Question

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

Answer 1

for a transverse wave
n=v/2l
v=√T/√nmu
=√mg/√m/l
=√gx (where x=l)
therefore
v=√gl
n=1/T
where T=2l/v

T=2l/√gl
=√4l^2/√gl
=√4l/√g

Answer 2

"$n = \frac {v} {2l}$

$v = \sqrt {\frac {T} {\mu}}$

Where v = velocity of wave propagation, T = tension of the string and µ = linear density of the string.

$v = \sqrt {\frac{mg}{\frac{m}{l}} }$

$= \sqrt{gx}$

$v=\sqrt{gl}$

$n = \frac {1}{T}$; where $T = \frac {2l}{v}$

$T = \frac {2l}{\sqrt{gl}}$

$T=\sqrt{\frac{4l^2}{gl}}$ is the time taken by the pulse to travel the full length of the rope."