Two wires W _ 1 and W _ 2 have the same radius r and respective,...

Let ${p}_{1}$ and ${p}_{2}$ be the number of antinodes of both wires.

Fundamental frequency remains the same for both wires.

${n}_{1} = {n}_{2}$

$T \to same$

$r \to same$

$l \to same$

$n = \dfrac{p}{2l}\sqrt{\dfrac{T}{\pi{r}^{2}ρ}}$

From the above equation, we have
$\dfrac{{p}_{1}}{\sqrt{{ρ}_{1}}} = \dfrac{{p}_{2}}{\sqrt{{ρ}_{2}}}$

$\to \dfrac{{p}_{1}}{{p}_{2}} = \sqrt{\dfrac{{ρ}_{1}}{{ρ}_{2}}}$

The ratio of antinodes is $\dfrac{{p}_{1}}{{p}_{2}} = \dfrac{1}{2}$.