We use the discrete velocity models to study the spectral problems related
to the 1D plane wave propagation in monatomic gases which are fundamental i
n the rarefied gases dynamics and nonequilibrium statistical thermodynamics
. The results show that 6- and 8-velocity models can only capture the propa
gation of diffusion mode (entropy wave) in the intermediate Knudsen number
regime. 4-velocity model instead captures the propagation of sound mode qui
te well after the comparison with the continuum-mechanic results.