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14. waves and sound — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
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
  • A
    $\sqrt{\frac{L}{2 g}}$
  • B
    $\sqrt{\frac{2 L}{g}}$
  • C
    $\sqrt{\frac{L}{g}}$
  • ✓
    $\sqrt{\frac{4 L}{g}}$
✓

Answer

Correct option: D.
$\sqrt{\frac{4 L}{g}}$
d
(d)

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

$\sqrt{\frac{4 l}{g}}$

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