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