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A person is producing wave in string by moving his hand first up and then down. If frequency is $\frac{1}{8}\,Hz$ then find out time taken by particle which is at a distance of $9\,m$ from source to move to lower extreme first time .... $s$ . (Given $\lambda = 24\, m$)
$3$
$5$
$9$
$8$
Solution
frequency is $\frac{1}{8} \mathrm{\,Hz}$
$\therefore $ Time period, $\mathrm{T}=8$ $sec.$
$\lambda=24 \mathrm{\,m}$
$\mathrm{v}=\mathrm{f} \lambda$
$=3 \mathrm{\,m} / \mathrm{s} \ldots \ldots \ldots(1)$
Time taken by particle to travel $9 \mathrm{\,m}$ is
$=\frac{9}{3}=3 \mathrm{\,sec}$
Now, time taken by particle to reach lower extreme first time
is $\frac{3 T}{4}=\frac{3}{4} \times 8$
$=6$ $sec.$ $\ldots \ldots(2)$
$\therefore $ Total time taken $=3 \mathrm{\,sec}+6 \mathrm{\,sec}$
$=9$ $sec$
