A linear approach to the phenomenon of irregular amplitude modulation of beam-driven Langmuir waves, developed in a previous paper, is extended to explain periodic modulation as well. It comes about by beating of the fastest growing mode of the instability with beam-aligned plasma oscillations. They are naturally generated in a uniform domain of beam–plasma interaction prior to the onset of the instability. Particle-in-cell (PIC) simulations support the results of the linear analysis.