$n_{2}=f n_{1}$$\ldots \ldots .(1)$

Also the natural freq of the source is $n_{0}$

Then we can write,

Q$n_{1}=\frac{V}{V-V_{s}} n_{0}$

$n_{2}=\frac{V}{V+V_{s}} n_{0}$

Substitute these values in equation $(1),$

And apply componendo-dividendo,

We will get, $\frac{V_{s}}{V}=\frac{1-f}{1+f}, \ldots \ldots \ldots \ldots \ldots .(2)$

we are asked, the difference of

$n_{1}-n_{2}=\left(\frac{1}{1-\frac{V_{s}}{V}}-\frac{1}{1+\frac{V_{s}}{V}}\right) n_{0}$

Substitute the value of $\frac{V_{s}}{V}$ from equation $(2)$

$n_{1}-n_{2}=\frac{1}{2} n_{0} \frac{1-f^{2}}{f}$