Question

A stretched string of $1\text{m}$ length fixed at both ends, having a mass of $5\times {10}^{-4}\text{kg}$ is under a tension of $20\text{N}$. It is plucked at a point situated at $25\text{cm}$ from one end. The stretched string would vibrate with a frequency of

• A. $400\text{Hz}$
• B. $100\text{Hz}$
• C. $200\text{Hz}$
• D. $256\text{Hz}$

Answer 1

The correct option is C $200\text{Hz}$

$\nu =\frac{2}{2l}\sqrt{\frac{T\times l}{M}}$ or $\nu =\sqrt{\frac{T}{Ml}}=\sqrt{\frac{20}{5\times {10}^{-4}\times 1}}$
$=\sqrt{4\times {10}^4}\text{Hz}=200\text{Hz}$