Question

A uniform rope of mass 0.1 kg and length 2.45 m hangs from the ceiling. Calculate the time taken by a transverse wave to travel the full length of the rope

• A. 1s
• B. 2s
• C. 3s
• D. 4s

Answer 1

The correct option is A

1s

Speed of wave at a distance x from free end is, v= $\frac{dx}{dt}$ =$\sqrt{xg}$ .Integrating over the length of rope, we get,

$t={\int }_0^{t}dt=\frac{1}{\sqrt{g}}{\int }_0^1\frac{dx}{\sqrt{x}}=1s$