a
(a) Comparing given equation with standard equation $y = 2a\sin \frac{{2\pi x}}{\lambda }\cos \frac{{2\pi vt}}{\lambda }$
gives us $\frac{{2\pi }}{\lambda } = \frac{\pi }{{15}} \Rightarrow \lambda = 30$
Distance between nearest node and antinodes
= $\frac{\lambda }{4} = \frac{{30}}{4} = 7.5$