Two identical pulses move in opposite directions with same uniform speeds on a stretched string. The width and kinetic energy of each pulse is L and k respectively. At the instant they completely overlap, the kinetic energy of the width L of the string where they overlap is

A

k

B

2k

C

4k

D

8k

The velocity of the profile of each elementary section of the pulse is shown in figure 1 and figure 2.
When both the pulses completely overlap, the velocity profiles of both the pulses in overlap region are identical. By superposition, the velocity of each elementary section doubles. Therefore K.E. of each section becomes four times.Hence the K.E. in the complete width of overlap becomes four times, i.e., 4k.