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A wave travelling along the x-axis is described by the equation $y (x, t) = 5 \sin (αx - βt)$ . If the wavelength and time period of the wave are 0.1 m and 2.0 s, respectively, then $α$ and $β$ in appropriate units are

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$α = 20 π, β = 2 π$

$α = 20 π, β = π$

$α = 10 π, β = 2 π$

$α = 10 π, β = π$

answer is B.

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Detailed Solution

The general equation of plane progressive simple harmonic wave is

$Y (x, t) = Asin (kx - ωt)$

Comparing this with the given equation :

$α = k = \frac{2 π}{λ} \Rightarrow α = \frac{2 π}{0.1} = 20 π$

and

$β = ω = \frac{2 π}{T} \Rightarrow β = \frac{2 π}{2} = π$

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