Question

A sonometer wire of length $1.5m$ is made of steel. The tension in it produces an elastic strain of $1\%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7\times {10}^{3}kg/m^3$ and $2.2\times {10}^{11}N/m^2$ respectively?

• A. $178.2Hz$
• B. $200.5Hz$
• C. $770Hz$
• D. $188.5Hz$

Answer 1

The correct option is A $178.2Hz$

Fundamental frequency $f=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$
$=\frac{1}{2\ell }\sqrt{\frac{T}{Ap}}$
$=\frac{1}{2\ell }\sqrt{\frac{stress}{\rho }}=\frac{1}{2\times 1.5}\sqrt{\frac{22\times {10}^{11}\times {10}^{-2}}{77\times {10}^3}}.$
$={10}^3\times 0.17817$ $=178.2Hz$