A distributed and dynamic strain sensing system based on frequency-scanning phase-sensitive optical time domain reflectometry is proposed and demonstrated. By utilizing an RF pulse scheme with a fast arbitrary waveform generator, a train of optical pulses covering a large range of different optical frequencies, short pulse width, and high extinction ratio is generated. Also, a Rayleigh-enhanced fiber is used to eliminate the need for averaging, allowing single-shot operation. Using direct detection and harnessing a dedicated least mean square algorithm, the method exhibits a record high spatial resolution of 20 cm, concurrently with a large measurable strain range (80µε, 60 demonstrated), a fast sampling rate of 27.8 kHz (almost the maximum possible for a 55 m long fiber and 60 frequency steps), and low strain noise floor (<1.8nε/√Hz for vibrations below 700 Hz and <0.7nε/√Hz for higher frequencies).