  We present a complete analysis of the dispersion relations for longitudinal
and transverse waves in a rarefied polyatomic gas based on Rational Extended
Thermodynamics (RET), which describes the evolution of a non-polytropic gas in
nonequilibrium. Observability of the second mode of the longitudinal wave and
the transverse wave is discussed although these waves are usually not payed
much attention. The cases of CO$_2$ gas and para-H$_2$ gas are specifically
analyzed as typical examples.
