Question

A 100 cm string fixed at both ends produces consecutive resonant modes at 460 Hz & 552 Hz, find the mass of thread (T = tension in the thread = 34 N)

• A. 1 gram
• B. 2 gram
• C. 3 gram
• D. 4 gram

Answer 1

The correct option is A 1 gram

$460=n.\left(\frac{v}{2l}\right)$
$552=(n+1)\left(\frac{v}{2l}\right)$
$\frac{552}{460}=\frac{n+1}{n}$
$\frac{6}{5}=\frac{n+1}{n}$
$6n=5n+5$
$n=5$
$460=5\left\{\frac{v}{2\times 100cm}\right\}$
$v=\frac{460\times 2}{5}\left(m/sec\right)=184m/s$
$v=\sqrt{\frac{T}{\mu }}$
$\mu =\frac{T}{v^2}=\frac{34}{34\times {10}^3}$
$={10}^{-3}k{g}^{-1}$
$m=\mu .l={10}^{-3}\times 1$
=1 gram