We perform a statistical study of 3-s ultra-low frequency (ULF) waves using MMS observations in the Earth’s foreshock region. The average phase velocity in the plasma rest frame is determined to be anti-sunward, and the intrinsic polarization is right-handed. We further examine the linear instability conditions based on drift-bi-Maxwellian distribution functions according to observed plasma conditions. The resulting instability is a solution to the common dispersion equation of the ion/ion right-hand non-resonant and left-hand resonant instabilities. The predicted wave propagation is also predominantly anti-sunward. The cyclotron resonant conditions of the solar wind and backstreaming beam ions are evaluated, and we find that in some cases, the anti-sunward propagating waves can be resonant with beam ions, which was overlooked in previous studies. The result suggests that the dispersion equation provides the 3-s ULF waves a fundamental explanation that unifies a rich variety of resonant conditions. In the later stage, the 3s ULF waves could further develop into Short Large Amplitude Magnetic Structures, contributing to the turbulence in the foreshock region.