A sensitive polymer diaphragm based fiber Fabry-Perot (F-P) sensor for aeroacoustic wave measurement is presented. A novel polymer material poly (phthalazinone ether sulfone ketone) (PPESK) diaphragm is used as the acoustic sensing element. The effective dimensions of the diaphragm are 4 mm in diameter and 6 \mu m in thickness. Owing to the good mechanical and optical features of the diaphragm and application of the interferometric/intensity demodulation, a system sensitivity of 31 mV/Pa is achieved in the frequency range of 0.1-12.7 kHz, and a signal-to-noise ratio (SNR) of 29 dB at 1 kHz is obtained. The linear response of the sensor is from 0.35 to 2.82 Pa, corresponding to 85-103 dB sound pressure level (SPL) (re: 20\mu Pa). The sensor has the potential to be used as a universal and low-cost optical microphone.