A uniform rope of length 12 mm 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?

Options

A. 0.6 m
B. 0.32 m
C. 0.24 m
D. 0.12 m

Answer

D

Explanation

Tension at the lower end of the rope = 2 kg weight
Tension at the top of the rope `= 6 +2 = 8kg` weight ltrbgt
`:' v = sqrt((T)/(m)) :' (v_("Top"))/(v_("Lower")) = sqrt((T_("Top"))/(T_("Lower"))) = sqrt((8)/(2)) = 2`…(1)
As the frequency (n) remains constant, equation (1) will be
`(v_("Top"))/(v_("Lower")) = (n lamda_("Top"))/(n lamda_("Lower")) = 2 " " :. (lamda_("Top"))/(0.06) = 2`
`lamda_("Top") = 0.12m`