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

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Infinity Learn · Accepted Answer

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.

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