A wave travelling along the x-axis is describ | vedclass

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(A) The general equation of a travelling wave is given by $y(x, t) = A \cos(kx - \omega t)$.Comparing this with the given equation $y(x, t) = 0.005 \c

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$\alpha = 25.00\pi, \beta = \pi$

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(A) The general equation of a travelling wave is given by $y(x, t) = A \cos(kx - \omega t)$.Comparing this with the given equation $y(x, t) = 0.005 \cos(\alpha x - \beta t)$,we identify $\alpha = k$ and $\beta = \omega$.The wave number $k$ is related to the wavelength $\lambda$ by the formula $k = \frac{2\pi}{\lambda}$.Given $\lambda = 0.08 \ m$,we have $\alpha = k = \frac{2\pi}{0.08} = 25\pi \ m^{-1}$.The angular frequency $\omega$ is related to the time period $T$ by the formula $\omega = \frac{2\pi}{T}$.Given $T = 2.0 \ s$,we have $\beta = \omega = \frac{2\pi}{2.0} = \pi \ rad/s$.Thus,$\alpha = 25\pi$ and $\beta = \pi$.

$A$ 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 $0.08 \ m$ and $2.0 \ s$ respectively,then $\alpha$ and $\beta$ in appropriate units are:

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