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 \lesssim 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 \lesssim 2.4 Gyr may aid in testing the theory of the degeneracy of the hydrogen-exhausted core .
Moreover , for the clusters with 1.1 \mathrm { M } _ { \odot } < M _ { hook } < 1.3 \mathrm { 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 .