An analytical solution is presented to the problem of non-isentropic a
coustic wave motion in a narrow circular tube in the presence of a bac
kground axial temperature gradient. The radial velocity component is r
etained in the analysis and an isentropic solution is also presented f
or comparative purposes. The effect of the temperature gradient upon t
he attenuation and phase speed of the pressure wave and upon the ampli
tude and cross-sectional profile of the axial velocity, acoustic tempe
rature and radial velocity is explored. The main application area is t
he study of the acoustic effects of catalytic converters.