  In: {\it "Three-dimensional direct numerical simulation (DNS) of
Rayleigh-Taylor instability (RTI) trigerred by acoustic excitation -- Sengupta
et al. {\bf 34},054108 (2022)"} the receptivity of RTI to pressure pulses have
been established. It has also been shown that at the onset of RTI these pulses
are one-dimensional and the dissipation of the pressure pulses are governed by
a dissipative wave equation. The propagation of these infrasonic to ultrasonic
pressure pulses have been studied theoretically and numerically by a high
fidelity numerical procedure in the physical plane. The numerical results are
consistent with the theoretical analysis and the DNS of RTI noted above. The
properties of pulse propagation in a quiescent dissipative ambience have been
theoretically obtained from the linearized compressible Navier-Stokes equation,
without Stokes' hypothesis. This analysis is extended here for a special class
of excitation, with combination of wavenumbers and circular frequencies for
which the phase shift results in an imposed time period is integral multiple of
$\pi$, and the signal amplification is by a real factor. Here, the governing
partial differential equation (PDE) for the free-field propagation of pulses is
solved by the Bromwich contour integral method in the spectral plane. This
method, for an input Gaussian pulse excited at a fixed frequency, is the
so-called signal problem. Responses for the specific phase shifts integral
multiple of $\pi$ can reinforce each other due to the phase coherence. It is
shown that these combinations occur at a fixed wavenumber, with higher
frequencies attenuated more in such a sequence.
