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

Question

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) √(L/2 g) (B) √(2 L/g) (C) √(L/g) (D) √(4 L/g)

Tardigrade Admin · Accepted Answer

Velocity of wave at a distance x from lower end is vx=√2 g x Time d t=(d x/√2 g x) Integrating for 0 to L we get √(4 l/g)

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

$\frac{L}{2 g}$

$\frac{2 L}{g}$

$\frac{L}{g}$

$\frac{4 L}{g}$

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

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

2gL​​

g2L​​

gL​​

g4L​​