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. $\sqrt{\frac{L}{2g}}$
• B. $\sqrt{\frac{2L}{g}}$
• C. $\sqrt{\frac{L}{g}}$
• D. $\sqrt{\frac{4L}{g}}$

Answer 1

Answer: (D)

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

For a transverse wave

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

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

Where $v=$ velocity of wave propagation

$T=$ tension of the string

$\mu =$ linear density of the string.

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

$=\sqrt{gx}$ (where $x=L$)

therefore

$v=\sqrt{gL}$

$n=\frac{1}{T}$

where $T=\frac{2L}{v}$

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

$=\sqrt{\frac{4L^2}{gL}}$

$=\sqrt{\frac{4L}{g}}$