Engineering
Physics
Energy in Prograssive Wave
Reflection Refraction and Superposition of Wave
Standing Wave on String
Question

The graphs show the standing wave on a string at two successive instants of time t1,t2. A, B, C are points on the string (so is the maximum displacement amplitude of the standing wave) Column - II gives observations about net mechanical energy for the time interval between t1 & t2.

Column - I Column - II
(A) A (P) Kinetic energy at this element is increasing.
(B) B (Q) Energy is flowing towards right through this point.
(C) C (R) Energy is flowing left through this point.
  (S) No net energy ever crosses this point.
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Solution
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In a standing wave, energy oscillates between kinetic and potential forms. Nodes (like C) have maximum kinetic energy variation but zero net energy flow. Antinodes (like A and B) have energy flow directions changing with time.

At point A (antinode at max displacement), kinetic energy is minimum but increasing as it moves toward equilibrium. Energy flows toward right (from higher to lower amplitude regions).

At point B (antinode at zero displacement), kinetic energy is maximum but decreasing. Energy flows toward left.

At point C (node), there is no net energy flow across it (energy is confined between nodes).

Final Answer: A matches P and Q; B matches R; C matches S.