A wave travelling along the x -axis is described by the equation y(x, t) = 0.005cos (α x - β t). 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 (a) α = 25.00π, β = π (b) α = (0.08)/(π), β = (2.0)/(π) (c) α = (0.04)/(π), β = (1.0)/(π) (d) α = 12.50π, β = (π)/(2.0)

Answer: (a). α = k = (2π)/(λ) = (2π)/(0.08) = 25π m⁻¹ β = ω = 2π/T = (2π)/(2.0) = π rad/s So the answer is (a) α = 25.00π, β = π.

A wave travelling along the x -axis is described by the equation y(x… | JEE Main 2008 (AIEEE)

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Progressive Wave Equation

A wave travelling along the $x$ -axis is described by the equation $y(x, t) = 0.005\cos(\alpha x - \beta t).$ If the wavelength and the time period of the wave are $0.08\text{ m}$ and $2.0\text{ s}$ , respectively, then $\alpha$ and $\beta$ in appropriate units are

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Answer: (a)

$\alpha = k = \dfrac{2\pi}{\lambda} = \dfrac{2\pi}{0.08} = 25\pi\text{ m}^{-1}$
$\beta = \omega = \dfrac{2\pi}{T} = \dfrac{2\pi}{2.0} = \pi\text{ rad/s}$
So the answer is (a) $\alpha = 25.00\pi$ , $\beta = \pi$ .

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