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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

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$α = 25.00 π, β = π$

$α = \frac{0.08}{π}, \frac{2.0}{π}$

$α = \frac{0.04}{π}, β = \frac{1.0}{π}$

$α = 12.50 π, β = \frac{π}{2.0}$

answer is A.

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Detailed Solution

y = 0.005 cos (αx − βt)
comparing the equation with the standard form,
$\begin{array}{l} y = Acos [(\frac{x}{λ} - \frac{t}{T}) 2 π] \\ 2 π / λ = α and 2 π / T = β \\ α = 2 π / 0.08 = 25.00 π \\ β = π \end{array}$

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