At high temperatures, a droplet can rest on a cushion of its vapor (the Leidenfrost effect). Application of an electric field across the vapor gap fundamentally eliminates the Leidenfrost state by attracting liquid towards the surface. This study uses acoustic signature tracking to study electrostatic suppression of the Leidenfrost state on solid and liquid surfaces. It is seen that the liquid-vapor instabilities that characterize suppression on solid surfaces can be detected acoustically. This can be the basis for objective measurements of the threshold voltage and frequency required for suppression. Acoustic analysis provides additional physical insights that would be challenging to obtain with other measurements. On liquid surfaces, the absence of an acoustic signal indicates a different suppression mechanism (instead of instabilities). Acoustic signature tracking can also detect various boiling patterns associated with electrostatically assisted quenching. Overall, this work highlights the benefits of acoustics as a tool to better understand electrostatic suppression of the Leidenfrost state, and the resulting heat transfer enhancement.