Question

A uniform rope of length 12 m and mass 6 kg 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 0.06 m 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. 0.06 m
• B. 0.12 m
• C. 0.09 m
• D. 0.24 m

Answer 1

The correct option is B

0.12 m

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

$\frac{f{\lambda }_{Top}}{f{\lambda }_{Bottom}}=2$ as frequency does not change

${\lambda }_{top}={\lambda }_{bot}\times 2=0.12m.$