Answer
$3.30\times10^{-6}$
Work Step by Step
The active medium in a particular laser that generates laser light at a wavelength of $\lambda=694\;nm$ is $L=6.00\;cm$ long and $d=1.00\;cm$ in diameter.
We treat the medium as an optical resonance cavity analogous to a closed organ pipe.
For closed organ pipe, the general formula wavelengths is
$\lambda=\frac{4L\mu}{2n-1}$
where, $n=1,2,3,4................$. The value of $n$ also corresponds to the number of nodes. $\mu$ is the refractive index of the material.
Then the general formula for the frequency is given by
$f=\frac{c}{\lambda}$
or, $f=\frac{c(2n-1)}{4L\mu}$
Partially differentiating both sides keeping $L$, $\mu$ constant, we obtain
$\Delta f=\frac{2c}{4L\mu}\Delta n$
Therefore,
$\frac{\Delta f}{f}=\frac{2\lambda}{4L\mu}\Delta n$
Substituting the given values, we obtain
$\frac{\Delta f}{f}=\frac{2\times694\times10^{-7}}{4\times6\times1.75}(1)$
or, $\frac{\Delta f}{f}\approx3.30\times10^{-6}$
