We present several examples of magnetospheric ultralow frequency pulsations associated with stream interaction regions and demonstrate that the observed magnetospheric pulsations were also present in the solar wind number density. The distance of the solar wind monitor ranged from just upstream of Earth's bow shock to 261 RE, with a propagation time delay of up to 90 min. The number density oscillations far upstream of Earth are offset from similar oscillations observed within the magnetosphere by the advection timescale, suggesting that the periodic dynamic pressure enhancements were time stationary structures, passively advecting with the ambient solar wind. The density structures are larger than Earth's magnetosphere and slowly altered the dynamic pressure enveloping Earth, leading to a quasi‐static and globally coherent “forced‐breathing” of Earth's dayside magnetospheric cavity. The impact of these periodic solar wind density structures was observed in both magnetospheric magnetic field and energetic particle data. We further show that the structures were initially smaller‐amplitude, spatially larger, structures in the upstream slow solar wind and that the higher‐speed wind compressed and amplified these preexisting structures leading to a series of quasiperiodic density structures with periods typically near 20 min. Similar periodic density structures have been observed previously at L1 and in remote images, but never in the context of solar wind shocks and discontinuities. The existence of periodic density structures within stream interaction regions may play an important role in magnetospheric particle acceleration, loss, and transport, particularly for outer zone electrons that are highly responsive to ultralow frequency wave activity.