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Identify the INCORRECT statement(s) about a standing wave set up in a string.

1. The total energy of any element of the medium remains constant over time.
2. The phase difference between any two particles in the string can be pi/2.
3. Energy can be transferred through the antinodes of the standing wave.
4. Energy can be transferred through the nodes of the standing wave.

Correct answer: Energy can be transferred through the nodes of the standing wave.

Solution

In a standing wave: (1) Energy oscillates locally — the KE and PE of an element exchange, so total mechanical energy of an element is NOT constant (it varies). (2) Phase difference between any two particles is always 0 or pi, so pi/2 is impossible. (3 & 4) Net power transfer through ANY cross-section (node or antinode) is zero, because equal and opposite wave components cancel net flow. Statements C and D (transfer through antinodes and nodes) are both incorrect, and statement A (energy constant) is also incorrect. Statement B (phase diff pi/2) is incorrect. All four are incorrect but the question asks to mark the incorrect ones.

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