Answer
$f = 960~Hz$
Work Step by Step
Note that $2.0~nm$ is $\frac{1}{3}$ of the maximum displacement.
We can find $\theta$ when $cos~\theta = \frac{1}{3}$:
$cos~\theta = \frac{1}{3}$
$\theta = cos^{-1}~(\frac{1}{3})$
$\theta = 1.23~rad$
We can find the wavelength:
$\frac{2.070~m-2.000~m}{\lambda} = \frac{1.23~rad}{2\pi~rad}$
$\frac{\lambda}{0.070~m} = \frac{2\pi~rad}{1.23~rad}$
$\lambda = (\frac{2\pi~rad}{1.23~rad})(0.070~m)$
$\lambda = 0.358~m$
We can find the frequency:
$f = \frac{v}{\lambda}$
$f = \frac{343~m/s}{0.358~m}$
$f = 960~Hz$
