  Within an isospin and momentum dependent transport model, the dynamics of
isospin particles (nucleons and light clusters) in Fermi-energy heavy-ion
collisions are investigated for constraining the isospin splitting of nucleon
effective mass and the symmetry energy at subsaturation densities. The mass
splitting of $m^{*}_{n}>m^{*}_{p}$ and $m^{*}_{n}<m^{*}_{p}$ in nuclear matter
and the different stiffness of symmetry energy are used in the model. The
single and double neutron to proton ratios of free nucleons and light particles
are thoroughly investigated in the isotopic nuclear reactions of
$^{112}$Sn+$^{112}$Sn and $^{124}$Sn+$^{124}$Sn at the incident energies of 50
and 120 MeV/nucleon, respectively. It is found that the both effective mass
splitting and symmetry energy impact the kinetic energy spectra of the single
ratios, in particular at the high energy tail (larger than 20 MeV). Specific
constraints are obtained from the double ratio spectra, which are evaluated
from the ratios of isospin observables produced in $^{124}$Sn+$^{124}$Sn over
$^{112}$Sn+$^{112}$Sn collisions. A mass splitting of $m^{*}_{n}<m^{*}_{p}$ is
constrained from the available data at the energy of 120 MeV/nucleon. A soft
symmetry energy with the stiffness of $\gamma_{s}=$0.5 is close to the
experimental double ratio spectra at both energies.
