We study the annual periodicity and the solar rotation periodicity of the in-ecliptic components of the interplanetary magnetic field (IMF). It is well known that the annual periodicity undergoes a phase reversal in 11 years, reflecting the 22-year Hale cycle of the solar magnetic field. We construct a model where the annual periodicity of the IMF components is phase/frequency modulated by the Hale cycle, and show that this model can reproduce the observed properties of the annual periodicity. We find that the solar rotation periodicity depicts an analogous nodal structure and a phase reversal with a period of about 3.2 years, implying a new periodicity in the properties of the IMF. We demonstrate that, using the observed spectral width, the phase/frequency modulation model can satisfactorily explain this structure. We also note that taking into account the observed phase reversal in the solar rotation periodicity implies that the most persistent synodic solar rotation period in the in-ecliptic IMF components is 27.6 days, i.e., somewhat longer than recently suggested.