  The Einstein Equivalence Principle (EEP) carries a pivotal role in
understanding theory of gravity and spacetime. It guarantees the gravity to be
understood as geometric phenomenon. Considering gravitational coupling of
matter in the standard model extension, we propose a novel scheme using
frequency measurements to limit the equivalence principle violations in normal
matter. The proposal consists of the comparison of high-precision clocks,
comoving with the freely falling frame. The experimental comparison of
identical kind of clocks on Earth surface can be used to carry out the proposed
test, which allows performing simultaneous tests of weak equivalence principle
and gravitational redshift. From the existing experiments of Sr optical clocks,
we present a simultaneous determination of Earth-dependent parameter
$\beta_{\text{E}}$ and clock-dependent parameter $\xi_{\text{Sr}}$ at the level
of $10^{-5}$, and in combination with the gravitational redshift experiments
and lunar laser ranging, we also obtain a limit on standard model extension
coefficients for Lorentz violation. This work provides another important
fundamental physics application for the continuous-improvement accuracy of
atomic or optical clocks.
