Question

A wire unit of density $\frac{9g}{cc}$ is stretched between two clamps 1 m apart while subjected to an extension of 0.05 cm. The lowest frequency of transverse vibrations in the wire is (Assume Young’s modulus $Y=9\times {10}^{10}N/m^2$)

• A. 35 Hz
• B. 45 Hz
• C. 75 Hz
• D. 90 Hz

Answer 1

The correct option is A 35 Hz

$T=y\frac{\Delta \ell }{\ell }AT=Y\frac{\Delta \ell }{\ell }.\frac{\mu }{\rho }\frac{T}{\mu }=\frac{Y\Delta \ell }{\rho \ell }=\frac{9\times {10}^{10}\times 5\times {10}^{-4}}{9\times {10}^3}=5000v=\sqrt{\frac{T}{\mu }}=\sqrt{50}\times 10m/s{\lambda }_{max}=2\ell and{f}_{min}=\frac{v}{{\lambda }_{max}}=\frac{\sqrt{50}\times 10}{2}35Hz$