  Using direct numerical simulations (DNSs), the interaction between linear
waves and turbulence under the compressible magnetohydrodynamic (CMHD) approach
was studied. A set of DNSs in three dimensions for a spatial resolution of
$128^3$ and $256^3$ were performed. A parametric study was carried out varying
the sonic Mach number, the mean magnetic field and the compressibility
amplitude of the forcing. Spatio-temporal spectra of the magnetic energy were
built and analyzed, allowing for direct identification of all wave modes in a
CMHD turbulent system and quantification of the amount of energy in each mode
as a function of the wave number. Thus, linear waves were detected, that is
Alfv\'en waves and fast and slow magnetosonic waves. Furthermore, different
responses of the plasma were found according to whether the Mach number or the
mean magnetic field was varied. On the other hand, making use of
spatio-temporal spectra and two different integration methods, we accurately
quantified the amount of energy present in each of the normal modes. Finally,
although the presence of linear waves was observed, in all the cases studied
the system was mainly dominated by the non-linear dynamics of the plasma.
