A uniform rope of length 12m 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 in the lower end of the rope. What is the wavelength of the pulse when it reached the top of the rope?


Correct option is

0.03 m

Because the rope has a finite mass, the tension in the rope is different at different points on the rope. At the top where the rope is rigidly fixed, the tension = weight of the rope + the weight attached to the free end of the rope = 6 kg + 2 kg = 8 kg wt. Tension at the free end of the rope = 2 kg wt. Since , if the tension becomes 4 times, the frequency is doubled. Since   Hence the wavelength is halved.



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