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  4. A transverse pulse generated at the bottom of a uniform rope of length L, travels in upward direction. The time taken by it to travel the full length of rope will be

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Q. A transverse pulse generated at the bottom of a uniform rope of length $L$, travels in upward direction. The time taken by it to travel the full length of rope will be

Waves

Solution:

Velocity of wave at a distance $x$ from lower end is
$v_{x}=\sqrt{2 g x}$
Time $d t=\frac{d x}{\sqrt{2 g x}}$
Integrating for 0 to $L$ we get
$\sqrt{\frac{4 l}{g}}$