A wave $y=a$ $\sin \left( {\omega t - kx} \right)$ on a string meets with another wave producing a node at $x=0.$ Then the equation of the unknown wave is
$y = a\,\sin \,\left( {\omega t + kx} \right)$
$y = - a\,\sin \,\left( {\omega t + kx} \right)$
$y = a\,\sin \,\left( {\omega t - kx} \right)$
$y = - a\,\sin \,\left( {\omega t - kx} \right)$
