling coefficient 𝜆 =10−16 and the initial value 𝜙𝑖 =1018  GeV, the resulting SGWB spectrum is expected to be observed by the future observers including LISA, Taiji, DECIGO, and BBO.