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A wave travelling along the x-axis is described by the equation y(x,t) = 0.005 cos (αx − βt). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are

1. α = 25.00π, β = π
2. α = 0.08/π, β = 2.0/π
3. α = 0.04/π, β = 1.0/π
4. α = 12.50π, β = π/2.0

Correct answer: α = 25.00π, β = π

Solution

alpha = 2*pi/lambda = 2*pi/0.08 = 25*pi rad/m, and beta = 2*pi/T = 2*pi/2.0 = pi rad/s. So alpha = 25.00*pi, beta = pi.

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