Comparison of ULF Waves - Pc5 range - in the solar wind and on the ground during high speed solar wind streams We show a clear correlation between the power in ULF waves (Pc5 range) inside and outside Earth's magnetosphere during high speed streams in 1995. We find that the peak power in high speed streams is in the 0-10 mHz range, particularly below 2 mHz, where the Pc5 range is defined as 1-10 mHz. We trace the waves beginning 200~$R_E$ upstream using Wind data to waves just upstream from Earth's bow shock and in the magnetosheath using Geotail data to waves on the ground at the Kilpisjarvi ground station. We compare the total power in the Pc5 frequency from the upstream waves to the total power from Pc5 pulsations at the Kilpisjarvi ground station. We find that the pattern of increases and decreases in ULF wave power at Pc5 frequencies correlates in all regions; between the solar wind and the ground the correlation coefficient is 0.61. The total power in the solar wind is about a factor of 10 less than that on the ground, but the total power increases in the magnetosheath to values comparable to the ground. This suggests that solar wind waves may provide a source of wave power for the magnetosphere; the solar wind waves may be acting as seed perturbations to drive boundary displacements that are amplified by the Kelvin-Helmholtz instability. We discuss features of the waves in all regions and suggest possible transmission scenarios.