The Los Alamos Scientific Laboratory experiments on the Vela 2-6 and Imp 6-8 satellites have provided more than 11 years of solar wind speed data. The length of this data set provides sufficient frequency resolution to study in detail the power spectrum of speed variations in the range near the solar rotational frequency. Year-by-year power spectra show such large differences that the solar wind time series is probably nonstationary. The spectrum of the entire 11-year time series shows broad bands of power near periods of 27 days (corresponding to the rotational period of the sun), 13.5 days, and higher harmonics. The band of power near 27 days extends from about 25 to about 31.5 days and contains a number of sharply defined peaks. Similar groups of peaks near a period of 27 days in a highly correlated time series, the geomagnetic index aa, have been explained as a solar latitude effect caused by differential rotation. However, recent observations indicate that the source regions of the solar wind during this last solar cycle did not participate in differential rotation; that is, there was a preferred range of longitudes for the sources. We suggest that the individual peaks in both the solar wind and the geomagnetic spectra are probably not due to differential rotation, although the band of power near 27 days almost certainly reflects solar rotation. Rather, the multipeak nature of the power spectra can be explained by a wave packet concept in which recurring high-speed streams are described as a series of pulses (separated by a constant period) that last for a varying number of solar rotations. Subsequent wave packets have the same period but are shifted in phase to mimic the range of possible longitudes for sources of solar wind streams. Power spectra obtained for such idealized wave packets closely resemble the measured spectra of the solar wind speed and geomagnetic activity. We do not find the frequencies predicted by a theory concerning the nonradial oscillation of the sun.