Two sound waves travel in the same direction: y₁ = 0.02 mm sin{(400π rad s⁻¹)[x/(330 m s⁻¹) - t]} and y₂ = 0.02 mm sin{(404π rad s⁻¹)[x/(330 m s⁻¹) - t]}. They superpose. Select the correct statements.
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Question

Two sound waves travel in the same direction: y₁ = 0.02 mm sin{(400π rad s⁻¹)[x/(330 m s⁻¹) - t]} and y₂ = 0.02 mm sin{(404π rad s⁻¹)[x/(330 m s⁻¹) - t]}. They superpose. Select the correct statements.

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G1 Physics · Accepted Answer

Step 1: The angular frequencies are 400π and 404π rad s⁻¹, so f₁=200 Hz and f₂=202 Hz; beat frequency is 2 Hz and beat period is 0.5 s. Step 2: The wave numbers differ by Δk=(ω₂−ω₁)/v=4π/330 rad m⁻¹, so adjacent simultaneous intensity maxima are 2π/Δk=165 m apart. Final: A and C.

Two sound waves travel in the same direction: y₁ = 0.02 mm sin{(400π rad s⁻¹)[x/(330 m s⁻¹) − t]} and y₂ = 0.02 mm sin{(404π rad s⁻¹)[x/(330 m s⁻¹) − t]}. They superpose. Select the correct statements.