Speed of sound in dense simple liquids

The speed of sound of simple dense fluids exhibits a pronounced freezing temperature scaling of the form c_{s}/v_{T}≃sqrt[γ]+α(T_{fr}/T)^{β}, where c_{s} is the speed of sound, v_{T} is the characteristic thermal velocity, γ is the ideal gas heat capacity ratio, T is the temperature, T_{fr} is the freezing temperature, and α and β are dimensionless parameters. For the Lennard-Jones fluid, we get γ=5/3, α≃7 with a weak temperature dependence, and β=1/3. Similar scaling works in several real liquids, such as argon, krypton, xenon, nitrogen, and methane. In this case, α and β are substance-dependent fitting parameters. A comparison between the prediction of this freezing temperature scaling and a recent experimental measurement of the speed of sound in methane under conditions of planetary interiors is presented and discussed. The results provide a simple, practical tool to estimate the speed of sound in regimes where no experimental data are yet available.