  In the classical theory of acoustic waves, Blackstock's model was proposed in
1963 to characterize the propagation of sound in thermoviscous fluids. In this
paper, we investigate large-time asymptotic behaviors of the linear Cauchy
problem for general Blackstock's model (that is, without Becker's assumption on
monatomic perfect gases). We derive first- and second-order asymptotic profiles
of solution as $t\gg1$ by applying refined WKB analysis and Fourier analysis.
Our results not only improve optimal estimates in [Chen-Ikehata-Palmieri,
\emph{Indiana Univ. Math. J.} (2023)] for lower dimensional cases, but also
illustrate the optimal leading term and novel second-order profiles of solution
with additional weighted $L^1$ data.
