A wave travelling along the $x-$axis is described by the equation $y\left( {x,t} \right) = 0.005cos\left( {\alpha x - \beta t} \right)$ If the wavelength and the time period of the wave are $0.08\ m$ and $2.0\ s$, respectively, then $\alpha$ and $\beta$ in appropriate units are
AIEEE 2008, Medium
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$\mathrm{y}(\mathrm{x}, \mathrm{t})=0.005 \cos (\alpha \mathrm{x}-\beta \mathrm{t})$ (Given)
Comparing it with the standard equation of wave
$\mathrm{y}(\mathrm{x}, \mathrm{t})=\mathrm{a} \cos (\mathrm{kx}-\omega \mathrm{t})$ we get
$\mathrm{k}=\alpha$ and $\omega=\beta$
$\therefore \frac{2 \pi}{\lambda}=\alpha \quad$ and $\quad \frac{2 \pi}{\mathrm{T}}=\beta$
$\therefore \alpha=\frac{2 \pi}{0.08}=25 \pi \quad$ and $\quad \beta=\frac{2 \pi}{2}=\pi$
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