b
(b) On comparing the given equation with standard equation

.\(y = 2a\sin \frac{{2\pi x}}{\lambda }\cos \frac{{2\pi vt}}{\lambda }\)

==>\(\frac{{2\pi x}}{\lambda } = \frac{{\pi x}}{3} \Rightarrow \lambda = 6\)

Separation between two adjacent nodes = \(\frac{\lambda }{2} = 3=\,cm\)