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A transverse wave is represented by y = A sin (ωt − kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

1. πA/2
2. πA
3. 2πA
4. A

Correct answer: 2πA

Solution

The wave velocity is given by v = ω/k, and the maximum particle velocity is ωA. Equating these, ω/k = ωA, which simplifies to k = 1/A. Since k = 2π/λ, substituting k = 1/A gives λ = 2πA.

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