See my response above about the FM modulation; I don't think it will work like that; it would be AM. Assuming the resonator diaphragm is linear and small signal (WRT to the sound pressure), you won't get a radiated carrier 2nd harmonic. A cavity resonator (2nd order) would produce a 2nd harmonic in AM audio as the carrier rides that resonator response.
If the diaphragm goes non-linear (say from high sound pressure), then perhaps you'd get harmonics and maybe an f/2 response. At this point it's acting like a parametric amplifier, with your carrier frequency and pump frequency. Parametric amps need a strongly non-linear reactance, hence pumping a varactor diode with a strong signal.
If the diaphragm goes non-linear (say from high sound pressure), then perhaps you'd get harmonics and maybe an f/2 response. At this point it's acting like a parametric amplifier, with your carrier frequency and pump frequency. Parametric amps need a strongly non-linear reactance, hence pumping a varactor diode with a strong signal.