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. $0.12m$
• C. $0.09m$
• D. $0.24m$

Answer 1

The correct option is B $0.12m$

velocity of wave pulse in a string is $v=\sqrt{\frac{T}{\mu }}$
now,
let $T_T$ be tension of the string at top and
$T_B$ be tension of the string at bottom
$T_B=2g$(mass of the block)
$T_T=6g+2g$ (mass of the block+mass of the string)

$\Rightarrow \frac{v_{top}}{v_{bottom}}=\sqrt{\frac{T_T}{T_B}}=\sqrt{\frac{(6+2)g}{2g}}=2$

As frequency does not change

$\frac{{\lambda }_{Top}}{{\lambda }_{Bottom}}=2$

${\lambda }_{Top}={\lambda }_{Bottom}\times 2=0.12m.$