Answer
$1208\;\rm Hz$
Work Step by Step
To find the frequency of the vibrating tuning fork, we need to find the wavelength of the standing waves inside the tube.
Recalling that
$$v=\lambda f$$
Hence,
$$f=\dfrac{v}{\lambda}\tag 1$$
We know that the wavelength in the three cases, when $L=\rm42.5\; cm, 56.7\; cm,70.9\;cm$, is constant since the frequency of the tuning fork is constant (and so so the speed of sound in air).
We can see that
$$\Delta L=L_2-L_1=L_3-L_2=\bf 14.2\;\rm cm\tag 2$$
Noting that increasing the length of the tube means going from $m$ to $m +1$
Recalling that, for an open-open tube,
$$\lambda_m=\dfrac{2L}{m}$$
So,
$$L=\dfrac{m\lambda}{2}$$
Hence,
$$\Delta L=L_2-L_1=\dfrac{(m+1)\lambda}{2}-\dfrac{m\lambda}{2}=\dfrac{\lambda}{2}$$
Thus,
$$\lambda=2\Delta L$$
Plugging from (2);
$$\lambda=2(14.2)=\bf 28.4\;\rm cm$$
Plugging into (1);
$$f=\dfrac{343}{28.4\times 10^{-2}} $$
$$f=\color{red}{\bf 1208}\;\rm Hz$$
