  Environmental noise coupling to mechanical experiments often introduces
low-frequency fluctuations to the resonators, adding noise to measurements and
reducing signal to noise. To counter these fluctuations, we demonstrate a
dynamic feedback system implemented by the locking of a microwave drive to the
noisy cavity. A homodyne interferometer scheme monitors the cavity resonance
fluctuations due to low-frequency noise, which is mitigated by
frequency-modulating (FM) the microwave generator. The feedback has a bandwidth
of $400$ Hz, with a reduction of cavity fluctuations by $84\%$ integrating up
to a bandwidth of $2$ kHz. Moreover, the cavity resonance frequency
fluctuations are reduced by $73\%$. This scheme can be scaled to enable
multi-tone experiments locked to the same feedback signal. As a demonstration,
we apply the feedback to an optomechanical experiment and implement a
cavity-locked, multi-tone mechanical measurement. As low-frequency cavity
frequency noise can be a limiting factor in many experiments, the multi-tone
microwave locking technique presented here is expected to be relevant for a
wide range of fields of research.
