A) 0.06 m
B) 0.03 m
C) 0.12 m
D) 0.09 m
Correct Answer: B
Solution :
Since, 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 + weight attached to the free end = 6 + 2 = 8 kg wt. Tension at the free end of the rope = 2 kg wt. \[\because \]\[v\propto \sqrt{T},\] if the tension becomes 4 times, the frequency is doubled. Since,\[v=\frac{v}{\lambda },\lambda =\frac{1}{v}.\]Hence, wavelength is halved. Hence, the correction option is [b].
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