Explanation:
C Given, length of wire $(l)=20 \mathrm{~cm}=0.2 \mathrm{~m}$ Tension $(\mathrm{T})=25 \mathrm{~N}$, Density $(\rho)=10^{4} \mathrm{~kg} / \mathrm{m}^{3}$ Cross sectional area $(A)=10^{-2} \mathrm{~cm}^{2}=10^{-6} \mathrm{~m}^{2}, \mathrm{f}=$ ? We know,
The fundamental frequency of the sonometer wire is,
$\mathrm{f}=\frac{1}{2 l} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}$
Then, mass per unit length is,
$\mathrm{m}=\rho \times \mathrm{V}=\rho(\mathrm{A} \times 1)$
$\mathrm{m}=10^{4} \times 10^{-6} \times 1$
$\mathrm{~m}=10^{-2}{\mathrm{~kg}-\mathrm{m}^{-1}}^{-1}$
Hence,
$f=\frac{1}{2 \times 0.2} \sqrt{\frac{25}{10^{-2}}}$
$f=\frac{1}{0.4} \times \sqrt{2500}$
$f=\frac{10}{4} \times 50$
$f=125 \mathrm{~Hz}$