  In the $f_2(1270)-f^\prime_2(1525)$ mixing framework, the isoscalar
singlet-octet mixing angle for 1$^3P_2$ tensor nonet is determined to be the
value of $27.5^\circ$ and the decays of the two states are investigated.
Comparing the predicted results of the decays of the two states with the
available experimental data, we find that the predicted results are in good
agreement with the experimental data, which shows that the $f_2(1270)$ and
$f^\prime_2(1525)$ wave functions don't need other components such as glueballs
or the 2 $^3P_2$,3 $^3P_2$,...$q\bar{q}$.
