For the phase induced signal fading, the principles of interferometric fiber acoustic sensors based on sinusoidal-wave frequency-modulated continuous wave (FMCW) and sawtooth-wave FMCW are introduced, and two corresponding digital demodulation methods are described. Based on the principles an experimental system is built including a fiber acoustic sensor with 7.5 m arm-difference and an FMCW laser source. Digital signal demodulations under 10 kHz sinusoidal-wave FMCW and 10 kHz sawtooth-wave FMCW are finished and comparative analysis between the demodulation results is performed. The experimental results show that both of the demodulation methods can detect the analog acoustic signal added to the acousthic sensor and eliminate the phase induced signal fading phenomenon of fiber interferometer. But the one based on sawtooth-wave FMCW possesses high and stable sensitivity with a simpler algorithm. Furthermore in this method a frequency division multiplexing system can be easily got by changing the arm difference of the fiber sensor.