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Question 31393
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Waves on String: Harmonics Advanced MCQ

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Harmonics AdvancedHardQuestion 31393

Question

A string vibrates simultaneously in 1st and 3rd harmonics with amplitudes A₁ and A₃. The waveform is:
  1. A
    y = A₁ sin(πx/L)cos(ωt) + A₃ sin(3πx/L)cos(3ωt)
    Correct
  2. B
    y = (A₁+A₃)sin(πx/L)cos(ωt)
  3. C
    y = A₁A₃ sin(πx/L)cos(3ωt)
  4. D
    y = A₁ sin(πx/L) + A₃ sin(3πx/L)

Correct answer

y = A₁ sin(πx/L)cos(ωt) + A₃ sin(3πx/L)cos(3ωt)

Explanation

Superposition of two modes: y = A₁ sin(πx/L)cos(ωt) + A₃ sin(3πx/L)cos(3ωt). Each mode has its own spatial pattern and temporal frequency.

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