Generated by the Physics Derivation Graph. Eq. \ref{eq:3293094} is an initial equation. \begin{equation} k = \frac{\omega}{v} \label{eq:3293094} \end{equation} Eq. \ref{eq:3294004} is an initial equation. \begin{equation} \lambda = \frac{v}{f} \label{eq:3294004} \end{equation} Eq. \ref{eq:9214650} is an initial equation. \begin{equation} \omega = 2 \pi f \label{eq:9214650} \end{equation} Eq. \ref{eq:8482459} is an initial equation. \begin{equation} T = 1 / f \label{eq:8482459} \end{equation} Substitute RHS of Eq. \ref{eq:8374556} into Eq. \ref{eq:3293094}; yields Eq. \ref{eq:8394853}. \begin{equation} k = \frac{2 \pi}{v T} \label{eq:8394853} \end{equation} Substitute RHS of Eq. \ref{eq:8482459} into Eq. \ref{eq:3294004}; yields Eq. \ref{eq:3993940}. \begin{equation} \lambda = v T \label{eq:3993940} \end{equation} Substitute RHS of Eq. \ref{eq:3993940} into Eq. \ref{eq:8394853}; yields Eq. \ref{eq:2934848}. \begin{equation} k = \frac{2 \pi}{\lambda} \label{eq:2934848} \end{equation} Multiply both sides of Eq. \ref{eq:8482459} by \(f\); yields Eq. \ref{eq:8341200}. \begin{equation} T f = 1 \label{eq:8341200} \end{equation} Divide both sides of Eq. \ref{eq:8341200} by \(T\); yields Eq. \ref{eq:9380032}. \begin{equation} f = 1/T \label{eq:9380032} \end{equation} Substitute RHS of Eq. \ref{eq:9380032} into Eq. \ref{eq:9214650}; yields Eq. \ref{eq:8374556}. \begin{equation} \omega = \frac{2\pi}{T} \label{eq:8374556} \end{equation} Eq. \ref{eq:2934848} is one of the final equations.