  We report and discuss phase-shift and phase travel time of low-frequency
({\nu} < 5.0 mHz) acoustic waves estimated within the photosphere and
photosphere-chromosphere interface regions, utilizing multi-height velocities
in the quiet Sun. The bisector method has been employed to estimate seven
height velocities in the photosphere within the Fe I 6173 {\AA} line scan,
while nine height velocities are estimated from the chromospheric Ca II 8542
{\AA} line scan observations obtained from the Narrow Band Imager instrument
installed with the Multi-Application Solar Telescope operational at the Udaipur
Solar Observatory, India. Utilizing fast Fourier transform at each pixel over
the full field-of-view, phase shift and coherence have been estimated. The
frequency and height-dependent phase shift integrated over the regions having
an absolute line-of-sight magnetic field of less than 10 G indicates the
non-evanescent nature of low-frequency acoustic waves within the photosphere
and photosphere-chromosphere interface regions. Phase travel time estimated
within the photosphere shows non-zero values, aligning with previous
simulations and observations. Further, we report that the non-evanescent nature
persists beyond the photosphere, encompassing the photospheric-chromospheric
height range. We discuss possible factors contributing to the non-evanescent
nature of low-frequency acoustic waves. Additionally, our observations reveal a
downward propagation of high-frequency acoustic waves, indicating the
refraction from higher layers in the solar atmosphere. This study contributes
valuable insights into the understanding of the complex dynamics of acoustic
waves within different lower solar atmospheric layers, shedding light on the
non-evanescent nature and downward propagation of the acoustic waves.
