This paper presents and discusses the temperature and frequency dependence of the longitudinal and shear viscoelastic response at MHz and GHz frequencies of the intermediate glass former glycerol and the fragile glass former tetramethyl-tetraphenyl-trisiloxane (DC704). Measurements were performed using the recently developed time-domain Brillouin scattering technique, in which acoustic waves are generated optically, propagated through nm thin liquid layers of different thicknesses, and detected optically after transmission into a transparent detection substrate. This allows for a determination of the frequency dependence of the speed of sound and the sound-wave attenuation. When the data are converted into mechanical moduli, a linear relationship between longitudinal and shear acoustic moduli is revealed, which is consistent with the generalized Cauchy relation. In glycerol, the temperature dependence of the shear acoustic relaxation time agrees well with literature data for dielectric measurements. In DC704, combining the new data with data from measurements obtained previously by piezo-ceramic transducers yields figures showing the longitudinal and shear sound velocities at frequencies from mHz to GHz over an extended range of temperatures. The shoving model's prediction for the relaxation time's temperature dependence is fairly well obeyed for both liquids as demonstrated from a plot with no adjustable parameters. Finally, we show that for both liquids the instantaneous shear modulus follows an exponential temperature dependence to a good approximation, as predicted by Granato's interstitialcy model.

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