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# 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 time period of the wave are $0.08 \: m$ and $2\: s$, respectively, then $\alpha$ and $\beta$ in appropriate units are

$\begin {array} {1 1} (a)\;\alpha = 25 \pi, \beta = \pi & \quad (b)\;\alpha = \large\frac{0.08}{\pi}, \beta = \large\frac{2}{ \pi} \\ (c)\;\alpha = \large\frac{0.04}{ \pi}, \beta = \large\frac{1}{ \pi} & \quad (d)\;\alpha = 12.5 \pi, \beta = \large\frac{\pi}{2} \end {array}$

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## 1 Answer

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$y(x,t) = 0.005\: \cos(\alpha x – \beta t)$
$\large\frac{2 \pi}{\lambda} = \alpha\: and\: \large\frac{ 2\pi}{T} = \beta$
So, $\alpha = \large\frac{2 \pi}{0.08} = 25 \pi\: and\: \beta = \large\frac{2 \pi}{2} = \pi$
Ans : (a)
answered Feb 28, 2014

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