  It has long been known that magnetic plage and sunspots are regions in which
the power of acoustic waves is reduced within the photospheric layers. Recent
observations now suggest that this suppression of power extends into the low
chromosphere and is also present in small magnetic elements far from active
regions. In this paper we investigate the observed power supression in plage
and magnetic elements, by modelling each as a collection of vertically aligned
magnetic fibrils and presuming that the velocity within each fibril is the
response to buffeting by incident $p$ modes in the surrounding field-free
atmosphere. We restrict our attention to modeling observations made near solar
disk center, where the line-of-sight velocity is nearly vertical and hence,
only the longitudinal component of the motion within the fibril contributes.
Therefore, we only consider the excitation of axisymmetric sausage waves and
ignore kink oscillations as their motions are primarily horizontal. We compare
the vertical motion within the fibril with the vertical motion of the incident
$p$ mode by constructing the ratio of their powers. In agreement with
observational measurements we find that the total power is suppressed within
strong magnetic elements for frequencies below the acoustic cut-off frequency.
We also find that the magnitude of the power deficit increases with the height
above the photosphere at which the measurement is made. Further, we argue that
the area of the solar disk over which the power suppression extends increases
as a function of height.
