The equation of a wave travelling along the positive x-axis, as shown in figure at $t = 0$ is given by
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$y=\sin (\omega t-k x+\phi)$
$v=\omega \cos (\omega t-k x+\phi)$
at $t=0, x=0, y=-0.5, v>0 \Rightarrow \phi=-\frac{\pi}{6}$
$\therefore y=\sin \left(\omega t-k x-\frac{\pi}{6}\right)$
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