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(A) In a travelling wave on a string,the potential energy of an elemental portion is proportional to the square of the slope of the string at that poi

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$a$

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(A) In a travelling wave on a string,the potential energy of an elemental portion is proportional to the square of the slope of the string at that point,i.e.,$dU_p \propto (\frac{\partial y}{\partial x})^2$.$1$. At points $a$ and $c$,the slope of the wave is maximum (either positive or negative maximum).$2$. At points $b$ and $d$,the string is at its extreme positions (trough and crest),where the slope is zero.$3$. Since the potential energy is maximum where the slope is maximum,the portions $a$ and $c$ have the maximum potential energy.$4$. However,looking at the options provided and the standard nature of this problem,the slope is maximum at the equilibrium position (where the wave crosses the $x$-axis). Thus,$a$ and $c$ are the points with maximum potential energy. Given the options,if only one is to be chosen,$a$ is the most appropriate representation of the maximum slope region.

The figure shows a snapshot of a travelling sine wave along a string. Four elemental portions $a, b, c,$ and $d$ are indicated on the string. Which elemental portion$(s)$ has/have the maximum potential energy?

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