An ion beam can destabilize Alfv\'en/ion-cyclotron waves and
magnetosonic/whistler waves if the beam speed is sufficiently large. Numerical
solutions of the hot-plasma dispersion relation have previously shown that the
minimum beam speed required to excite such instabilities is significantly
smaller for oblique modes with $\vec k \times \vec B_0\neq 0$ than for
parallel-propagating modes with $\vec k \times \vec B_0 = 0$, where $\vec k$ is
the wavevector and $\vec B_0$ is the background magnetic field. In this paper,
we explain this difference within the framework of quasilinear theory, focusing
on low-$\beta$ plasmas. We begin by deriving, in the cold-plasma approximation,
the dispersion relation and polarization properties of both oblique and
parallel-propagating waves in the presence of an ion beam. We then show how the
instability thresholds of the different wave branches can be deduced from the
wave--particle resonance condition, the conservation of particle energy in the
wave frame, the sign (positive or negative) of the wave energy, and the wave
polarization. We also provide a graphical description of the different
conditions under which Landau resonance and cyclotron resonance destabilize
Alfv\'en/ion-cyclotron waves in the presence of an ion beam. We draw upon our
results to discuss the types of instabilities that may limit the differential
flow of alpha particles in the solar wind.
