A rope of mass m and length L is suspended vertically. A mass M is suspended from bottom of the rope. A transverse wave is produced on the rope, which travels the length of rope in time t. Choose the correct statement (s)

A

$$t = 2\sqrt{\frac{L}{mg}}\left(\sqrt{M + m} - \sqrt{M}\right)$$

B

For $$m \ll M$$ the time $$t = \sqrt{\frac{mL}{Mg}}$$

C

For M = 0 (that is no mass hanging) the time $$t = \sqrt{\frac{L}{g}}$$

D

Time to travel the lower half of the rope by the wave is less than that to travel the upper half