The time-varying magnetic field with electromagnetic perturbation is regarded as an important parameter to the thermomagnetic stability of superconducting film devices. In this work, using the thermomagnetic model, we investigate the sensitivity of thermomagnetic instability in the superconducting film exposed to a linear ramp magnetic field, superposed by additional AC magnetic perturbation with tunable amplitude and oscillation frequency. Surprisingly, we find that the thermomagnetic instability is a non-monotonic function with the increasing oscillation frequency of magnetic perturbation, depending on the working temperature and oscillation amplitude. The unexpected non-monotonic sensitivity of thermomagnetic instability is revealed by the characteristic oscillation of electric field which can not be aggravated by the AC magnetic perturbation with very high frequency. The findings of this paper demonstrate that the magnetic perturbation of very low or high frequency is not the main factor that triggers the thermomagnetic instability of superconducting films. Furthermore, using the magnetic moment measurement, we propose a possible electromagnetic interference detection by the superconducting film based on such non-monotonic sensitivity of the thermomagnetic instability, which can be used to detect the tunable target electromagnetic interference with characteristic frequency in a complex electromagnetic environment.