  Stellar distance is an important basic parameter in stellar astrophysics.
Stars in a cluster are thought to be formed coevally from the same interstellar
cloud of gas and dust. They are therefore expected to have common properties.
These common properties strengthen our ability to constrain theoretical models
and/or to determine fundamental parameters, such as stellar mass, metal
fraction, and distance when tested against an ensemble of cluster stars. Here
we derive a new relation based on solar-like oscillations, photometric
observations, and the theory of stellar structure and evolution of red giant
branch stars to determine cluster distance moduli through the global
oscillation parameters $\Delta\nu$ and $\nu_{\rm max}$, and photometric data
\textit{V}. The values of $\Delta\nu$ and $\nu_{\rm max}$ are derived from
\textit{kepler} observations. At the same time, it is used to interpret the
trends between \textit{V} and $\Delta\nu$. From the analyses of this newly
derived relation and observational data of NGC 6791 and NGC 6819 we devise a
method in which all stars in a cluster are regarded as one entity to determine
the cluster distance modulus. This approach fully reflects the characteristic
of member stars in a cluster as a natural sample. From this method we derive
true distance moduli of $13.09\pm0.10$ mag for NGC 6791 and $11.88\pm0.14$ mag
for NGC 6819. Additionally, we find that the distance modulus only slightly
depends on the metallicity [Fe/H] in the new relation. A change of 0.1 dex in
[Fe/H] will lead to a change of 0.06 mag in the distance modulus.
