We study two examples of broadband ultra‐low frequency (ULF) waves observed near the dayside polar cap boundary using data from multiple instruments on Cluster. These waves lie in a frequency range of ∼1–100 mHz with variable amplitudes. We have focused on their characteristics around the lowest frequency end. In the first event, the magnetic variations consist of oscillations mainly transverse to the background field. These waves are inferred to be the shear Alfvén waves whose phase velocity is approximately perpendicular to the magnetic field. A possible source is located in reconnection, probably of transient variety. In the second event, the magnetic variations include compressional components. These waves are suggested to be fast mode waves. It is possible that the waves are generated by the pressure variations in the solar wind impinging on the magnetosphere. The estimated wave modes and generation mechanisms of these two events are different, even though the waves have broadband spectra at similar spacecraft locations. The results from our observations may be useful when comparing with theories in realistic situations.