As we know, frequency

$f \propto \sqrt{m g}$ or $f \propto \sqrt{g}$

In water, $f _{ w }=0.8 f _{ air }$

$\frac{ g ^{\prime}}{ g }(0.8)^2=0.64$

$\Rightarrow 1-\frac{\rho_{ w }}{\rho_{ m }}=0.64$

$\Rightarrow \frac{\rho_{ W }}{\rho_{ m }}=0.36$

In liquid, $\frac{ g ^{\prime}}{ g }=(0.6)^2=0.36$

$1-\frac{\rho_1}{\rho_{ m }}=0.36 \frac{\rho_1}{\rho_{ m }}=0.64$

From eq. $(1)$ and $(2)$

$\frac{\rho_l}{\rho_n}=\frac{0.64}{0.36} \quad \therefore \quad \rho_l=1.77$