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(D) The given wave equation is $y = 4 \sin \frac{\pi}{2} (8t - \frac{x}{8})$.Expanding the equation,we get $y = 4 \sin (4\pi t - \frac{\pi x}{16})$.Co

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$64 \, cm/s$ in $+x$ direction

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(D) The given wave equation is $y = 4 \sin \frac{\pi}{2} (8t - \frac{x}{8})$.Expanding the equation,we get $y = 4 \sin (4\pi t - \frac{\pi x}{16})$.Comparing this with the standard wave equation $y = A \sin (\omega t - kx)$,we identify the angular frequency $\omega = 4\pi \, rad/s$ and the wave number $k = \frac{\pi}{16} \, rad/cm$.The wave velocity $v$ is given by the formula $v = \frac{\omega}{k}$.Substituting the values,$v = \frac{4\pi}{\pi/16} = 4\pi 	imes \frac{16}{\pi} = 64 \, cm/s$.Since the sign between the $t$ and $x$ terms is negative,the wave is traveling in the positive $x$ direction.

For a progressive wave given by the equation $y = 4 \sin \frac{\pi}{2} (8t - \frac{x}{8}) \, cm$,what is the wave velocity and its direction?

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