  In this work, we make the first step to derive non-radial pulsation equations
in extra dimensions and investigate how the $f$- and $p_1$-mode frequencies of
strange quark stars, within the Cowling approximation, change with the number
of dimensions. In this regard, the study is performed by solving numerically
the non-radial pulsation equations, adjusted for a $d$-dimensional space-time
$(d\geq4)$. We connect the interior to a Schwarzschild-Tangherlini exterior
metric and analyze the $f$- and $p_1$- mode frequencies. We found that the
frequencies could become higher than those found in four-dimensional
space-time. The $f$-mode frequency is essentially constant and only for large
gravitational radius values grows monotonically and fast with the gravitational
radius. In a gravitational radius range, where $f$-mode frequencies are
constant, they increase for space-time dimensions $4\leq d\leq6$ and decrease
for $d\geq7$. Regarding $p_1$-mode frequencies they are always larger for
higher dimensions and decay monotonically with the increase of the
gravitational radius. In extra dimensions, as it happens for four-dimensional
space-time, we found $p_1$-mode frequencies are always larger than the
$f$-modes ones. In the Newtonian gravity, for a homogeneous star in $d$
dimensions, we observe that the $f$-mode eigenfrequencies are constant and
given by the relation $\omega^2=l\, M\, G_d/R^{d-1}$; where $l$ represents the
spherical harmonic index, $M\,G_d$ being the total star mass and $R$ the
stellar radius.
