Question

A uniform rope of mass $6 \, kg$ and length $6 \, m$ hangs vertically from a rigid support. A block of mass $2 \, kg$ is attached to the free end of the rope. A transverse pulse of wavelength $0.075 \, m$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $K \, cm$ where $K$ is

Answer 1

$T_{1}= \, 2 \, \times \, 10 \, = \, 20 \, N$
$T_{2} \, = \, \left(\right.2 \, + \, 6\left.\right) \, 10 \, = \, 80 \, N$
$\frac{V_{2}}{V_{1}}=\sqrt{\frac{80}{20}}=2$
Frequency remains unchanged
So $\frac{\lambda _{2}}{\lambda _{1}}=2$
$\lambda _{2}=2\times 0.075$
$= \, 0.15 \, m$
$K=15 \, cm$