Part of JWAVE-02 — Waves: Standing Waves, Beats & Doppler Effect

Standing Waves — Formation and Properties

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Standing waves form by superposition of two identical waves travelling in opposite directions. Result: y=2Asin(kx)cos(ωt)y = 2A\sin(kx)\cos(\omega t). Properties: (1) No energy transfer — energy oscillates between KE and PE locally. (2) Amplitude varies with position: 2Asin(kx)2A|\sin(kx)|. (3) All particles between two nodes oscillate in phase. (4) Particles on opposite sides of a node are in antiphase. (5) Nodes are permanently at rest; antinodes have maximum amplitude 2A2A. Distance between consecutive nodes = λ/2\lambda/2; between a node and adjacent antinode = λ/4\lambda/4.

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