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Question 31318
JEE Physics · Hard

Waves on String: Wave Equation MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Wave EquationHardQuestion 31318

Question

Relationship between transverse particle velocity (v_y) and wave speed (v) for a transverse wave:
  1. A
    v_y = v × (∂y/∂x)
  2. B
    v_y = −v × (∂y/∂x)
    Correct
  3. C
    v_y = v²/A
  4. D
    v_y = v

Correct answer

v_y = −v × (∂y/∂x)

Explanation

∂y/∂t = −v × ∂y/∂x (from wave equation ∂²y/∂t² = v²∂²y/∂x²'s first integral). Transverse particle speed = −v × slope.

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