We demonstrate experimentally the pulse-to-pulse coherence of the beat note produced by a dual-polarization passively Q-switched Nd:YAG laser subjected to a frequency-shifted, polarization-rotated, optical feedback. The reinjection of one laser eigenstate into the other eigenstate ensures the phase-locking of the beat note against an external acoustic reference wave at the onset of each pulse, circumventing the intrinsic memory loss of the optical phase between successive pulses. It opens the possibility to generate optically a coherent pulsed beat note in the radio-frequency range with a subhertz linewidth, i.e., over thousands of pulses. An application to lidar radar is discussed.