(c) $y_{1} = a\sin{(\omega t - kx)}$;
$y_{2} = b\cos\left( \omega t - \frac{k}{x} \right) = b\sin\left( \omega t - \frac{k}{x} + \pi/2 \right)$
$\therefore$ Phase difference$= \left( \omega t - \frac{k}{x} + \pi/2 \right) - (\omega t - kx)$
$= \pi/2$