Question

The wire of a sonometer has a length of $1m$ and mass $5\times {10}^{-4}kg$. It has a tension of $20N$. If the wire is pulled at a point $25cm$ away from one end and released, the frequency of its vibrations will be

• A. $200Hz$
• B. $150Hz$
• C. $250Hz$
• D. $100Hz$

Answer 1

The correct option is A $200Hz$

$L=1m$

$m=5\times {10}^{-4}kg$

$T=20N$

$\mu =5\times {10}^{-4}kg/m$

when the wire is packed from $25cm$, it forms an antinode.

The vibrations formed would be of $2^{nd}$ harmonic motion.

$\therefore L=\lambda$

$\lambda =1m$

$f=\frac{v_0}{\lambda }=\frac{1}{1}\sqrt{\frac{T}{\mu }}$

$=\sqrt{\frac{20}{5\times {10}^{-4}}}$

$=2\times {10}^2=200H_3$

$\therefore$ Option (A) is correct.