We report here detailed statistical studies of power spectra of 1 hour average interplanetary magnetic field (IMF) data that were acquired by the magnetometer instrument on the Ulysses spacecraft in the ecliptic plane of the heliosphere during Ulysses' cruise phase from Earth to Jupiter (October 1990 through January 1992). We have pursued these studies in order to examine in a critical manner our previously published conclusions [Thomson et al., 1995> that energetic particle fluxes in the interplanetary medium carried signatures of discrete modes. We attributed these signatures to the existence of solar acoustic and gravitational modes (p and g modes, respectively) in the heliosphere. Here we first examine the statistical distributions of g modes (less than ~200 &mgr;Hz) that are predicted by a theoretical model of the solar interior. With this background information we formulate the time series and statistical analysis procedures that must be used in order to provide information on possible modal signals in the IMF, independent of the source. We show from the statistical analyses that the modal components that are present in the IMF fluctuations can amount to ~20% to ~70% of the IMF fluctuation power in the frequency range of ~10--140 &mgr;Hz. We discuss these findings in the context of previously published work on searches for optical signatures of solar g modes in the solar photosphere as well as published research papers that have called into question some of the conclusions of Thomson et al. [1995>. We conclude that the interplanetary medium is not a totally chaotic medium, but can sustain high power levels of discrete, low-frequency modes, probably of solar origin, over a long interval of time. ¿ 2001 American Geophysical Union