Practice question
Question
Two waves \( y_1 = 6 \sin (8x - 16t) \) and \( y_2 = 6 \sin (8x - 16t + \frac{2\pi}{3}) \) interfere.
What is the amplitude of the resultant wave?
Explanation
**Interference of waves** produces enhancement or cancellation based on phase. Two equal amplitude waves out of phase by π cancel completely, A = 0, while in-phase superposition doubles amplitude to 2a, demonstrating energy redistribution without violation of conservation. Amplitude: A = 2a cos (Φ/2) , a = 6 m , Φ = (2π/3) . A = 2 × 6 cos (π/3) = 12 × (1/2) = 6 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 6 m, illustrating frequency-length-speed interdependence and quantization by boundaries.
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