  Oscillations in coronal loops are usually interpreted in terms of uncoupled
magnetohydrodynamic (MHD) waves. Examples of these waves are standing
transverse motions, interpreted as the kink MHD modes, and propagating slow
modes, commonly reported at the loop footpoints. Here we study a simple system
in which fast and slow MHD waves are coupled. The goal is to understand the
fingerprints of the coupling when boundary conditions are imposed in the model.
The reflection problem of a fast and slow MHD wave interacting with a rigid
boundary, representing the line-tying effect of the photosphere, is
analytically investigated. Both propagating and standing waves are analysed and
the time-dependent problem of the excitation of these waves is considered. An
obliquely incident fast MHD wave on the photosphere inevitably generates a slow
mode. The frequency of the generated slow mode at the photosphere is exactly
the same as the frequency of the incident fast MHD mode, but its wavelength is
much smaller, assuming that the sound speed is smaller than the Alfv\'en speed.
The main signatures of the generated slow wave are density fluctuations at the
loop footpoints. We have derived a simple formula that relates the velocity
amplitude of the transverse standing mode with the density enhancements at the
footpoints due to the driven slow modes. Using these results it is shown that
there are possible evidences in the observations of the coupling between these
two modes.
