An approximate method of estimating shear velocity from specific heat

The purpose of this letter is to point out that the isotropic shear velocity vs of inorganic materials such as of minerals and rocks can be estimated from low-temperature specific heat measurements. This property promises to be very useful because it enables one to determine the seismic shear velocity of a material without regard to the state of aggregation of the samples. This correspondence between acoustics and calorimetry is based upon a principle of lattice dynamics, namely, that at sufficiently low temperatures the optical vibrations of a solid are quiescent and the vibrational energy results solely from acoustic vibrations. This correspondence is conveniently stated in terms of Debye temperatures.