Question

A string of length 0.3 m and mass ${10}^{-2}kg$ is clamped at both its ends. The tension in the string is 1.2 N. When a pulse travels along the string, the shape the string is found to be the same at times t and $t+\Delta t$. The minimum value of $\Delta t$ is $\frac{1}{2k}s$. Find the value of k. ___

Answer 1

The string has same shape in figures first and last.
The distance travelled by the pulse (between these two situations)
$=2\times 0.3=0.6m$

$v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{1.2}{{10}^{-2}/0.3}}=6m{s}^{-1}$
$\therefore \Delta t=\frac{0.6}{6}=0.1=\frac{1}{2\times 5}s$
$\therefore k=5$