Dispersion and Absorption of Ultrasounds

In view of the low probability of translational-vibrational energy exchange, vibrational excitation at the expense of translation of the colliding molecules and the inverse process of vibrational energy dissipation are manifested in the disper- 

If the sound frequency v is low, i.e. the time of adiabatic gas compression is longer than the vibrational relaxation time T ib, the molecular vibrational heat capacity can be considered to be close to the equilibrium heat capacity c.  

On the other hand, if the frequency is high, i.e. vTyib 1, the vibrational heat capacity will be virtually zero, i.e. all the energy of the gas molecules will be in the form of translational and rotational energy. 

Detailed studies show that the relaxation time T ib can be calculated from the frequency v found from the inflection point in the dispersion curve, or from the maximum of sound absorption ([192]). For molecules simulated by harmonic oscillators, Tyib is expressed via (Pi,o) by Eq. (8.45). Then, one can ultimately find the transition probability (Pio) or a related quantity Z ib = l/Pi,o which is the number of collisions needed for the deactivation of the first vibrational energy level. 

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