V.2 No 1

31

Homogeneous 1d resistant line

Altenburg in his model considers an 1D chain of equidistant molecules under condition that each of them interacts only with two neighbouring molecules. Naturally he comes to the conventional solution like

(here = 2arcsin /₀ and  ₀ = 2(s/m)^1/2). Further, reducing this solution to a nonlinear description of the above regularity of velocity with respect to pressure and temperature, Altenburg considers the sound propagating in a face-centred lattice, though he studies a liquid model.

Kudryavtcev [18] proceeds from the following relation between adiabatic compressibility of substance and its internal energy U:

where S is the entropy,  p is the pressure, and in this case is the compressibility of substance.

Kudryavtcev also supposes a full order of molecules and calculates the derivative of (42) under variation of intermolecular distance along some direction. In fact, he also reduces the problem to the vibration of 1D chain of elastically constrained molecules. Further, supposing that the interior energy of liquid is the potential energy of the intermolecular affection and that when calculating, one can consider only the neighbouring molecules interaction, he yields

where the relationship of the interaction potential  (r) is taken after Lennard – Jones. ''Selecting the numerical coefficients for equations, we can achieve in this case a satisfying conformity of the measured and calculated values of the sound velocity'' [16, p. 89- 90].