  We consider a family of 4-dimensional black hole solutions from Dehnen et al.
( Grav. Cosmol. 9:153, arXiv: gr-qc/0211049, 2003) governed by natural number
$q= 1, 2, 3 , \dots$, which appear in the model with anisotropic fluid and the
equations of state: $p_r = -\rho (2q-1)^{-1}$, $p_t = - p_r$, where $p_r$ and
$p_t$ are pressures in radial and transverse directions, respectively, and
$\rho > 0$ is the density. These equations of state obey weak, strong and
dominant energy conditions. For $q = 1$ the metric of the solution coincides
with that of the Reissner-Nordstr\"om one. The global structure of solutions is
outlined, giving rise to Carter-Penrose diagram of Reissner-Nordstr\"om or
Schwarzschild types for odd $q = 2k + 1$ or even $q = 2k$, respectively.
Certain physical parameters corresponding to BH solutions (gravitational mass,
PPN parameters, Hawking temperature and entropy) are calculated. We obtain and
analyse the quasinormal modes for a test massless scalar field in the eikonal
approximation. For limiting case $q = + \infty$, they coincide with the
well-known results for the Schwarzschild solution. We show that the Hod
conjecture which connect the Hawking temperature and the damping rate is obeyed
for all $q \geq 2$ and all (allowed) values of parameters.
