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Question 31286
JEE Physics · Hard

Sound Waves: Acoustic Beats MCQ

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Acoustic BeatsHardQuestion 31286

Question

Two waves y₁ = A sin(ω₁t) and y₂ = A sin(ω₂t) superimpose (ω₁ ≈ ω₂). Amplitude of resultant oscillates at:
  1. A
    (ω₁+ω₂)/2
  2. B
    (ω₁−ω₂)/2
    Correct
  3. C
    ω₁−ω₂
  4. D
    ω₁+ω₂

Correct answer

(ω₁−ω₂)/2

Explanation

y = 2A cos((ω₁−ω₂)t/2) × sin((ω₁+ω₂)t/2). Amplitude envelope oscillates at (ω₁−ω₂)/2. Beat frequency (full amplitude cycle) = (ω₁−ω₂)/(2π) × 2π = ω₁−ω₂ in terms of angular frequency difference.

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