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

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(B) The given wave equation is $y(x, t) = 0.005 \cos(\alpha x - \beta t)$.Comparing this with the standard wave equation $y(x, t) = a \cos(kx - \omega

Vedclass · Accepted Answer

$\alpha = 25\pi, \beta = \pi$

Vedclass · Answer

(B) The given wave equation is $y(x, t) = 0.005 \cos(\alpha x - \beta t)$.Comparing this with the standard wave equation $y(x, t) = a \cos(kx - \omega t)$,we identify the wave number $k = \alpha$ and the angular frequency $\omega = \beta$.The wave number is defined as $k = \frac{2\pi}{\lambda}$. Given $\lambda = 0.08 \ m$,we have $\alpha = \frac{2\pi}{0.08} = 25\pi \ rad/m$.The angular frequency is defined as $\omega = \frac{2\pi}{T}$. Given $T = 2.0 \ s$,we have $\beta = \frac{2\pi}{2.0} = \pi \ rad/s$.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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