  In a first study of thermoelastic waves, such as on the textbook of Landau
and Lifshitz, one might at first glance understand that when the given period
is very short, waves are isentropic because heat conduction does not set in,
while if the given period is very long waves are isothermal because there is
enough time for thermalization to be thoroughly accomplished. When one pursues
the study of these waves further, by the mathematical inspection of the
complete thermoelastic wave equation he finds that if the period is very short,
much shorter than a characteristic time of the material, the wave is
isothermal, while if it is very long, much longer than the characteristic time,
the wave is isentropic. One also learns that this fact is supported by
experiments: at low frequencies the elastic waves are isentropic, while they
are isothermal when the frequencies are so high that can be attained in few
cases. The authors show that there is no contradiction between the first glance
understanding and the mathematical treatment of the elastic wave equation: for
thermal effects very long periods are so short and very short periods are so
long.
