Two identical pulses (one is inverted w.r.t other) move in opposite directions with same uniform speeds on a stretched string. The width and kinetic energy of each pulse are L and k respectively. At the instant they completely overlap, the kinetic energy of the width L of the string in overlapped part is

The velocity 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, velocity of each elementary sectiondoubles. Therefore, KE of each section becomes four times. Hence the K.E. in the complete width of overlap becomes four times.