b
(b) \({y_1} = {a_1}\sin \,\left( {\omega \,t - \frac{{2\pi x}}{\lambda }} \right)\) and

\({y_2} = {a_2}\cos \,\left( {\omega \,t - \frac{{2\pi x}}{\lambda } + \phi } \right)\)

\( = {a_2}\sin \,\left( {\omega \,t - \frac{{2\pi x}}{\lambda } + \phi + \frac{\pi }{2}} \right)\)

So phase difference =\(\phi + \frac{\pi }{2}\) and \(\Delta\) =\(\frac{\lambda }{{2\pi }}\left( {\phi + \frac{\pi }{2}} \right)\)