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Using spatio-temporal spectra we show direct evidence of excitation ofmagnetosonic and Alfv\'en waves in three-dimensional compressiblemagnetohydrodynamic turbulence at small Mach numbers. For the plasma pressuredominated regime, or high $\beta$ regime (with $\beta$ the ratio between fluidand magnetic pressure), and for the magnetic pressure dominated regime, or low$\beta$ regime, we study magnetic field fluctuations parallel and perpendicularto a guide magnetic field $\textbf{B}_0$. In the low $\beta$ case we findexcitation of compressible and incompressible fluctuations, with a transfer ofenergy towards Alfv\'enic modes and to a lesser extent towards magnetosonicmodes. In particular, we find signatures of the presence of fast magnetosonicwaves in a scenario compatible with that of weak turbulence. In the high$\beta$ case, fast and slow magnetosonic waves are present, with no clear traceof Alfv\'en waves, and a significant part of the energy is carried bytwo-dimensional turbulent eddies.

Interplay between Alfv\'en and magnetosonic waves in compressible magnetohydrodynamics turbulence