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  4. A wire of density 9 gm cm -3 is stretched between two clamps 100 cm apart which is subjected to an extension of 0.05 cm. What is the lowest frequency of transverse vibration in the wire ? ( y =9 × 1010 Nm -2) ⇒ y = young's modules

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Q. A wire of density $9 \,gm \,cm ^{-3}$ is stretched between two clamps $100\, cm$ apart which is subjected to an extension of $0.05\, cm$. What is the lowest frequency of transverse vibration in the wire ? $\left( y =9 \times 10^{10} Nm ^{-2}\right) \Rightarrow y =$ young's modules

Solution:

$\therefore y =\frac{ T / A }{\Delta L / L }=\frac{ TL }{\Delta LA }$
$\frac{ T }{ A }= y \frac{\Delta L }{ L }=9 \times 10^{10} \times \frac{0.05}{100}=45 \times 10^{6}$
$n =\frac{1}{2 \ell} \sqrt{\frac{ T }{\mu}}=\frac{1}{2 \ell} \sqrt{\frac{ T }{ A \rho}}$
$n =\frac{1}{2 \times 1} \sqrt{\frac{45 \times 10^{6}}{9 \times 10^{3}}}$
$n =35.4$