Question

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

• A. 35 Hz
• B. 36.3 Hz
• C. 35.4 Hz
• D. 34.3 Hz

Answer 1

Answer: (C)

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