  Ponderomotive squeezing of the output light of an optical cavity has been
recently observed in the MHz range in two different cavity optomechanical
devices. Quadrature squeezing becomes particularly useful at lower spectral
frequencies, for example in gravitational wave interferometers, despite being
more sensitive to excess phase and frequency noise. Here we show a
phase/frequency noise cancellation mechanism due to destructive interference
which can facilitate the production of ponderomotive squeezing in the kHz range
and we demonstrate it experimentally in an optomechanical system formed by a
Fabry-P\'{e}rot cavity with a micro-mechanical mirror.
