To capture sound from solid mediums, such as the human body or musical instruments, transducers designed for airborne sound pickup are typically used. Acoustic impedance mismatches between the medium and transducer decrease the energy captured and increase noise corruption. Here, we demonstrate the improved sensitivity and airborne noise rejection of an electrostatic transducer with an acoustic impedance matched to the medium of interest. The transducer produces an electrical response when mechanical vibrations compress the distance between an elastomer with patterned microstructures and a charged electret film. Using a statistical model generated through an I-optimal design of experiments, the elastomer is fabricated with a specific polymer and concentration of nanoparticles to possess a targeted acoustic impedance. Transducers containing elastomers with impedances in the range of 1 to 2.2 MRayls are assembled and characterized on simulators emulating the human body and a wooden instrument. The noise rejection is quantified using the coherence between the captured transducer signal and the simulated ambient noise. Sensitivities are similarly characterized by comparing the transducer signal and input simulator signal. With an impedance closely matched to the medium of interest, the transducer demonstrates a 2V/N sensitivity and 35 dB SNR improvement compared to an airborne transducer.