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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 the time period of the wave are $0.08 \mathrm{~m}$ and $2.0 \mathrm{~s}$, respectively, then $\alpha$ and $\beta$ in appropriate units are
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Verified Answer
The correct answer is:
$\alpha=25.00 \pi, \beta=\pi$
$\alpha=25.00 \pi, \beta=\pi$
$$
y=0.005 \cos (\alpha x-\beta \mathrm{t})
$$
comparing the equation with the standard form,
$$
\begin{aligned}
& y=A \cos \left[\left(\frac{\mathrm{x}}{\lambda}-\frac{\mathrm{t}}{\mathrm{T}}\right) 2 \pi\right] \\
& 2 \pi / \lambda=\alpha \text { and } 2 \pi / T=\beta \\
& \alpha=2 \pi / 0.08=25.00 \pi \\
& \beta=\pi
\end{aligned}
$$
y=0.005 \cos (\alpha x-\beta \mathrm{t})
$$
comparing the equation with the standard form,
$$
\begin{aligned}
& y=A \cos \left[\left(\frac{\mathrm{x}}{\lambda}-\frac{\mathrm{t}}{\mathrm{T}}\right) 2 \pi\right] \\
& 2 \pi / \lambda=\alpha \text { and } 2 \pi / T=\beta \\
& \alpha=2 \pi / 0.08=25.00 \pi \\
& \beta=\pi
\end{aligned}
$$
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