  We investigate the relation between the parameters of the energy spectrum and
the frequency and amplitude of the kilohertz quasi-periodic oscillations (kHz
QPOs) in the low-mass X-ray binary 4U 1636$-$53. We fit the $3-180$-keV
spectrum of this source with a model that includes a thermal Comptonisation
component. We show that the frequencies of both kHz QPOs follow the same
relation as a function of the parameters of this spectral component, except for
a systematic frequency shift, whereas the rms fractional amplitude of each QPO
follows a different relation with respect to those same parameters. This
implies that, while the dynamical mechanism that sets the frequencies of the
QPO can be the same for both kHz QPOs, the radiative mechanisms that set the
amplitudes of the lower and the upper kHz QPO are likely different. We discuss
the implications of these results to the modelling of the kHz QPOs and the
possibility that the lower kHz QPO reflects a resonance between the
Comptonising medium and the photons from the accretion disc and/or the neutron
star surface.
