The equation of a wave travelling on a string | vedclass

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(D) The given wave equation is $y = 4\sin \frac{\pi }{2}\left( {8t - \frac{x}{8}} \right)$.Expanding the term inside the sine function,we get:$y = 4\s

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

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(D) The given wave equation is $y = 4\sin \frac{\pi }{2}\left( {8t - \frac{x}{8}} ight)$.Expanding the term inside the sine function,we get:$y = 4\sin \left( {4\pi t - \frac{{\pi x}}{{16}}} ight)$.The standard form of a travelling wave is $y = A\sin(\omega t - kx)$.Here,the angular frequency $\omega = 4\pi$ and the wave number $k = \frac{\pi}{16}$.The velocity of the wave is given by $v = \frac{\omega}{k}$.Substituting the values: $v = \frac{4\pi}{\pi/16} = 4\pi 	imes \frac{16}{\pi} = 64\, cm/s$.Since the sign between $\omega t$ and $kx$ is negative,the wave is travelling in the $+x$ direction.

The equation of a wave travelling on a string is $y = 4\sin \frac{\pi }{2}\left( {8t - \frac{x}{8}} \right)$. If $x$ and $y$ are in $cm,$ then the velocity of the wave is:

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