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

Options

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

Answer

C

Explanation

As the rope has a mass and a mass is also suspended from the lower end, the tension in the rope will be `v = sqrt(T/mu)` different at different points `v = sqrt(T/mu)` where `mu` is mass per unit length of the string.
`v_(A)/v_(B) = sqrt(T_(A)/T_(B))= sqrt((6+2)/2) = 2`
As `v = f lambda, therefore v_(A)/v_(B) = f_(A)/f_(B).lambda_(A)/lambda_(B)`
Since frequency is the characteristic of the source producing the wave.
`lambda_(A) = v_(A)/v_(B).lambda_(B) = 2 xx 0.6 m = 0.12 m`