A part of snapshot of progressive wave propagating in a uniform string is shown in figure-1 and a snapshot of standing wave in a string (identical to case-1) is shown in figure -2.
The amplitude, frequency and wave length of waves in both cases is same. A and B (anti node) are material cross-section on strings. At the instant shown both A & B are at their respective maximum displacement. dE represents wave energy of small element of length dx.

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At the instant shown, power transfer at cross-section A and B is zero

Instantaneous power transfer through A changes periodically but through B remain zero

$at the instant shown in figure \frac{d E}{d x} {|_{_{_{_{_{_{a t A}}}}}} = \frac{d E}{d x}|}_{a t B} = 0$

$\frac{d E}{d x} |_{a t A}$ Changes periodically, while $\frac{d E}{d x} |_{a t B}$ remain zero all the time

answer is A, B, C.

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Detailed Solution

In case of a vibrating string , power transferred = T $\frac{δ y}{δ x} w h e r e T i s t h e t e n s i o n i n t h e s t r i n g .$

Slope $\frac{δ y}{δ x}$ is zero instantaneously at A and B , that’s why instantaneous power transfer in both case is zero. At point ‘B’ slope remains zero all the time.

Again for a vibrating string , $d E = μ V^{2} {(\frac{δ y}{δ x})}^{2} d x, w h e r e μ = m a s s p e r u n i t l e n g t h a n d V = v e l o c i t y o f p r o p a g a t i o n o f w a v e .$