Two forms of Wien's displacement law

There are two forms of Wien's displacement law that can be derived from Planck's equation. They are: \begin{equation} \label{eq1} \lambda _m T=2.8977685\times 10^{-3}{\begin{array}{*{20}c} \hfill & {\mbox{m}\cdot \mbox{K}} \hfill \\ \end{array} } \end{equation} \begin{equation} \label{eq2} \frac{f_m }{T}=5.879\times 10^{10}{\begin{array}{*{20}c} \hfill & {\mbox{Hz/K}} \hfill \\ \end{array} } \end{equation} Where $\lambda _{m}$ and $f_{m}$ are wavelength and frequency corresponding to the maximum intensity $I_{m}$ of radiation of the black body, and $T$ is the temperature of the black body. Suppose that we have known a black body's temperature, then $\lambda _{m}$ and $f_{m}$ can be obtained from Eqs. (1) and (2). For example, the Sun's surface temperature, $T$ = 5778 K, then according to Eqs. (1) and (2), we get \[ \lambda _m =5.015\times 10^{-7}{\begin{array}{*{20}c} \hfill & \mbox{m} \hfill \\ \end{array} } \] And \[ f_m =3.397\times 10^{14}{\begin{array}{*{20}c} \hfill & {\mbox{Hz}} \hfill \\ \end{array} } \] However, if we apply $c=\lambda f$, and take $c$ = 3$\times $10$^{8}$ m/s, then from $\lambda _{m}$ = 5.015$\times $10$^{-7}$ m, we get $f$ = 5.982$\times $10$^{14}$ Hz, which is not the $f_{m}$ obtained from eq. (2). In this paper, I have shown the reason why.