Distributed acoustic sensing has been traditionally implemented using optical reflectometry. Here we describe an alternative to the common interrogation approaches. According to the new method the frequency of the source is varied sinusoidally with time. For a sufficiently high scan frequency there is a position along the fiber, z0, for which the roundtrip time is half the scan period. Back-reflections from this point will generate a linear chirp at the receiver output. The Fractional Fourier Transform (FrFT) is used to analyze the receiver output and yields the reflection profile at z0 and its vicinity. The method, which enables high spatial resolution at long distances with high scan rates, is demonstrated by detecting deliberate perturbations in the Rayleigh backscatter profile at the end of a 20km fiber with a scanning frequency of ∼2.5kHz. The spatial resolution at this range and scan-rate is characterized by a measurement of the backscatter profile from a FBG's-array and is found to be ∼2.8m.