  We present a Random-Phase-Approximation formalism for the collective spectrum
of two hyperfine species of dilute 40K atoms, magnetically trapped at zero
temperature and subjected to a repulsive s-wave interaction between atoms with
different spin projections. We examine the density-like and the spin-like
oscillation spectra, as well as the transition density profiles created by
external multipolar fields. The zero sound spectrum is always fragmented and
the density and spin channels become clearly distinguishable if the trapping
potentials acting on the species are identical. Although this distinction is
lost when these confining fields are different, at selected excitation
frequencies the transition densities may display the signature of the channel.
