  Using a stellar population-synthesis method, we studied the distributions of
{\nu}_max and {\Delta}{\nu} of simulated clusters with various ages and
metallicities. Except for the confirmed peak (RC peak) of {\Delta}{\nu} of
red-clump (RC) stars, i.e. core-helium burning stars, there are a gap and a
main sequence (MS) peak in the distributions of {\nu}_max and {\Delta}{\nu} of
young clusters. The gap corresponds mainly to the Hertzsprung gap phase of
evolution. The RC peak is caused by the fact that the radius of many RC stars
near the zero-age horizontal branch concentrates in a certain range. The MS
peak also results from the fact that many MS stars which are located in a
certain mass range have an approximate radius in the early phase of MS. The MS
peak barely exists in the simulated clusters with age < 1.0 Gyr. The location
of the MS peak moves to a lower frequency with increasing age or metallicity,
which may be applied to constrain the age and metallicity of young clusters.
For the simulated clusters with Z = 0.02, the frequency of the location of the
dominant RC peak increases with age when age < 1.2 Gyr, and then decreases with
age when age > 1.2 Gyr; but it scarcely varies when age > 2.4 Gyr. This is
relative to the degeneracy of the hydrogen-exhausted core at the time of helium
ignition. In addition, the RC peak is not sensitive to the metallicity,
especially for the clusters with age > 2.4 Gyr. Asteroseismical observation for
clusters with age < 2.4 Gyr may aid in testing the theory of the degeneracy of
the hydrogen-exhausted core. Moreover, for the clusters with 1.1 M{\odot} <
M_hook < 1.3 M{\odot}, there are a MS gap and a peak on the left of the MS gap
in the distributions of{\nu}_max and {\Delta}{\nu}, which may be applied to
constrain the central hydrogen abundance of stars in the MS gap and the peak.
