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The wave function of a triangular wave pulse is defined by the relation below at time t=0 sec.
$y = {\begin{matrix} m x & f o r 0 \leq x \leq \frac{a}{2} \\ - m (x - a) & f o r \frac{a}{2} \leq x \leq a \\ 0 & e v e r y w h e r e e l s e \end{matrix}$
The wave pulse is moving in the +X direction in a string having tension T and mass per unit length $μ .$ The kinetic energy contained in the wave pulse is (Assume that $m < < 1$ and neglect permanent deformations at the sharp edges)

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$\frac{m^{2} T a}{μ}$

$\frac{m^{2} T a}{2}$

$\frac{m^{2} T a}{2 μ}$

$m^{2} T a$

answer is A.

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Detailed Solution

$\frac{d U}{d x} = \frac{1}{2} T {(\frac{\partial y}{\partial x})}^{2} = \frac{d K E}{d x}$

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