Question

A uniform rope of length $12m$ and mass $6kg$ hangs vertically from a rigid support. A block of mass $2kg$ is attached to the free end of the rope. A transverse pulse of wavelength $0.06m$ is produced at the lower end of the rope. What is the wavelength of the pulse when it reaches the top of the rope?

• A. $0.06m$
• B. $0.03$
• C. $0.12m$
• D. $0.09m$

Answer 1

The correct option is C $0.12m$

As rope is heavy, Tension is different at different points. $T$ at lower end is $2g$ and at upper end is $6g$

$V=v\lambda$

$\sqrt{\frac{F}{\mu }}=v\lambda$

$\frac{\sqrt{F}}{\lambda }=v\sqrt{\mu }$

$\frac{\sqrt{F}}{\lambda }$ is constant

$\frac{\sqrt{2g}}{0.00}=\frac{\sqrt{8g}}{{\lambda }_1}$

$\Rightarrow {\lambda }_1=0.12m$