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Question

A stationary wave is given by \( y = 0.06 \sin (\frac{\pi x}{2}) \cos (120\pi t) \), where \( x \) and
\( y \) are in meters and \( t \) in seconds. What is its wavelength?

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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. Form: y = A sin (kx) cos (ω t) , k = (π/2) rad/m . λ = (2π/k) = (2π/(π/2)) = 4 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 8 m, illustrating frequency-length-speed interdependence and quantization by boundaries.

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