We report Alfvén-wave experiments with liquid rubidium at the Dresden High Magnetic Field Laboratory. Reaching up to 63 T, the pulsed magnetic field exceeds the critical value of 54 T at which the Alfvén speed coincides with the sound speed. At this threshold, we observe a period doubling of an applied 8 kHz cw excitation, which is consistent with the theoretical expectation of a parametric resonance between magnetosonic waves and Alfvén waves. Similar mode conversions are discussed as a possible mechanism for heating the solar corona.