One end of a 60 m long rope of mass 1.8 kg is tied to a rigid horizontal support held high above tlie ground. The rope hangs vertically and kept taut by a weight W suspended at its lower end. Aperson jerks the lower end of the rope sideways in a sinusoidal manner and a transverse wave of freqeuncy 2 Hz and amplitude 10 cm passes along the rope such that there are 2 cycles of the wave in the total length of the rope.

Neglecting the weight of the rope as compared to the suspended weight W and with `g = 10 m//s^2`, answer the following questions.
In the questions above, weight of the rope has been neglected as compared to the suspended weight. However, if we also account for the weight of the rope, the speed of the wave at the top of the rope will-be:

Options

A. 60 m/s
B. 64.8 m/s
C. 62.6 m/s
D. 68.4 m/s

Answer

B

Explanation

`T = (10.8 + 1.8) xx 10 = 12.6 xx 10 = 126, v= sqrt(T/m) = sqrt(126/0.03) = 64.8 m//s`