  KHz QPOs have now been detected in more than twenty accreting neutron stars
in low-mass binary systems. Two kHz QPOs are usually detected in each star.
Burst oscillations and two kHz QPOs have recently been detected in the 401 Hz
accretion-powered X-ray pulsar SAX J1808.4-3658. In this star the frequency of
the burst oscillation is approximately equal to the star's spin frequency
nu_spin whereas the frequency separation of the two kHz QPOs is approximately
nu_spin/2. If as expected the frequency of the burst oscillations in other
stars is also approximately nu_spin, the frequency separation is approximately
nu_spin in some stars but approximately nu_spin/2 in others. A frequency
separation approximately equal to nu_spin/2 is unexplained in all existing
models of the kHz QPOs. Here we propose a modified version of the sonic-point
beat-frequency model that can explain within a single framework why the
frequency separation is close to nu_spin in some stars but close to nu_spin/2
in others. As in the original sonic-point model, the frequency nu_QPO2 of the
upper kHz QPO is close to the orbital frequency nu_orb at the radius r_{sp} of
the sonic point in the disk flow. We show that magnetic and radiation fields
rotating with the star will preferentially excite vertical motions in the disk
at the "spin-resonance'' radius r_{sr} where nu_orb - nu_spin is equal to the
vertical epicyclic frequency, producing vertical motions in the disk that
modulate the X-ray flux at approximately nu_QPO2 - nu_spin or approximately
nu_QPO2 - nu_spin/2, depending on whether the disk flow at r_{sr} is smooth or
clumped. This sonic-point and spin-resonance model can also explain
quantitatively the decrease of the kHz QPO frequency separation with increasing
accretion rate that is observed in many sources.
