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 \((2)\)

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