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?

Answer 1

$V_{\left(Lowerend\right)}=\sqrt{\frac{mg}{0.5}}$

$=\sqrt{2mg}$

$=\sqrt{2\times 2\times 10}$

$=6.26$

$V_{upper}=\sqrt{\frac{(2+6)g}{0.5}}$

$=\sqrt{16\times 9.8}$

$=12.52$

$\therefore V_{upp}=V_{low}$

$\frac{V_{upp}}{{\lambda }_{upp}}=\frac{V_{low}}{{\lambda }_{low}}$

$={\lambda }_{upp}=\frac{12.52}{6.26}\times 0.06$

$=0.12m$