Answer
The proof is below.
Work Step by Step
We know the following equation:
$\frac{2L}{v}=mT$
Since $T=\frac{1}{f}$, it follows:
$\frac{2L}{v}=\frac{m}{f} \\ L = \frac{mv}{2f}$
Recall, $v=\lambda f$. Thus:
$ L = \frac{m\lambda f}{2f}=\frac{m \lambda}{2}$
