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 velocity of wave is
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(d) The given equation can be written as
$y = 4\sin \,\left( {4\pi t - \frac{{\pi x}}{{16}}} \right)$ $(v) = \frac{{{\rm{Co - efficient of}}\,t(\omega )}}{{{\rm{Co - efficient of}}\,x(K)}}$
==> $v = \frac{{4\pi }}{{\pi /16}} = 64\,cm/sec$ along $+x$ direction.
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