# Propagation of Weak Signals Through Continua

V.F. KuropatenkoThe paper considers a method of determining the velocity of weak signals in different media - ideal, non-ideal (nonzero stress deviator), and multi-component. As for the ideal media, the placeLaplace's formula for sound velocity \[C^{2} =\left(\frac{\partial P}{\partial \rho } \right)_{S} \] has long been such a widely used expression that it is understood as a definition of sound velocity. It is shown here that the formula is not a definition, but corollary from the consideration of mass, momentum and energy conservation laws in case of small perturbations in a medium described by an arbitrary equation of state. A similar consideration for an elastic isotropic medium gives expressions for longitudinal and transverse perturbation velocities dependent on the properties of solids. These relationships are studied rather well in the theory of elasticity though some papers on continuum mechanics provide somewhat different formulas for longitudinal and transverse perturbation velocities versus hydrodynamic sound velocity. Their consideration here was caused by the need to demonstrate universality of the method. Finally, for multi-component media, an equation for sound velocity is provided; it is principally different from what is widely used. The new equation is validated. It expresses sound velocity in a mixture versus sound velocities and concentrations of its components.Full text

- Keywords
- mathematical model, sound velocity, ideal medium, mixture, elasticity, concentration, equation of state.
- References
- 1. Loytzyansky L.G. Fluid Mechanics. Moscow, TEKHTEORLIT, 1957. 784 p. (in Russian)

2. Kuropatenko V.F., Glushak B.L., Novikov S.A. Strength of Materials under Dynamic Loads. Novosibirsk, NAUKA, 1992. 294 p. (in Russian)

3. Bezukhov N.I. Foundations of Elasticity, Plasticity and Creep Theory. Moscow, Vysshaya shkola, 1988. 512 p. (in Russian)

4. Kuropatenko V.F. New Models of Continuum Mechanics. Engineering Physics J., 2011, vol. 84, no. 1, pp. 74-92.

5. Kuropatenko V.F. Momentum and Energy Exchange in Non-Equilibrium Multi-Component Media. Applied Mechanical and Engineering Physics J., 2005, vol. 46, no. 1, pp. 7-15.

6. Wood A.B. Textbook of Sound. London, Bell&Sons Ltd, 1941.

7. Loytzyansky L.G., Fluid Mechanics. Moscow, NAUKA, 1973. 640 p. (in Russian)

8. Kutateladze S.S. Heat Exchange and Waves in Fluid Systems. Novosibirsk, NAUKA, 1984. 301 p. (in Russian)

9. Loboyko B.G., Dikov O.Y., SmirnovE.B. Explosion Hydrodynamics Problem Book. Snezhinsk, RFNC-VNIITF, 2006. 249 p. (in Russian)

10. Kuropatenko V.F., Kovalenko G.V., Kuznetsova V.I., Mikhaylova G.I., Sapozhnikova G.N. 'Wave', Code and Inhomogeneous Difference Method for Simulating Non-Equilibrium Compressible Continuum Flows. Problems in Nuclear Science and Engineering Journal, Series: Mathematical Modeling of Physical Processes, 1989, issue 2, pp. 9-17. (in Russian)